EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics the Open University Milton Keynes MK7 6AA, UK E-Mail: R.J.Wilson@Open.Ac.Uk

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CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected]

ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania e-mail: [email protected] NEWSLETTER No. 47 KRZYSZTOF CIESIELSKI Mathematics Institute March 2003 Jagiellonian University Reymonta 4 EMS Agenda ...... 2 30-059 Kraków, Poland e-mail: [email protected] Editorial by Sir John Kingman ...... 3 STEEN MARKVORSEN Department of Mathematics Executive Committee Meeting ...... 4 Technical University of Denmark Building 303 Introducing the Committee ...... 7 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] An Answer to the Growth of Mathematical Knowledge? ...... 9

SPECIALIST EDITORS Interview with Vagn Lundsgaard Hansen ...... 15 INTERVIEWS Steen Markvorsen [address as above] Interview with D V Anosov ...... 20 SOCIETIES Krzysztof Ciesielski [address as above] Israel Mathematical Union ...... 25 EDUCATION Tony Gardiner Society of Mathematicians, Physicists and Astronomers in Slovenia ...... 26 University of Birmingham Birmingham B15 2TT, UK Problem Corner ...... 28 e-mail: [email protected] MATHEMATICAL PROBLEMS Mathematical Biography ...... 31 Paul Jainta Werkvolkstr. 10 Forthcoming Conferences ...... 34 D-91126 Schwabach, Germany e-mail: [email protected] Recent Books ...... 39 ANNIVERSARIES June Barrow-Green and Jeremy Gray Designed and printed by Armstrong Press Limited Open University [address as above] e-mail: [email protected] Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK and [email protected] telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 e-mail: [email protected] CONFERENCES Vasile Berinde [address as above] Published by European Mathematical Society RECENT BOOKS ISSN 1027 - 488X Ivan Netuka and Vladimir Sou³ek Mathematical Institute The views expressed in this Newsletter are those of the authors and do not necessarily Charles University represent those of the EMS or the Editorial team. Sokolovská 83 18600 Prague, Czech Republic NOTICE FOR MATHEMATICAL SOCIETIES e-mail: [email protected] Labels for the next issue will be prepared during the second half of May 2003. and [email protected] Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: ADVERTISING OFFICER [email protected] Vivette Girault Laboratoire d’Analyse Numérique INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER Boite Courrier 187, Université Pierre Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, et Marie Curie, 4 Place Jussieu Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- 75252 Paris Cedex 05, France mail: ([email protected]). Please include the name and full address (with postal code), tele- e-mail: [email protected] phone and fax number (with country code) and e-mail address. The annual subscription fee (including mailing) is 80 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS March 2003 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE 2003 PRESIDENT Prof. Sir JOHN KINGMAN (2003-06) 15 May Isaac Newton Institute Deadline for submission of material for the June issue of the EMS Newsletter 20 Clarkson Road Contact: Robin Wilson, e-mail: [email protected] Cambridge CB3 0EH, UK e-mail: [email protected] 18-23 May VICE-PRESIDENTS Prof. LUC LEMAIRE (2003-06) IPAM-SIAM-EMS Conference in Los Angeles (UCLA Lake Arrowhead Department of Mathematics Conference Center), USA Université Libre de Bruxelles Applied Inverse Problems: Theoretical and Computational Aspects C.P. 218 – Campus Plaine Bld du Triomphe webpage: http://www.ipam.ucla.edu/programs/aip2003 B-1050 Bruxelles, Belgium e-mail: [email protected] 30 June-4 July Prof. BODIL BRANNER (2001–04) Department of Mathematics EMS Summer School at Porto (Portugal) Technical University of Denmark Dynamical Systems Building 303 Organiser: Maria Pires de Carvalho, e-mail:[email protected] DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] webpage: http://www.fc.up.pt/cmup/sds SECRETARY Prof. HELGE HOLDEN (2003-06) 6-13 July Department of Mathematical Sciences CIME-EMS Summer School at Bressanone/Brixen (Italy) Norwegian University of Science and Stochastic Methods in Finance Technology Alfred Getz vei 1 Organisers: Marco Frittelli and Wolfgang J. Runggaldier NO-7491 Trondheim, Norway e-mail: [email protected] e-mail: [email protected] webpage: www.math.unifi.it/~cime TREASURER Prof. OLLI MARTIO (2003-06) Department of Mathematics 15 August P.O. Box 4, FIN-00014 Deadline for submission of material for the September issue of the EMS University of Helsinki, Finland Newsletter e-mail: [email protected] ORDINARY MEMBERS 12-14 September Prof. VICTOR BUCHSTABER (2001–04) Steklov Mathematical Institute SPM-EMS Weekend Meeting at the Calouste Gulbenkian Foundation, Lisbon Russian Academy of Sciences (Portugal) Gubkina St. 8, Moscow 117966, Russia Organiser: Rui Loja Fernandes, e-mail: [email protected] e-mail: [email protected] Prof. DOINA CIORANESCU (2003–06) Laboratoire d’Analyse Numérique 14-15 September Université Paris VI EMS Executive Committee meeting at Lisbon (Portugal) 4 Place Jussieu 75252 Paris Cedex 05, France Contact: Helge Holden, e-mail: [email protected] e-mail: [email protected] Prof. PAVEL EXNER (2003-06) 2004 Mathematical Institute Charles University 25-27 June Sokoloská 83 EMS Council Meeting, Stockholm (Sweden) 18600 Prague, Czech Republic e-mail: [email protected] Prof. MARTA SANZ-SOLÉ (2001-04) 27 June-2 July Facultat de Matematiques 4th European Congress of Mathematics, Stockholm Universitat de Barcelona webpage: http://www.stocon.se/4ecm/ Gran Via 585 E-08007 Barcelona, Spain e-mail: [email protected] 2-6 September Prof. MINA TEICHER (2001–04) EMS Summer School at Universidad de Cantabria, Santander (Spain) Department of Mathematics and Computer Science Empirical processes: theory and statistical applications Bar-Ilan University Ramat-Gan 52900, Israel e-mail: [email protected] Cost of advertisements and inserts in the EMS Newsletter, 2003 EMS SECRETARIAT Ms. T. MÄKELÄINEN (all prices in British pounds) Department of Mathematics P.O. Box 4 Advertisements FIN-00014 University of Helsinki Commercial rates: Full page: £210; half-page: £110; quarter-page: £66 Finland Academic rates: Full page: £110; half-page: £66; quarter-page: £40 tel: (+358)-9-1912-2883 Intermediate rates: Full page: £160; half-page: £89; quarter-page: £54 fax: (+358)-9-1912-3213 telex: 124690 Inserts e-mail: [email protected] Postage cost: £13 per gram plus Insertion cost: £52 website: http://www.emis.de 2 EMS March 2003 EDITORIAL Editorial:Editorial: AnAn OceanOcean ofof MathematicsMathematics Sir John Kingman (EMS President)

The European Mathematical Society covers the whole of what is conventionally called pure and applied mathematics, from the most abstract and theoretical to applications in diverse fields of science and technology. Attempts to define or delimit the scope of mathematics always fail to cap- ture the richness of the subject. The best I can offer is the circular definition: mathematics is what mathematicians do, and mathematicians are people who do mathematics. What is often not sufficiently understood by those outside mathematics is how important it is to see the subject as a whole, and we inside sometimes make the situation worse by putting ourselves into com- partments. We set up departments of pure mathematics, applied mathematics, statistics, operational research; we argue about the relative merits of algebra and geometry; we quote G. H. Hardy on the useless- will be repeated several times, and other less logs until they spy a target nearby, ness of mathematics. In doing so, we mathematicians with other expertise will when they spring ashore with frightening underplay the interconnected nature of the transform the original problem into almost speed and open jaws. I leave my readers to subject and the extent to which, through- unrecognisable form. It is however impor- construct their own examples, to describe out history, unexpected links and novel tant that a chain of communication should the variety of behaviour in highly devel- applications are discovered. not be broken, so that those concerned oped fields like mathematical physics. In thinking about the unity of mathe- with real problems know what is being Unfortunately, there are contrasting matics, I find it helpful to consider a done at a more abstract level, and can both continents in which the waves beat against metaphor in the form of a great ocean. use the more general theory and challenge high cliffs of incomprehension, on top of Isaac Newton spoke of himself as playing its relevance. which the inhabitants look down on the on a seashore, while the whole ocean of This whole process is very like the way mathematicians in the sea, who in turn truth lay undiscovered, but my analogy the flora and fauna in different levels of the shout in vain to those on land. In time, takes mathematics itself as the ocean. The ocean feed off those in adjacent levels. We some of these cliffs will crumble, but mean- areas to which it is applied, with which it may for administrative convenience give while we lose opportunities because of an interacts, are the continents and islands distinct names to different levels, but they inability to communicate. against whose shores the ocean breaks. remain interdependent. In the depths On the other hand, there are some areas Observers see these shores and admire the there are strange creatures that never see where mathematics gets inextricably mixed foaming breakers, and they see too the sur- the sunlight above, while on the surface are with difficult non-mathematical disci- face of the waters far from land, but they those who never venture below, but they all plines. The science of statistics, for exam- miss what is going on in the depths, and depend on each other, perhaps through ple, is neither a subset nor a superset of the fact that the whole ocean is one great long and subtle chains of mutual need. mathematics, and resembles those land- ecosystem in which the health of the life in There also great leviathans of the sub- scapes that are neither land nor sea but different parts depends on that of the ject, whales that descend to the deepest some admixture of the two. whole. water and then rise to the surface with Meanwhile, far out to sea, it is possible to When mathematicians attack a problem spouts of profound new mathematical forget the existence of land altogether, but in physics or biology or economics, they understanding. We celebrate this year the the nature of the ocean is in fact influenced may be able to make progress in a direct centenaries of two such, von Neumann and strongly by the nature of the invisible con- and straightforward way, writing down Kolmogorov, who brought the purest of tinents that bound it. And they in turn are equations and solving them analytically or pure mathematics to bear on a variety of sometimes radically affected by what hap- numerically, but if the problem is at all applied fields with a power and authority pens over the horizon. In the depths of the challenging, obstacles will soon arise that that defied the distinctions of lesser math- ocean an event may show on the surface as stand in the path and frustrate simple solu- ematicians. We need more such who dis- a wave a few centimetres high. But as the tions. The mathematician will try to turb the ocean and shake our preconcep- wave travels towards the land it may grow understand these obstacles, assessing how tions. into a tsunami with dramatic consequences fundamental they are. Often it will be The continents against which the waters for those on shore. realised that they are similar to difficulties lap are very different from one another. We live in a world that has been deci- that have arisen in other areas, and that The best known is of course that of physics, sively shaped by the applications of mathe- methods developed in those other areas which has gentle beaches and broad bays in matics. Mathematics will advance, faster can be fruitfully transferred. A process of which play amphibious creatures who than ever, in response to practical chal- abstraction and generalisation can often hardly know or care whether they are lenges and its internal momentum of prove extremely powerful, and may lead to mathematicians or physicists. But even mathematical curiosity. New connections more subtle solutions, or at least to a deep- here there are penguins, clumsy on land will be discovered between apparently dif- er understanding of why a solution is elu- but beautiful swimmers in the water. And ferent fields, and good mathematicians will sive. there are crocodiles, which lie half sub- continue to spring surprises on their col- In practice, this process of abstraction merged in the shallows looking like harm- leagues and on the world. EMS March 2003 3 EMS NEWS ExecutiveExecutive CommitteeCommittee MeetingMeeting Nice (France), 8-9 February 2003 David Salinger

Our hosts, the French mathematical societies SMF and SMAI, had arranged for good food and pleasant weather, so it was rather a shame to sit indoors and transact the Society’s business. All members of the Executive Committee were there, together with Tuulikki Mäkeläinen, our invaluable executive secretary, the energetic figure of our past president, Rolf Jeltsch, saying that he could now sit in a quiet corner, Robin Wilson, the Editor of the Newsletter (with a garish two-sided tie), Saul Abarbanel (making sure that applied mathematics was not disregarded) and myself, listening for anything that could be turned into publicity. Our new President, Sir John Kingman, presided imperturbably over the business of what was a very amicable meeting. Gentle reader, not even the muses could make all that business interesting. The would give the Committee Scientific advice some aspects, but the main funding would routine ratification of appointments to the about proposed meetings, and who also have to come from other sources. standing committees of the society and could be nominated as a panel of experts Robin Wilson confirmed that, due to decisions about terms of office will be for the 6th Framework programme. extra responsibilities at the Open reflected in due course on EMIS. Several of the Society’s committees University, the June issue of the Newsletter Decisions to support (or not to support) reported. The Committee on Eastern would be his last as Editor-in-Chief. The meetings and other activities may not Europe was in charge mainly of distribut- Committee thanked Robin for his work: appear here, because the applicants should ing travel grants to young Eastern under his guidance, the Newsletter had be informed first. So I shall try to give a European mathematicians. The Commit- become a major asset to the Society. general idea of what was discussed and, tee for Developing Countries was very SMAI and SMF and (particularly) Doina where I can, of the more important deci- active and sought working capital from the Cioranescu, were thanked, not only for sions taken, which I shall list at the end. EMS. The Executive Committee was sym- their warm welcome and the smooth run- In a year when subscriptions have risen, pathetic, but it had limited funds at its dis- ning of the arrangements for the meeting, it may not be politic to report that the posal: however there was an unspent but also for their organisation of AMAM03, Society made a small surplus overall of amount that it could allocate. The which promised to be a great success. 4754 euros. However, this represented an Education Committee was drawing up operating loss, principally because of the position papers on The preparation of stu- Some Decisions expense of holding our Council meeting in dents for university, The supply of maths teach- • The Society should have a booth at Oslo. Even the auditors agreed that costs ers, Technology in teaching and ICIAM in Sydney. in Oslo could be high. The apparent sur- Popularisation. The Raising Public Aware- • The Committee approved academic plus arose from receiving income on pro- ness Committee reported that it had institutional membership for the Central jects whose expenditure was incurred in a received 26 articles for its competition. European University (Budapest) and the different financial year. Income from The Committee for Women and Faculty of Mathematics at the University membership fees had increased, reflecting Mathematics reported on a scheme for of Barcelona. a significant rise in membership. mentoring young women mathematicians, • The Committee agreed to support the The President, Past President, and Vice- run by European Women in Mathematics. Cortona Scuola Matematica Interuniver- Presidents reported on the many meetings The Special Events Committee submitted sitaria on the same basis as the Banach at which they had represented, or would amended rules governing the Diderot Centre. The Committee resolved that, represent, the Society. These included sci- Maths Forum. The Committee for in principle, it could provide this kind of entific meetings, representation on organ- Developing Countries has been very active support where there was direct EMS isations, and meetings to do with with its book distribution programme, but input and a measure of internationalisa- European funding. The President also is also getting new facets of its activities tion, but that each application would be reported on the ‘hand-over’ meeting in under way. considered on its merits. Zürich. He thanked Rolf Jeltsch and David Ari Laptev joined the committee on • It was agreed to accept the bid of the Brannan for their devotion to, and bril- Sunday to tell us about progress on 4ecm Netherlands Mathematical Society to liant work for, the EMS. (see page 5). That day, we moved from an hold 5ecm in Amsterdam in 2008, sub- Under the 6th Framework arrange- anonymous hotel conference room to the ject to a site visit. ments, Luc Lemaire explained, the imposing Maison du Séminaire on the sea • It was agreed to provide 4000 euro as European Union would accept applica- front. working capital for the Committee for tions only for series of meetings: either Rolf Jeltsch reported on his meeting at Developing Countries. large meetings or events such as summer Berlingen about the project to digitise all • A common letterhead incorporating the schools for training young researchers. He past mathematical literature. Although logo was agreed. had therefore issued a call for proposals: this had been agreed by the IMU, neither • It was agreed in principle that EMS some had already been received, and the the NSF in the USA nor the European should become a full member of the Committee approved a number of them. Union would fund the main costs of digiti- EULER Consortium. He had also asked the Committee for help sation. An application could still be made • It was agreed that the Committee should in drawing up a list of mathematicians who to the 6th Framework programme for not support individuals for prizes. 4 EMS March 2003 EMS NEWS Preparations for 4ecm: the Fourth European Congress of Mathematics 4ecm: Stockholm, 27 June – 2 July 2004 The poster for the congress has been distributed. A letter will be sent to all participants in 3ecm (Barcelona, 2000). A number of Nobel prizewinners have been asked to speak to the congress about the role of mathematics in their subject. So far, six expressions of interest in organising satellite conferences have been received. Fourteen EU networks have responded to the call to hold their network meetings in Stockholm. The conference fee will be 200 euros, with a 20% discount for EMS members.

Call for Nominations of Candidates for Ten EMS Prizes Fourth European Congress of Mathematics Principal Guidelines Any European mathematician who has not reached his/her 35th birthday on 30 June 2004, and who has not previously received the prize, is eligible for an EMS Prize at 4ecm. A total of 10 prizes will be awarded. The maximum age may be increased by up to three years in the case of an individual with a corresponding ‘broken career pattern’. Mathematicians are defined to be ‘European’ if they are of European nationality or their normal place of work is within Europe. ‘Europe’ is defined to be the union of any country part of which is geographically within Europe or that has a corporate member of the EMS based in that country. Prizes are to be awarded for the best work published before 31 December 2003. The Prize Committee shall interpret the word ‘best’ using its judgement: for example, it may refer to innate quality or impressive- ness, influence, etc. Nomination for the Award The Prize Committee, headed by Prof. Nina Uraltseva (St Petersburg), is responsible for solicitation and evaluation of nominations. Nominations can be made by anyone, including members of the Prize Committee or by the candidates themselves. It is the responsibility of the nominator to provide all relevant information to the Prize Committee, including a resume and documentation. The nomination for the awards should be reported by the Prize Committee to the EMS President at least three months prior to the date of the awards. The nomination for each award must be accompanied by a written justification and a citation of about 100 words that can be read out at the award ceremony. The prizes cannot be shared. Description of the Award The award comprises a certificate including the citation and a cash prize of 5000 euro. Award Presentation The prizes will be presented at the Fourth European Congress of Mathematics by the President of the European Mathematical Society. The recipients will be invited to present their work at the conference. Prize Fund The money for the Prize Fund will be raised by the organisers of the Fourth European Congress of Mathematics in Stockholm. Deadline for Submission Nominations for the prize must reach the office in Stockholm at the following address, no later than 1 February 2004: 4ECM Organising Committee, Prof. Ari Laptev, Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. e-mails: [email protected], [email protected] http://www.math.kth.se/4ecm/ fax: +46-8-723-17-88, phone: +46-8-790-84-86

Instructions for Organisers of 4ecm Satellite Conferences

The Organising Committee of the 4ecm offers the following advantages to organisers of satellite activities. • A summary of information about each satellite activity will be freely distributed through the printed and electronic systems of the 4ecm. • The reduced registration fee offered to participants of the 4ecm registered before April 2004 will be extended until the beginning of the 4ecm for participants of satellite activities. • Addresses of satellite activity participants may be included in the mailing list of the 4ecm for distribution of information. The Organising Committee requires the following information in order to decide if an activity can be considered as a satellite of the 4ecm. • Title and a short presentation of the activity (periodicity, objectives, etc.). • Location and dates. • Organising Committee and Scientific Committee, if applicable. • Preliminary list of speakers, if applicable. The experience from previous EMS conferences and other international events shows that it is also convenient to request the following. • The dates of satellite activities should be close to the dates of the 4ecm (27 June – 2 July 2004). • People responsible for each satellite activity should provide their participants with information about the 4ecm. In addition, they should assist them in organising their trip to or from Stockholm. The organisers of the 4ecm will also assist 4ecm participants who are registered in some satellite activity in arranging their travel plans. Contact details for organisers: Mikael Passare, e-mail: [email protected] website: http://www.math.kth.se/4ecm/Instructions.htm The deadline for proposals for satellite activities is 1 February 2004. We regret that activities communicated after this date cannot be acknowledged by the Organising Committee.

EMS March 2003 5 EMS NEWS Nizar Radwan Poland New members 2002 Amitai Regev Teresa Lenkowska-Czerwinska Andre Reznikov Joseph Roseman Romania Australia Jacques Istas Mozes Shahar Dan Barbosu Matthew Brown Christian Lecot Yehuda Shalom Gheorghe Micula Bernard Marchand Vladimir Shevelev Constantin Niculescu Austria Victor Filipe Martins da Rocha Eduard Yakubov Nicolae Pop Herbert Fleischner Guy Metivier Zvi Ziegler Ali Ünlü Régis Monneau Russia Franz Winkler Dumitry Motreanu Italy Vyacheslav S. Kalnitsky Jean-Philippe Nicolas Elisabetta Alvoni Belgium Ashkan Nikeghbali Maria Artale Spain Jan Adriaenssens Pierre Orenga Luca Barzanti Sonia Esteve Frigola Pierre Caprace Annie Raoult Rita Capodaglio Jorge Galindo Pastor Stefaan De Winter Bruno Rey Gaetano Cavallaro Garcia Bellido I.E.S.A. Cindy De Wolder Joel Rivat Alfredo Ciano Isabel Marrero Rodriguez Sandy Ferret Benoit Rottembourg Paolo Custodi Ricard Marti Miras Nicholas Hamilton Raphael Rouquier Franca Degani Cattelani Carlos Romero Chesa Georges Hansoul Léon Saltiel Gerardo De Maio Natalia Katilova Lionel Schwartz Luigi D’Onofrio Sweden Thierry Lucas Ngoc Nam Tram Margherita Fasano Petroni Anders Björn Pierre Mathonet Jacques Levy Vehel Eva Ferrara Dentice Jana Björn Cedric Rivière Charles Walter Marianna Fornasiero Lars Hörmander Koen Thas Donato Fortunato Ulf Ottoson Jan van Geel Germany Lorenzo Fucci Gunnar Mossberg Peter Eichelsbacher Federica Galluzzi Bulgaria Ulrich Pinkall Alessandro Giacomini Switzerland Ivailo Mladenov Nikolai Sapunarow Ugo Gianazza Herbert Amann Norbert Schappacher Gian Mario Gianella Demetrios Christodoulou Canada Ralf Schumacher Gennaro Infante Norbert Hungerbühler Nicolas Juge Onnen Siems Giovanni Landi Wesley Petersen Luise Unger Marta Macri Richard Pink China Antonio Manna Bert Reinold Huafei Sun Greece Cristina Marcelli René Sperb Chryssa Ganatsiou Emanuela Maresi Michel Thiebaud Czech Republic S. Molho Francesco Marino Pavel Exner N. Papoulas Antonino Maugeri Tunisia Alessandra Micheletti Patrick Cabau Finland Hungary Michele Mininni Seppo Heikkilä Andras Batkai Luciana Misso Ukraine Ilkka Holopainen Marco Modugno Eugene Tokarev Matti Honkapohja Ireland Gioconda Moscariello Loianno Timo Karvi Eimear Byrne Franco Nardini United Arab Emirates Mika Koskenoja Michael McGettrick Paolo A. Oliverio Raymond F. Tennant Petri Ola James T. Ward Carlo Domenico Pagani Matti Rantanen David Wilkins Rita Pardini United Kingdom Leo Salo Fulvio Ricci R. E. Abraham Mari Savela Israel Pietro Rigo John Bibby Samuli Siltanen Flavian Abramovici Carla Rossi J. F. Bradley Eero Tamminen Buma Abramovitz Rodolfo Salvi D. Brown Zvi Artstein Claudia Scarani in Tampieri Luminita Manuela Bujorianu France Gill Barequet Alessandro Scarselli H. J. Carvill Denis Aubry Eugene Barsky Antonino Surdo Paul J. Flavell Pierre Balvay David Blanc Sandra Tucci Greig J. Fratus Mohammed-Najib Achi Brandt Mariacristina Uberti Ting Guo Ho Benbourhim Daoud Bshouty Antonio Zitarosa S. J. Lewis Sylvie Benzoni-Gavage Gideon Ehrlich R. S. McDermott Nicole Berline Elsa Fisman Japan E. J. Park Valérie Berthé Maria Gorelik Takao Matumoto S. C. Roy Stéfanella Boatto Vladimir Hinich Anthony E. Solomonides Frédéric J. Bonnans Yoram Hirschfeld Luxembourg J. Trevor Stuart Nicole Bopp Alexander Ioffe Denise Kass-Hengesch Ola Törnkvist Alain Bretto Shmuel Kantorovitz Gérard Lorang Sheung Tsun Tsou Pierre Cartier Yael Karshon Reidun Twarock Denise Chenais Meir Katchalski Netherlands John Wright Guillaume Douard David Kats Wilfred W. J. Hulsbergen Ioannis Zois Jean Charles Gilbert Victor Khatskevich Vivette Girault Juri Kifer Nigeria United States of America Marc Grandotto Vladimir Korman J. A. Oguntuase Francis Bonahon Fabien Granger Eran London L. E. Domino Georges Griso Iakov Lutsky Norway Sigurdur Helgason Jean-Claude Guillot Shahar Mozes Harald Hanche-Olsen Ricardo Perez Marco Francois Hamel Bernard Pinchuk Arne B. Sletsjoe Loki Quaeler Paul-Louis Hennequin Allan Pinkus 6 EMS March 2003 EMS NEWS IntrIntroducingoducing thethe CommitteeCommittee (part 1)

Sir John Kingman (President) is the Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, a post he has held since 2001. Cambridge was his first university, which he left in 1965 for professorships at the Universities of Sussex and Oxford. He was Chair of the UK Science and Engineering Research Council from 1981- 85, and then served for 16 years as Vice-Chancellor (equivalent to Rector) of the University of Bristol. Sir John works on probability theory and its applications to random processes in a variety of applications, including population genetics and operational research. He became a Fellow of the Royal Society in 1971, and has been President of both the Royal Statistical Society and the London Mathematical Society. He also chairs the Statistics Commission, which monitors the integrity of official statistics in the UK.

Luc Lemaire (Vice-President) received a Doctorat from the Université Libre de Bruxelles in 1975 and a Ph.D. from the University of Warwick in 1977. From 1971 to 1982 he held a research position at the Belgian F.N.R.S., and has been a professor at the Université Libre de Bruxelles since then. His research interests lie in differential geometry and the calculus of variations, with a particular interest in the theory of harmonic maps. A former chairman of the Belgian Mathematical Society, Luc has been associated with the European Mathematical Society since its creation in 1990, being a member of the Council from 1990 to 1997, a member of the group on relations with European Institutions since 1990, Liaison Officer with the European Union since 1993, Vice-President 1999, and now Chair of the General meetings committee.

Bodil Branner (Vice-President) is a professor at the Technical University of Denmark, Lyngby (Copenhagen). She graduated from the University of Aarhus in 1967 in algebraic topology, but for the last 20 years has concentrated on problems within dynamical systems, in particular in holomorphic dynamics. She has been a visiting professor at Cornell University and the Université de Paris- Sud, and a visitor at the Max-Planck-Institut für Mathematik in Bonn and the Mathematical Sciences Research Institute (MSRI) in Berkeley. Bodil has been involved in establishing the network of European Women in Mathematics from its beginning in 1986. Since 1992 she has been a delegate of the EMS Council, representing individual members, and has been a member of the Executive Committee since 1997. She was recently President of the Danish Mathematical Society and a member of the Danish Natural Science Research Council. She is currently a member of the EURESCO committee under the European Science Foundation, representing the EMS.

Helge Holden (Secretary) was born in Oslo, Norway in 1956. He received his Ph.D. from the University of Oslo in 1985. After a year as a postdoc at the Courant Institute in New York, he accepted a position in Trondheim at the Norwegian University of Science and Technology, where he was promoted to full professor in 1991. Helge’s area of research is partial differential equations. His first work was in the mathematical theory of Schrödinger operators, and he then moved on to stochastic partial differential equations, flow in porous media, hyperbolic conservation laws, and completely integrable systems. He is currently Vice-President of ECMI, the European Consortium for Mathematics in Industry.

Olli Martio (Treasurer) received his Ph.D. at the University of Helsinki in 1967. He became an Associate Professor at the University of Helsinki in 1972, a professor at the University of Jyväskylä in 1980, and from 1993 he has been a professor and Head of Department of Mathematics in Helsinki. He has been a visiting professor in the University of Michigan, Norwegian Institute of Technology and Universidad Autonoma de Madrid. He has been an editor of Mathematica Scandinavica and Acta Mathematica. he is a member of several editorial boards and currently edits the Finnish journal Ann. Acad. Sci. Fenn. Math. His research interests include function theory (quasiconformal maps), non-linear potential theory and associated partial differential equations. He has organised several conferences and edited nine international conference proceedings, starting with the Nordic Summer School in quasiconformal mappings in Helsinki in 1971. Olli has held various positions in the Finnish Mathematical Society. He has been the President of the Finnish Academy of Sciences and Letters and a member of the Committee for Natural Sciences in the Academy of Finland, as well as a member of several European Union Scientific Panels for Mathematics. He is a honorary doctor of the Linköping Institute of Technology, the University of Volgograd and the University of Jyväskylä, as well as a honorary professor of the University of Brasov. EMS March 2003 7 EMS NEWS

8 EMS March 2003 FEATURE An Answer to the Growth of Mathematical Knowledge? The Répertoire Bibliographique des Sciences Mathématiques Laurent Rollet & Philippe Nabonnand

In March 1885, the Société Mathématique de scholars perceived the constant increase of matical articles in 1700; in 1900, probably France (SMF) conceived the project of a bib- printed matter as a serious problem. Two more than 600 journals published mathe- liographical catalogue of nineteenth-century simple figures can give some idea of this sit- matical works (see [Gispert 2000]). Facing mathematical sciences. Facing the constant uation: in 1890, international statistics of such an increase, many mathematicians increase of mathematical journals and the printed matters estimated that 100,000 were strongly in favour of the creation of exponential growth of mathematical knowl- items a year were published. In 1900, one bibliographical catalogues, and bibliography edge, the SMF members felt the lack of a estimated the annual production at 20,000 rapidly became a major part of scientific bibliographical tool for advanced students books, 76,000 journals and approximately research. and mathematicians. The Répertoire 600,000 articles (see [Goldstein 2001], Many bibliographical indices were pro- Bibliographique des Sciences Mathématiques was [Rasmussen 1995], and [Otlet 1900]). duced during the nineteenth century. The to be the SMF’s answer to the expansion of The first scientific journals appeared dur- most important national libraries in Europe mathematics. ing the seventeenth century. At that time, started to publish their exhaustive cata- This long-term bibliographical these journals were usually published by logues, and many scholars or members of enterprise – which was directed by Henri academies and learned societies, and they learned societies tried to set up various bib- Poincaré – rapidly became an international didn’t exclusively contain mathematical liographic catalogues for specific fields of endeavour: for almost 27 years, about 50 publications (one could find, for instance, knowledge: bibliographical catalogues on mathematicians from 16 different countries articles devoted to botanical or zoological index cards; monthly, quarterly or annual went through more than 300 mathematical issues): the Journal des scavants (1665) or the bibliographical reviews; chronological, journals. Between 1885 and 1912, more Philosophical Transactions of the Royal Society of alphabetical and methodical bibliographies; than 20,000 bibliographical references to London (1665) are two good examples of bibliographies centred on a particular disci- mathematical works (articles, books, treatises, such publications. pline such as mathematics or covering a etc.) were identified, collected, and pub- The first issue of Gergonne’s Annales de larger field (such as the International lished, using a methodical and systematic mathématiques pures et appliquées was pub- Catalogue of Scientific Literature, with sections classification. lished in 1810, and this was probably the devoted to mathematics, zoology, etc.), or This repertoire constitutes an important first significant mathematical journal exclu- even universal repertoires, such as Paul stage for the history of nineteenth-century sively devoted to mathematics. It ceased in Otlet’s Répertoire Bibliographique Universel science. The reconstitution of its history 1831, but several other journals took over: (see [Rasmussen 1995], [Otlet 1906, 1908, represents an interpretative key for the the Journal für die reine und angewandte 1918] and [Rayward 1990]). study of the internationalisation of science. Mathematik (1826), the Journal de mathéma- There were also such bibliographical Moreover, it may be an essential source for tiques pures et appliqués (1836) and the Annali endeavours before the nineteenth century: investigations concerning the organisation di scienze mathematiche e fisiche (1850). One for mathematics, at least two bibliographies of disciplinary frontiers within mathematical should add that, during the second half of are significant: J.E. Scheibel’s Einleitung zur sciences. the nineteenth century, the appearance of mathematischen Bücherkenntnis (Breslau) The aim of this article is to set out the first various learned societies was followed by the 1769-98, and F.W.A. Murhard’s Literatur der elements of an investigation devoted to the creation of several specialised journals; for mathematischen Wissenschaften (Leipzig), history and operation of the Répertoire instance, the SMF was created in 1872 and 1797-1805, each recording about 10,000 Bibliographique des Sciences Mathématiques. We the first issue of its journal, the Bulletin de la mathematical works. first describe the scientific and intellectual Société Mathématique de France, was published The following table gives an indication of context of its emergence. Next, we relate in 1873. the most important catalogues for mathe- the history of its creation. Finally, using a According to Neuenschwander [1994, pp. matics in the second half of the nineteenth few elements extracted from our computer 1534-5], only 15 journals contained mathe- century: database, we try to give a general survey of the contribution of this bibliography to the history of mathematics.

Nineteenth-century science: a growing concern for bibliography During the second half of the nineteenth century, a large number of disruptions affected European science: an unprecedent- ed increase of research and a growing spe- cialisation in every domain; the organisation of institutions in networks; an institutionali- sation of research in most European countries via the creation of academies, learned societies and universities; an increase in the number of university students, notably in France after the 1880 and 1890 reforms; and the considerable acceleration of the internationalisation of science (for instance, the organisation of the first international congresses). Besides these disruptions, one should add an important phenomenon: the exponential growth of the number of scientific journals. At the end of the nineteenth century many The most important mathematical bibliographies (1850-1900) EMS March 2003 9 FEATURE For further information concerning the Brioschi, Eneström and Mittag-Leffler tional dimension of the project was coun- bibliographical repertoires devoted to var- contain numerous discussions about the terbalanced by the fact that the bibliogra- ious fields, see [Besterman 1949]. This logical organisation of mathematical phy was created in Paris, directed from table should be complemented by the dif- domains in the index. A 67-page Projet de Paris, subsidised by French authorities and ferent editions of Poggendorf’s classification détaillée pour le Répertoire published in France. It is very difficult to Biographisch-literarisches Handwörterbuch der Bibliographique des Sciences Mathématiques know whether it met with success or was exakten Naturwissenschaften and by the was published by Gauthier-Villars in June distributed outside of France. Répertoire Bibliographique des Sciences 1888. The first edition of the index was At the beginning, the SMF had planned Mathématiques. Houzeau’s and Lancaster’s finally published in 1893, and several later to publish the bibliography as a book – but bibliographies for astronomy ([Houzeau editions were printed (see [Commission per- this would have implied a very slow publi- 1878], [Houzeau /Lancaster 1882, 1887]) manente du Répertoire Bibliographique des cation process, since it would have been had a strong influence on the mathemati- Sciences Mathématiques [1893], [1898], necessary to wait for the end of the perusal cal repertoire [1908], [1916]). process before printing anything. All these bibliographical attempts consti- Noting the occasion of the 1889 World Consequently Maurice d’Ocagne and tute a sign for a general consensus on sci- Fair, the commission of the repertoire, Roland Bonaparte proposed to publish the entific research around 1900. Many math- chaired by Henri Poincaré, decided to mathematical bibliography as a collection ematicians agreed that it was almost organise the first Congrès International de of printed index cards. This option impossible to be certain that other scholars Bibliographie des Sciences Mathématiques. enabled the publication to start as soon as had not yet studied their ideas. Moreover, The purpose of the organisers (Paul a sufficient number of bibliographical they were increasingly upset by the time Appell, Gaston Darboux, Charles Rouché, items had been collected. Despite this lag between the publication of an article Jules Tannery and Georges Humbert) was arrangement, the publication lasted for and its registration in a mathematical bib- to gather in Paris all those involved in almost 20 years: the first set of cards was liography (up to three years in the Jahrbuch mathematical research and eager to con- published in 1894 and the last one (the über die Fortschritte der Mathematik (see tribute to the project at an international 20th) in 1912. [Neuenschwander 1994, p. 1836]) or in the level. The perusal of mathematical periodicals Catalogue of Scientific Papers). Consequent- During this congress, which was support- probably began in 1888, but acquired its ly, many mathematical journals paid great ed by the Ministry of Trade, Industry and cruising speed after the 1889 congress. attention to bibliographical issues in the Colonies, several decisions were taken: The following procedure was adopted for 1880s and the 1890s: what is the best bib- • The bibliography should consist of an the preparation and the publication of the liographical system for mathematical sci- inventory of the titles of memoirs in series: ences? what kind of classification should pure and applied mathematics pub- • All the memoirs and periodicals of a be adopted? who should do the biblio- lished from 1800 to 1889, as well as given country were placed under the graphical work? should mathematicians works concerning the history and the responsibility of a member of the per- adopt an alphabetical classification, or philosophy of mathematics from 1600 to manent commission living and working should they elaborate a systematic and 1889: the purpose was to establish a sys- in the country. consensual classification at an internation- tematic list of all articles and memoirs • This representative directed the perusal al level? (For echoes of these discussions, published in the most important mathe- and redaction of individual bibliograph- see [Eneström 1890].) matical journals. ical index cards for each memoir and • The titles of memoirs should be classi- article that had been identified; for each The first years: 1885-94 fied, not by the authors’ names, but memoir or article one index card con- The SMF formulated the idea of a biblio- according to the logical order of sub- taining its bibliographical references was graphical repertoire for mathematics in jects. made. 1885, and the Society rapidly diffused a • Publications on astronomy already men- • Each individual index card contained preliminary project within the internation- tioned in the astronomical bibliography the common bibliographical informa- al mathematical community. A first men- of Houzeau and Lancaster in the 1880s tion (title, name of review, date, etc.), as tion of the project appears in a lettre circu- should be excluded. well as a classification code correspond- laire of March 1885 entitled Projet de réper- • The titles of works written in languages ing to a specific domain of research (this toire bibliographique. This letter began with other than French, Italian, German, code was furnished by the Index du an acknowledgement of the incapacity of Spanish or Latin should be translated Répertoire Bibliographique des Sciences mathematicians regarding the increase of into French. Mathématiques). mathematical publications, and continued The commission appealed to a general • Individual index cards were then regu- with a presentation of the different steps of adoption of the classification index by larly sent to Paris, and were centralised the project: compilation of bibliographical mathematicians and mathematical jour- and prepared for publication. references on individual index cards; nals. • The Paris secretariat directed the ordering of the cards with the help of a Finally, it was decided to establish a per- process of publication, which was very suitable classification; and publication. manent commission, based in Paris: its slow: they had to gather together indi- According to Eneström [1890], this propo- composition was Henri Poincaré, Désiré vidual cards according to their classifica- sition was warmly welcomed; consequently, André, Georges Humbert, Maurice tion, but the index cards concerning a a month later, the SMF sent another circu- d’Ocagne, Henry (France), E. Catalan specific division were not published until lar that gave more precise instructions. (Belgium), D. Bierens de Haan (Holland), they contained a sufficient number of Nevertheless, the project was not Glaisher (Great Britain), G. Gomes- bibliographical references: for instance, defined and accepted until four years later, Texeira (Portugal), Holst (Norway), Georg if there weren’t enough references for in 1889, and the first set of a hundred Valentin (Germany), E. Weyr (Austria), the code A1, no card was published and printed index cards was not to be pub- Guccia (Italy), G. Eneström (Sweden), J.P. they had to wait for the sending of other lished until 1894. Such a time lag finds its Gram (Denmark), Liguine (Russia) and C. bibliographical references concerning main source in the complexity and the Stephanos (Greece). this classification code. sophistication of the classification adopt- However, despite this strong interna- Each printed card contained approximate- ed. tional participation, one should not expect ly ten references. Each set of 100 index The intention of the SMF was to differ- that every country worked at the same cards contained about 1000 bibliographic entiate its project from other bibliographi- level: it is likely that several countries items. The illustration on page 11 is a cal endeavours by proposing a logical clas- never sent any bibliographical reference to reproduction of a standard index card: the sification of items based on a thematic the Paris office. This was certainly the case figure in the upper right corner indicates index. This index probably started to cir- for Great Britain and United States, partly the number of the card and the framed culate in an informal way in 1887: the let- because they were involved in other biblio- code indicates the classification code ters of Poincaré, Perott, Mathieu, Schlegel, graphical projects. Moreover, the interna- according to the index. 10 EMS March 2003 FEATURE Is the mathematical repertoire a new tool tury mathematics. At first glance, this for historians of mathematics? bibliography can constitute an interesting The intention of the SMF was to create a tool for the study of mathematical pro- bibliographical tool for scholars in math- duction over a large period: its 20,000 ematics. Some journals adopted the clas- bibliographical references constitute a sification of the index (for instance, the valuable source of investigation for histo- Bulletin de la Société Mathématique de rians of mathematics. However, this is France), but it is quite difficult to deter- probably not the main point. Indeed, mine whether the mathematical commu- with its specific and complex classifica- nity really used it. We are in possession tion, the mathematical repertoire gives of various documents concerning the cre- an outline of a specific conception of ation and the publication of this bibliog- mathematics. It gives access to mathe- raphy, but there remain many points matics, and also to the conception of about which our information is still frag- mathematics constructed by the mathe- mentary. How many copies did the com- matical community at that time. Does it mission permanente print and sell? Was the give an adequate description of nine- bibliography largely distributed outside teenth-century mathematics? In the light France? Why is it so difficult to find of recent works in history of science, copies of the index cards in French or should its classification be considered as foreign libraries? (As far as we know, it is conservative or modern? Did the classifi- impossible to find a complete set of the cation really take into account all the 20 series of the repertoire in any library existing mathematical domains of nine- in France, even in the Bibliothèque teenth-century mathematics? Did the Nationale de France: we had the opportu- classification contain gaps, and if so, what nity to work on a complete set thanks to were they? Jean-Luc Verley.) The creators of the project didn’t only There are some further questions con- propose a thematic ordering of mathe- Reproduction of a printed index card cerning the general context of its cre- matical fields; they also elaborated a per- ation: it would be useful to determine the sonal definition of the mathematical cor- Three main mathematical domains were relationships between this project and the pus that the repertoire should take into distinguished in the classification of the universalistic and internationalist trends account. They were, for instance, con- index: mathematical analysis, geometry at the turn of the nineteenth century. vinced that most of the works concerning and applied mathematics. Within these The mathematical repertoire constitutes pure and applied mathematics published domains, several classes were identified a modest project, compared to similar since 1800 would be of interest for schol- and designated by a capital letter (see the attempts in Germany, Belgium and Great ars. On the other hand, they excluded table below). For instance, class A con- Britain: there were three major chal- classical works that didn’t contain gener- tained works devoted to elementary alge- lengers: al results, notably those intended for stu- bra, theory of algebraic and transcendent • The mathematical bibliography compiled by dents and for the preparation of exami- equations, Galois groups, rational fractions Hermann Georg Valentin. Valentin was a nations. In a similar way, they decided and interpolation. Each class (A to X) was chief librarian at the Berlin Library and that works in applied mathematics would generally divided into subclasses, divisions, he started the compilation of a mathe- be mentioned only when they implied sections and subsections: for instance, the matical bibliography in 1885, at the progress in pure mathematics. The intro- code L14cá was used to designate the class same time as the SMF. His aim was to duction of such a separation between of conics and surfaces of second degree collect all mathematical publications since pure and applied mathematics is quite (L), the subclass of conics (1), the division the invention of typography. After several astonishing, particularly in the context of corresponding to tangents (4), the section years of strained relations with the rep- the development of engineer training in dealing with tangents satisfying specific resentatives of the French bibliogra- all European countries. conditions (c) and the subsection corre- phy, Valentin finally became a member What can historians of mathematics sponding to the case of right angles (á). of the permanent commission (see learn from such a bibliographical endeav- [Eneström 1911], [Valentin 1885, 1900, our? In order to study precisely the struc- Mathematical domain Classes 1910]). His bibliography was probably ture of the catalogue, we created a com- Mathematical analysis A-J never published, partly because of the puter database. Although we are a long Geometry K-Q First World War. way from the end of the data entry Applied mathematics R-X • The Universal Bibliographical Repertoire. process, we can give an overview of the The Belgians Paul Otlet and Henri information that may be extracted from Repartition of the classes in each Lafontaine created this repertoire such a database. Our database currently mathematical domain around 1895. It was conceived as a uni- contains 3692 bibliographical items, cor- The repertoire was published from 1894 versal bibliography of human thought, responding to the first four series of the until 1912, during which 20 series of 100 and had some success for some years, repertoire (400 index files out of 2000). index cards were published. Each series but French mathematicians had some It is accessible on-line, thanks to Laurent contained about 1000 bibliographical ref- serious reservations. Guillopé at the Cellule MathDoc: erences, and thus these series represent a • The International Catalogue of Scientific http://math-sahel. ujf-grenoble.fr/RBSM/. list of 20,000 mathematical works. More Literature. The London Royal Society A general investigation covering 1700 precisely, we can distinguish three created this project in the 1890s. Its index files (17 series) provides informa- moments in the publication of the series; aim was to publish, at an international tion concerning the repartition of biblio- they correspond to the three attempts to level, regular bibliographies on every graphical references within the three cover the whole classification, as shown in field of scientific research. Although main mathematical domains: mathemati- the following table: the French scientific community was cal analysis (A to J) represents 50% of the involved in this project, professional references, applied mathematics (R to X) Period Number of Covered mathematicians (especially in France) 33%, and geometry (K to Q) 17%. For series published classes also expressed strong reservations (see mathematical analysis, the most impor- 1894-1895 3 A1-X7 [Rasmussen 1995]). tant classes are those devoted to algebra 1896-1905 12 A1-V9 From a scientific point of view, the math- (A), theory of functions (D), differential 1906-1912 5 B12-X8 ematical repertoire raises the problem of equations (H) and arithmetic (I). For The three periods of publication the internal structure of nineteenth-cen- applied mathematics, one can distinguish EMS March 2003 11 FEATURE three significant classes: mathematical see, the presence of Austria probably Russia (95 items, 4 journals), Italy (59 physics (T), general mechanics (R) and finds its origin in the strong activity of items, 1 journal) and Norway (52 items, 1 fluid mechanics (S). Finally, the main Emil Weyr’s crew at the beginning of the journal): in contrast, 920 bibliographical classes in geometry are those devoted to perusal work. As an illustration, when for references concerned French mathemati- elementary trigonometry (K), algebraic each class of the index we take into cal journals, 783 were published in curves and surfaces (M) and conics (L). account the most important journals list- German journals and 539 in Austrian Apart from these general figures, we can give some precise descriptive information concerning the first 300 index files (3 series) of the repertoire. These figures concern only 2723 bibliographical references, and it would be hazardous to claim that they provide an adequate account of the whole repertoire. Nevertheless, these items correspond to the first attempt to cover the whole classification (from A to X), and may be interesting, for two reasons: they furnish some indications about the complexity of this bibliography, and they give some idea of the richness of the classification and of the extent of the work that had been done in 1895. Very significantly, the figures of Repartition of the mathematical domains according to the place of edition of the most the repartition of items among the three important journals mathematical fields is similar to the previous ones, which concerned 17 series: ed (more than 20 references for each periodicals. (Of course, these figures mathematical analysis represented 53%, periodical), the only remaining ones are don’t furnish any information about the geometry 13%, and applied mathematics those edited in France, Germany and authors’ nationality!) 34%. Austria. We can then give an overview of In a 1900 report concerning the There are 850 mathematicians listed in the repartition of these countries accord- progress of the repertoire, Charles the first three series of the repertoire. ing to the three mathematical fields (see Laisant gave some information about the Although impressive, this figure requires the graph below). Of course, these data number of bibliographical references further analysis: in fact, most of these are still fragmentary and must be con- submitted by each country. At that time, authors have between 1 and 5 biblio- firmed by a more precise investigation of only the half of the bibliography (ten graphical references, and there are only the whole set of 20 series. series) had been printed and the most 120 mathematicians with more than 5 ref- The perusal of memoirs and periodi- important suppliers were still France erences. The prominent authors of the cals of a given country was placed under (10,682 items, 6 journals: 7200 references three series (with 20 items or more) are: the responsibility of one or several math- come from the Comptes rendus de A. Cauchy (101), N.H. Abel (55), L. ematicians living and working in the l’Académie des Sciences), Germany (3593 Gegenbauer (49), C.-G.-J. Jacobi (42), M. country. Nevertheless, it is quite clear items, 7 journals) and Austria (1843 Chasles (37), A.L. Crelle (31), Sophus Lie that, at the beginning of the project, very items, 8 journals). The graph below pro- (29), F.-J. Studnicka (23), C. Duhamel few countries put a lot of effort into the vides an overview of the participation of (23), J. Liouville (22), P. Tannery (21), constitution of the bibliography. Apart each country: Russia, Italy, Holland, Th. Clausen (21), A. Cayley (21), E. Heine from France, Germany and Austria, only Portugal, Belgium and Spain are the (20) and S.D. Poisson (20). four countries sent more than 15 biblio- most significant suppliers: these figures The 2723 listed items come from 83 graphical references to the Paris office: come from Charles Laisant’s report mathematical journals: this figure should Portugal (100 items, 3 journals perused), [Laisant 1900]. be compared with the list of 227 journals of the Index du repertoire. Moreover, 62 of these journals contain less than 20 bibliographical references. Only 8 periodicals contain more than 50 references and represent 71% of the total number of items: Journal für die reine und angewandte Mathematik (712), Comptes Rendus des Séances de l’Académie des Sciences (500), Sitzungsberichte der Königliche Akademie der Wissenschaften in Wien (299), Journal de l’É- cole Polytechnique (134), Bulletin de la Société Mathématique de France (117), Casopis pro pèstovàni mathematiky a fysiky (a journal published in Prague, then part of the Austrian territory) (80), Annales Scientifique de l’École Normale Supérieure (78), Journal de mathématiques pures et appliqués (58). The repertoire also took mathematical monographs (books, treatises, etc.) into account; the first three series contain around 50 items of this type. These eight journals were published in Germany, Austria or France, a phenomenon explained by the strong mathematical domination of France and Germany during the nineteenth century. As we will Number of bibliographical references submitted by each country in 1900 12 EMS March 2003 FEATURE The absence of Great Britain and Who was in charge of the perusal mathematicians for a specific style of United States is not surprising, since the process and how was it done? Most of the mathematical (that is, ‘official’) academic two countries were engaged in a compet- German and Austrian contributions arises and professional mathematics, to the ing project, the International Catalogue from perusal of the Journal für die reine detriment of mathematics for education, of Scientific Literature. The case of und angewandte Mathematik and the a domain that was not much recognised. Sweden is also quite paradoxical: Sitzungsberichte der Königliche Akademie der We believe that this mathematical bibli- Eneström was the representative of the Wissenschaften in Wien. Emil Weyr essen- ography can constitute a valuable source country within the Commission Permanente tially did this work. He was the Austrian for historians of mathematics. In partic- and he had written several articles in representative in the Commission perma- ular, it gives access to the conception of favour of the constitution of a mathemat- nente and the leader of a small crew. He mathematics that was constructed by the ical bibliography during the 1880s. was certainly the most dynamic foreign nineteenth-century mathematical com- Nevertheless, he rapidly showed some contributor and his work ensured the munity. Our analyses will be completed serious reservations about the French international representation of the reper- at the end of the data entry process. project, partly because of its system of toire for the first three series. In a letter Moreover, a possible development of this classification. His growing inertia to Henri Poincaré (25/04/1892), Weyr research could consist in a comparison towards the French repertoire is a plausi- wrote: “J’ai l’honneur de vous signaler between this bibliography and some ble explanation for the absence of qu’il nous sera possible de remplir votre other repertoires, such as the Belgian Sweden. demande au moins quant aux principaux Répertoire Bibliographique Universel or the To a great extent, the references sent recueils allemands. M. Le baron de Jahrbuch über die Fortschritte der by Holland, Russia and Spain correspond Lichtenfels, professeur de mathématiques Mathematik. Finally, an understanding of to the heading Mémoires ou ouvrages à l’École Polytechnique de Graz s’est the expectations, difficulties, illusions, séparés. These nations were taking part in chargé de dépouiller avec moi le Journal etc. raised by this first attempt to organ- the broadening of mathematical produc- de Crelle. […] Cette collection de fiches ise mathematical activity at an internation, and it is likely that they used the déjà finie, concernant les Sitzungsbericht et tional level might be helpful for contem- repertoire in order to gain some recogni- les Denksschriften de Vienne et de Prague, porary mathematicians, at a time when tion at an international level. Moreover, les publications polonaises et quelques many international projects are devoted one can assume that the mathematicians autres publications, vous parviendra en to the numerisation of past or present of these countries judged that their quelques jours par la poste”. On the mathematical works. national periodicals were not important other hand, it seems that his work was not enough, and that monographs and books at all exhaustive. For instance, according Bibliography constituted the best illustration of their to his collected works, Jacobi published Theodore Besterman [1949]: A World national production. 104 articles in the Journal für die reine und Bibliography of Bibliographies and of Only 157 classification codes were used angewandte Mathematik, but one can only Bibliographical Catalogues, Calendars, Abstracts, for the ordering of the first three series, find 36 references to Jacobi’s works in the Digests, Indexes, and the Like, Genève, although the Index du Répertoire first three series of the repertoire. Societas Bibliographica, 3rd ed. Bibliographique des Sciences Mathématiques Judging from this example (and from Commission permanente du Répertoire bibli- proposed around 2000 possible codes. several others), it appears that considera- ographique des sciences mathématiques: (Moreover, in his report, Charles Laisant tions concerning the mathematical [1888]: Projet de classification détaillée pour [1900] confirmed that the first ten series domains, the length, or the theoretical le Répertoire bibliographique des sciences that had been printed at that time didn’t importance of publications were not auto- mathématiques (Gauthier-Villars), 67 pages. use more than 300 classification codes of matically seen as relevant criteria. [1893]: Index du Répertoire bibli- the index.) Concerning these 300 index Most of the French contribution arises ographique des sciences mathématiques files, it is important to notice that 113 of from perusal of the Comptes rendus de (Gauthier-Villars). [1894]: Index du the 157 codes refer to bibliographical l’Académie des sciences. This was made by Répertoire bibliographique des sciences mathéma- items that were equally published before Henri Brocard, who was the director of tiques – Errata, additions et modifications 1840 as after 1870. We can therefore the Alger Meteorology Institute and one (Octobre 1894) à joindre à l’édition (1893) de conclude that most of the mathematical of the French representatives of the com- l’index (Gauthier-Villars). [1898]: Index du domains designated by these codes were mission. His work concerned only publi- Répertoire bibliographique des sciences mathéma- active over a large period of the nine- cations in applied mathematics (classes R, tiques, 2nd ed. (Gauthier-Villars). [1908]: teenth century. Furthermore, 11 classifi- S, T, U, V, X) – this would require further Index du Répertoire bibliographique des sciences cation codes are exclusively devoted to analysis since the situation is similar for mathématiques, new ed. (Gauthier- mathematical works published after other French journals – but it was exhaus- Villars /H.C. Delsman). [1916]: Index du 1860; 8 of these concern mathematical tive: in his report, Laisant [1900] noticed Répertoire bibliographique des sciences mathéma- domains that emerged in the second half that the Comptes rendus had been com- tiques, 3rd ed. (Gauthier-Villars /H.C. of the nineteenth century: determinants pletely perused: “Il n’y a cependant peut- Delsman). (2 codes), Dedekind and Kronecker’s être que les Comptes rendus de l’Académie Gustaf Eneström [1890]: Sur les arithmetical theory of algebraic functions des Sciences de Paris qui soient tout à fait Bibliographies des sciences mathématiques, (2 codes), properties of ϕ (n), Lie’s theory au courant, grâce au dévouement de M. le Bibliotheca math. (2) 4, 37-42. [1895]: of continuous groups, Gyldén’s theory Commandant Brocard ; c’est lui qui a pris Répertoire Bibliographique des Sciences and nomography. The presence of two cette si lourde tâche, et il s’en est acquit- Mathématiques, Bibliotheca math. (2) 9, 29. other domains – the properties of gener- té avec une exactitude et une régularité [1898]: Über die neuesten mathematisch- al involutions according to Chasles, and véritablement admirable”. bibliographischen Unternehmungen, one devoted to axonometric or isometric To conclude, we note that two major Verhandlungen der ersten internationalen perspective – reveals the active role of mathematical journals seem to be absent Mathematiker-Kongresses, Leipzig, 280-288. Emil Weyr at the beginning of the perusal from the whole repertoire: the [1911]: Wie soll die Herausgabe der work, since most of these bibliographical Mathematische Annalen and the Nouvelles Valentinschen mathematischen references come from the Sitzungsberichte annales de mathématiques. The former is Bibliographie gesichert werden?, Bibliotheca der Königliche Akademie der Wissenschaften astonishing, since Weyr announced the math. (3) 11, 227-232. in Wien. The last domain (descriptive beginning of the perusal of this journal to Hélène Gispert [2000]: Les journaux scien- geometry on curves and surfaces) gives an Poincaré in 1892: “Mr le Dr Krohn, tifiques en Europe, L’Europe des sciences: con- illustration of the vitality of this old theo- Privatdozent dans notre université, s’oc- stitution d’un espace scientifique (ed. M. Blay ry: this can be explained by the impor- cupera avec les Mathematische Annalen…”. and E. Nicolaïdis), Seuil, Paris, 191-211. tance of descriptive geometry training in The case of the Nouvelles annales is quite Catherine Goldstein [2001]: Sur quelques pra- Engineer Schools and Faculties of different, and probably reveals the tiques de l’information mathématique, Science. (intentional?) choice made by French Philosophia Scientiæ 5, 125-160. EMS March 2003 13 FEATURE J.C. Houzeau [1878]: Catalogue des ouvrages d’Astronomie et de météorologie qui se trouvent Two Mathematics dans les principales bibliothèques de la Belgique, NSF, SCIENCE préparé et mis en ordre à l’Observatoire Royal de Digitisation Bruxelles; suivi d’un appendice qui comprend JOURNAL tous les autres ouvrages de la bibliothèque de cet Projects établissement, Bruxelles, Hayez, imprimeur ANNOUNCE de l’Académie Royale. While the mathematics community gears J.C. Houzeau and A. Lancaster: [1882]: up to digitise the whole of the mathe- Bibliographie générale de l’astronomie ou cata- matics literature, it’s a good idea to look SCIENCE logue méthodique des Ouvrages, des Mémoires ou at two projects already up and running. des observations astronomiques publiés depuis l’o- These are the Jahrbuch Project at VISUALIZATION rigine de l’imprimerie jusqu’en 1880, mémoires et Göttingen and the Cellule MathDoc group notices, Bruxelles, Imprimerie Xavier based at Grenoble. Havermans. [1887]: Bibliographie The Jahrbuch über die Fortschritte der CONTEST Mathematik was the first comprehensive générale de l’astronomie, Ouvrages imprimés et The National Science Foundation and manuscrits, Bruxelles, Hayez, imprimeur de journal of reviews of the mathematical literature. It was founded in 1868 and the journal Science are now accepting l’Académie Royale de Belgique. entries for the inaugural 2003 Science Charles Laisant [1900]: Sur l’état d’avance- appeared until 1942. The project has as its centrepiece the goal of making the and Engineering Visualization ment des travaux du Répertoire bibli- Challenge. ographique des sciences mathématiques, entire Jahrbuch electronically available. Much has already been done. If you Winning selections will be featured in Bibliotheca mathematica (3) 1, 246-249. a special section of Science’s 12 Charles Laisant and Georges Humbert go to the EMIS homepage (www.emis.de) and click on the Jahrbuch project, you can September issue and winners will [1894]: Sur l’état d’avancement des travaux receive an expenses-paid trip to the du Répertoire bibliographique des sciences use the search facility, for instance, by author. I typed in ‘Hardy, G.H.’ and got foundation for its Art of Science Project mathématiques, 32° Congrès des Sociétés exhibit and accompanying lecture. savantes, extrait du Journal Officiel du 31 mars a list of 314 titles, starting in 1899. From there, it’s not hard to access the Jahrbuch This new international contest will 1894, Paris, Imprimerie des Journaux offi- recognise outstanding achievement by ciels. review for the titles selected. For some publications, including scientists, engineers and visual informa- Armand Mattelart [2000]: Histoire de la tion practitioners in the use of visual Société de l’Information, Paris, Éditions de la Mathematische Annalen, Mathematische Zeitschrift and Journal de Mathématiques media to promote understanding of Découverte. research results. Philippe Nabonnand and Laurent Rollet Pures et Appliqués, the project provides direct access to facsimiles of the articles The contest is open to individual sci- [2002]: Une bibliographie mathématique entists, engineers, visual information idéale? Le Répertoire Bibliographique des themselves. This is a fascinating site, a window into both the past and the future practitioners, and scientific teams – Sciences Mathématiques, Gazette des mathé- including technicians and support team maticiens 92, 11-25. of mathematics. Cellule MathDoc has recently opened a members – who produce or commission E. Neuenschwander [1994]: Les Journaux photographs, illustrations, animations, mathématiques, Companion Encyclopedia of the website, www.numdam.org. From this page you can search by author, title or interactive media, video sequences or History and Philosophy of the Mathematical computer graphics for research. Sciences (ed. I. Grattan-Guinness), keyword summaries of the articles in the Annales de l’Institut Fourier and the Entries must have been produced Routledge, London-New York, 1533-1539. after 1 January 2000. The contest dead- Paul Otlet: [1900]: La statistique interna- Journées équations aux dérivées partielles. Again, you can summon the articles line for postmarked entries is 31 May tionale des imprimés, Revue de l’Institut 2003. The contest rules and entry sub- International de Bibliographie 5, 109-121. themselves to your computer screen. This service is entirely free if your insti- mission instructions are available on the [1906]: L’office International de web at Bibliographie, Le mouvement scientifique en tution subscribes to the journals and, in any case, free for the Annales for articles http://www.nsf.gov/od/lpa/events/sevc/ Belgique. [1908]: La sociologie bibli- Prospective entrants are encouraged to ologique, Le mouvement sociologique interna- up to 1996. Cellule MathDoc intends, in time and review the contest rules before submit- tional. [1918]: Transformations opérées ting an entry. Entry forms are available dans l’appareil bibliographique des sciences, subject to publishers’ permission, to make all French mathematical journals at that web address as well. Revue scientifique 58, 236-241. Science is published by the American Anne Rasmussen [1995]: L’Internationale scien- available in this way. David Salinger Association for the Advancement of tifique: 1890-1914, Paris, EHESS. Science. W.B. Rayward (ed.) [1990]: International EMS Publicity Officer Organization and Dissemination of Knowledge. Selected Essays of Paul Otlet, Amsterdam, Elsevier. Georg Hermann Valentin: [1885]: Vorläufige EMS Committees Notiz über eine allgemeine mathematische Bibliographie, Bibliotheca Mathematica (1) 2, A list of the EMS committees, together with their Chairs, is as follows. 90-92. [1900]: Die Vorarbeiten für die allgemeine mathematische Bibliographie, Applied Mathematics Committee [Saul Abarbanel] Bibliotheca Mathematica (3) 1, 237-245. Developing Countries [Herbert Fleischner] [1910]: Über den gegenwärtigen Stand der Eastern and Central Europe [Andrzej Pelczar] Vorarbeiten für die allgemeine mathematis- Electronic Publishing [Bernd Wegner] che Bibliographie”, Bibliotheca Mathematica Group of Relations with European Institutions [Sir John Kingman (EMS President, (3) 11, 153-157. ex officio] European Research Centres of Mathematics (ERCOM) [Manuel Castellet] Laboratoire de Philosophie et d’Histoire des Education [Tony Gardiner] Sciences – Archives Henri-Poincaré, UMR Raising Public Awareness [Vagn Lundsgaard Hansen] 7117 du CNRS, Université Nancy 2, 23 General Meetings [Luc Lemaire] Boulevard Albert Ier, 54015 Nancy Cedex. Women and Mathematics [Emilia Mezzetti] e-mail: philippe.nabonnand@univ- Special Events [Jochen Bruening] nancy2.fr, [email protected] Publications [Rolf Jeltsch] 14 EMS March 2003 INTERVIEW

InterviewInterview withwith VVagnagn LLundsgaarundsgaardd HansenHansen Interviewers: Bodil Branner and Steen Markvorsen (Lyngby)

Vagn, please tell us a little about your child- a whole generation of mathematicians in hood and background. Denmark. I was born in 1940 in the beautiful town of In 1960, Aarhus was still a young univer- Vejle, lying at the end of one of the Danish sity and the Mathematical Institute was fjords along the east coast of Jylland. only a few years old. There was a pioneer- Close to forests and the fjord, it was an ing spirit and Svend Bundgaard made the ideal place for children to grow up. best out of the positive economical situa- With a working class background, it was tion for the sciences. He made sure that a unusual at the time to attend secondary constant flow of eminent mathematicians school beyond grade 7, and later the gym- visited Aarhus, some of them for long peri- nasium, but with the full support of my ods. Naturally, this created a very stimu- parents, I broke the social barrier, and fin- lating atmosphere, and also the social life Vagn Lundsgaard Hansen. ished gymnasium in 1960 with excellent of the institute was legendary. results. For my final studies of mathematics, I good students emerged from the course. It was not always easy – and often rather specialised in topology with Professor Leif Karsten Grove, now professor at the lonely – to step outside your social class, Kristensen as adviser. The subject for my University of Maryland, was one of the very but altogether, I had a very happy child- masters thesis in 1966 was Morse theory and best and went on to make a brilliant career hood with much love. Outside school, I Smale’s proof of the generalised Poincaré con- as a research mathematician. In connec- was an eager soccer player – almost jecture. This subject was along a different tion with my teaching, Professor Ebbe mandatory in my native town, which has line from the main emphasis in topology in Thue Poulsen followed the full course. He fostered several famous soccer players. Aarhus, namely algebraic topology, where claimed that it was out of pure interest. Many happy hours were also spent as a Leif Kristensen himself was a leading Whether this was the full truth or not, I Scout, where I ended up as group leader. expert on the Steenrod algebra. Leif was found this caring from an experienced and A musician and music teacher living in not very much older than his students and excellent teacher very comforting. the same house as us persuaded my par- we had a very friendly relationship with From time to time, I discussed my plans ents to buy a piano. At the time, I was him. with Svend Bundgaard and he encouraged more interested in football and other phe- Immediately after obtaining my degree, me to go abroad to do a PhD. I was nomena exhibiting curvature, but I I was appointed to a temporary position in extremely well motivated for this: my learned the notes and music became Aarhus. In the fall of 1967, I was appoint- teaching had gone very well and I had writ- important to me – in particular, jazz. ed assistant professor with the special task ten a complete set of lecture notes offering Today I prefer improvisation, and have a of developping a contemporary and new an original introduction to a relatively special weakness for Fats Waller. course in differential geometry for the advanced subject. I really felt eager to do upper undergraduate level. I wrote a com- original research in order to qualify myself After gymnasium you went to Aarhus to prehensive set of lecture notes for the properly for a permanent university posi- study. Why did you choose mathematics as course, laying the foundations of smooth tion. your main subject? manifolds and developing the calculus of In September 1960, I matriculated at the differential forms and integration on man- How did England become your choice? University of Aarhus to study mathematics ifolds, culminating in a complete proof of In the summer of 1968, Professor Zeeman and physics. There was never any real the generalised Stokes’ theorem. It was a (now Sir Christopher) was one of the main doubt in my mind that these subjects were rather ambitious course for the given level, lecturers at a Summer School in Aarhus. It my favourite subjects and my teachers at but it was a great success and several very hardly comes as a surprise to anyone who school had several times pushed me in this direction. The 1960s was a tremendous time for mathematics and the natural sciences. In the opening paragraph of the handbook for these studies, it said something like: ‘For everyone completing these studies, the future is bright with a multitude of very diverse possible appointments ...’. With such words, you could fully submit yourself to the study of the sciences without any worries for the future. As a matter of fact, I think one could say the same today! Originally, I thought that I would end up with physics as my main subject. But at the Mathematical Institute reigned Professor Svend Bundgaard, an energetic and all- time-consuming enthusiast for mathematics. After less than three weeks of intensive bombardment with lovely mathematical Vagn Lundsgaard Hansen in the Study for House 4, Mathematics Research Centre, University concepts, mathematics became dominant. of Warwick. The family lived in this marvellous house during the first year of their stay at Svend Bundgaard has placed his mark on Warwick, 1969-72. EMS March 2003 15 INTERVIEW several newly appointed young staff members of high quality. I was very kindly received and quickly accepted. In addition to research and teaching, I now also became involved in administration and ended up as Chair of the committee of study affairs in the science faculty. At the time, the universities in Denmark were run very democratically, implying that students had 50% of the seats in this influential committee. Obviously, this caused many discussions, but being fond of discussions leading to democratic decisions, I found this stimulating and inspiring. In connection with a graduate course on singularity theory in 1976, I was inspired to define the notion of polynomial covering maps. In addition to my continued interest and work on the topology of mapping spaces, I now began a study of these special covering maps, defined by project- ing the zero sets for parametrised families Vagn Lundsgaard Hansen presents a lecture on catastrophe theory in connection with an open of complex polynomials onto the parame- house arrangement for the public at the Faculty of Sciences, University of Copenhagen, in 1977 ter space. An account of my work in this field was given in the book Braids and knows him that Professor Zeeman made a In Warwick, I found everywhere the bub- Coverings, published by Cambridge strong impression on me, and I discussed bling enjoyment of mathematics that I had University Press in 1989. This book is my interests in mathematics with him to felt inside myself for years, but somehow based on a set of lectures delivered while I seek his advice. I got, as it turned out, had suppressed in Denmark. I came to was a visiting professor at the University of tremendously good advice. know many excellent mathematicians and Maryland, College Park, in the fall of 1986. Professor Zeeman was the founder of the several of them became my very good Institute of Mathematics at the University friends, including many of the young staff Finally you came to Lyngby. of Warwick in Coventry, established in members at the institute and some of the In 1978, I was contacted by mathemati- 1964, and was for many years a charismat- foreign visitors. cians from the Technical University of ic leader of the institute. Combining in I defended my thesis in the summer of Denmark about whether I would apply for one person an eminent researcher, a bril- 1972: it contained work on the topology of a position as professor at this university. I liant teacher and a visionary and clever mapping spaces. As one of my results, I saw some challenges and promising possi- administrator and organiser, the Institute had succeeded in giving a complete divi- bilities at the Technical University of of Mathematics at the University of sion into homotopy types of the (countably Denmark, situated in Lyngby in the out- Warwick under his direction quickly many) components in the space of contin- skirts of Copenhagen, so I applied for the gained a reputation as a very strong uous mappings of the n-sphere for all n. position. At that time, a professor was research school for mathematics with a The result is rather surprising, and a paper appointed as a civil servant by the Queen, large visitors’ programme. about it was published in the Quarterly and the whole process with selection com- From Professor Zeeman, I learned that Journal of Mathematics, Oxford, 1974. mittee, approval by the democratically they were about to hire the American composed senate of the university, etc., mathematician James Eells as a professor Then you went back to Denmark? took some time. In 1979, our son Martin of mathematics at the University of Yes, but I must first mention that another had been born. And then, on 1 February Warwick to develop the then relatively new major result obtained during our stay in 1980 I was appointed professor of mathe- field of global analysis. Combining strong Warwick was our second daughter Helle. matics at the Technical University of elements of analysis, geometry and topolo- And then I felt ready for a permanent job. Denmark. gy, this clearly matched my interests in In 1972, the job market in mathematics mathematics, and I eagerly went to was tightening up. I got some offers for During the late 1970s the DTU Department Warwick in September 1969 to study with temporary positions from different coun- of Mathematics went through a somewhat Professor Eells. tries, but I was relieved when an applica- turbulent period of reorganisation. At the This was the best decision in my life, only tion for a position as associate professor at same time, it was fighting for survival exceeded by my marriage to Birthe in the University of Copenhagen was success- against the old idea that the staff teaching 1964. Together with our eldest daughter ful. In August 1972 we moved to and doing research in mathematics ought to Hanne, we spent three extremely happy Copenhagen and a new period in our life be distributed into the other departments in and unforgettable years in Warwick. In the began. order to serve the applied disciplines best. second year of our stay, Birthe was The University of Copenhagen is the How did you see these challenges and your appointed mathematics teacher at a gram- oldest, and was for hundreds of years the own possibilities at DTU at that time? mar school, so we got altogether a magnif- only, university in Denmark. The eminent I knew about these difficulties, but I icent insight into the British school system Danish mathematicians from the past focussed on the fact that the senate of the at the time. therefore all had relations with this univer- University, after thorough considerations, Studying with Jim Eells was an enjoy- sity. Such strong historical traditions add a had decided that the Department of ment. His good spirit and sense of flavour to a university and gave me valu- Mathematics should survive as an indepen- humour were a perfect match for me. He able experiences, in addition to the expe- dent department. I also had the impres- had a way of encouraging you so that you riences I had enjoyed at the younger uni- sion that influential members of the senate really felt that you could do it. Most often, versities in Aarhus and Warwick. during the process had recognised that I found the problems to work on myself, The senior professors at the University mathematicians need to be members of a but Jim was there putting it all in perspec- of Copenhagen counted among others mathematical community in order to tive and due to his scholarly knowledge of Thøger Bang, Werner Fenchel, Bent maintain a level of mathematical expertise, the literature, you felt sure that you were Fuglede and Børge Jessen, all first-class whereas it was useful for our colleagues in not just reinventing old things. mathematicians. In addition there were the engineering sciences to consult their 16 EMS March 2003 INTERVIEW mathematicians with mathematical prob- public. This may be a good approach in own tracks, some of them with extremely lems. I think they also recognised that private firms, but is not necessarily good in good results. I was deeply touched when mathematical research is necessary to universities. I am not in favour of this for two days in November 2000, many of ensure that the teaching of mathematics development, but I am still confident in them delivered excellent and inspired lec- should not stagnate. mathematics. tures at a symposium organised by my department in collaboration with the asso- Is it fair to say that the idea behind your ciation of secondary school teachers of construction of the Department’s logo was mathematics, in celebration of my sixtieth to iconise that mathematics is strongest birthday. when considered a unity across the disci- I have had a wonderful time at DTU. I plines? have come to know many first-rate people Yes, I think that this is a fair description. I from other departments. In the period certainly wanted to iconise the major 1988-93, I was Dean of the Faculty of Basic research fields in our department – geom- Sciences. In the period 1992-98, I was a etry, analysis and discrete mathematics – as member of the Science Research Council appear together in the logo. At the same of Denmark, four of these years as vice- time, it gave me the opportunity to con- chair. Also, in this connection, I met some nect with some of the major Danish math- very interesting researchers from other ematicians who have been associated with fields. This is also true for the Danish DTU – namely, Jakob Nielsen and Julius Academy of Natural Sciences, of which I Petersen. Our department has much to be have been president since 1984. proud of in the past. This is a good level The logo of the DTU Department of to strive for. And your own scientific work flourishes as Mathematics shows a geodesic immersion of the Problems from applications do not come well! Could you tell us about some of the Petersen graph into the Poincaré disc of con- divided into mathematical specialities highlights? stant negative curvature, emphasising the sym- from the beginning. So, maybe instinctive- In a paper published 1983 in the Bulletin of biosis between global analysis and discrete ly, I also wanted to signal that in order to the London Mathematical Society, I succeeded mathematics. Julius Petersen was Reader at be valuable mathematical members of an in determining the complete homotopy DTU from 1871-86 and Jakob Nielsen was engineering community, it is important to type of the space of homotopy equiva- one of the founding fathers of global analysis; be broadly educated in mathematics and to lences of the 2-sphere – that is, the space of he was Professor at DTU from 1925-51. keep an open mind for mathematics on a maps of degree 1 on the 2-sphere. Earlier broader scope than isolation into narrow in 1926, Kneser had proved that the corre- I felt that I had something to offer after specialities will admit. sponding space of homeomorphisms has the experiences I had gained at other uni- A very special enjoyment has been the the homotopy type of the orthogonal versities, and I appreciated very much the many excellent students I have met at group SO(3), and in 1959 Smale proved expectations and the great confidence in DTU. Around 1985, I planned and that the same holds true for the smaller me shown by my new colleagues. I knew a designed a new course on Fundamental con- space of diffeomorphisms. I think that it is few of them very well from earlier, and I cepts in modern analysis; the course material fair to say that topologists had expected was sure that the large majority of the staff developed eventually into a book with the that the same would also be true for the members would do their utmost to help same title, published by World Scientific in larger space of homotopy eguivalences. creating a good department. 1999. I have been fortunate to be the But, as it turned out, I proved in my paper As I have said earlier, the universities adviser at Masters and PhD levels for some that the space of homotopy equivalences of were run very democratically at the time, of the very best and able students, and in the 2-sphere is the product of SO(3) and and you had to argue your points of view. very diverse areas of mathematics. I am the double loop space of the 2-sphere, I went for open discussions of strategies happy that they all developped indepen- which is a highly non-trivial space. Very and attitudes, since I am convinced that dence and an inner drive to follow their recently my work on mapping spaces has this kind of leadership is the only one giving lasting results in research institutions with qualified staff members. I tried to be the first in the morning and the last in the evening at work, keeping up positive discussions about mathematics and our duties. I think maybe I functioned as a good catalyser in these discussions, and over the years the department has reached a high degree of consensus about our role as mathematicians at a university with its main emphasis on the engineering sciences. I am very fond and proud of my colleagues: many of them have developed as research mathematicians in a way that could not have been foreseen in 1980. Trust and confidence in people are strong and indispensable tools for keeping up good spirits. Lately there have been many changes in the university structure in Denmark, moving very far away from a democratic elec- tion of leaders. The current mantra appears to be strong leaders of the universities, appointed by small boards dominat- ed by outside members, and the ability for Nordic Summer School on Differential Geometry, Technical University of Denmark, Summer quick decision-making seems to be more 1985. In the front row from left to right are Jerry Kazdan, Karsten Grove, Flemming Damhus valued than the ability to make wise deci- Pedersen, Lone Aagesen (secretary), Vagn Lundsgaard Hansen, Jean-Pierre Bourguignon and sions based on arguments presented in Cliff Taubes. In the second row is Jim Eells (third from the left). EMS March 2003 17 INTERVIEW ination in short stories. Without really thinking clearly about it at the time, somehow such writings became an ideal for me. When I started university, mathematics was not a topic you really thought about in connection with pleasure reading or with high-class stylistic exposition: there was no story telling spirit. However, I came to admire the short and precise language of mathematics, and I was often amazed by the amount of information you can put in a few well-selected sentences. Being a topologist, I was particularly keen on the writings of John Milnor: I have read many of his books from cover to cover, enjoying both the mathematics and the elegant exposition. I suppose I have always been thinking about how to get an element of good story- telling into the precise conceptual world of mathematics, both when lecturing and writing. Good story-telling involves leav- ing something to the imagination, and good mathematics requires that you give enough precise details in your arguments. Over the years I have become more and more daring in my attempts to combine story-telling with mathematics. I try to commit myself never to write about mathematics without presenting a concrete mathematical result and elements of a mathematical argument. This is difficult to do, A mathematical family photo taken during the symposium ‘Facets of Mathematics’, held in especially when addressing the public. A November 2000 to celebrate the 60th birthday of Vagn Lundsgaard Hansen. Here he is sur- fruitful way is to combine the abstract rounded by several of his students and Jim Eells. structures of mathematics with concrete manifestations of mathematics from the attracted some interest, in connection with 1986. Throughout the whole process, I world around us. The symbiosis between topological aspects of the calculus of varia- had an intensive and very close collabora- the abstract and the concrete is the essence tions. This is the type of application I have tion with Werner Fenchel, who for many of mathematics for me: I see it like yin and always hoped for. years had been a close co-worker of Jakob yang in Chinese philosophy – both abstrac- Around 1980, the Danish Mathematical Nielsen. On many Saturdays, Werner came tion and concreteness are necessary ingre- Society decided to investigate the possibil- to our house where we proof-read the dients for the health of mathematics and ity of publishing the collected mathemati- translations and had lunch and dinner for its vitality. cal works of the Danish mathematician together. It was very rewarding for me to Jakob Nielsen, renowned for his pioneer- come to know this noble and modest schol- You have certainly applied this principle ing work in combinatorial group theory ar so well. with success, not least during World and for his investigations of the fixed-point Mathematical Year 2000. How did you get structure of homeomorphisms of surfaces You have written several books – bestsellers, involved? of genus = 2. Such surfaces are covered by like those listed in the references below. Do In 1995, Jean-Pierre Bourguignon, then the hyperbolic plane, and you can transfer you find it easy choosing what to write and president of the European Mathematical the investigations to an investigation of how to write it? Society, asked me whether I would be will- homeomorphisms in the hyperbolic plane. Writing essays on a narrow and uninspired ing to chair the World Mathematical Year This opens possibilities for exploiting topic was not my strongest side in school, committee that the society was about to methods from non-Euclidean geometry, and spelling was something I had to work establish. I agreed to this, and in October which Nielsen mastered to perfection. I hard at: but now and then, when I found was happy when the Society asked me to be the topic engaging, I surprised my teach- the editor of the collected works. My ers. Nevertheless, I never thought about research on mapping spaces and covering myself as a good writer. Writing is some- spaces were not directly related to thing I had to work at, but over the years it Nielsen’s work, but it did contain some of has become an enjoyment and great stimu- the same basic ingredients, and Jakob lus to me. Nielsen had been professor at the As a child I often went to the local Technical University of Denmark for library, sometimes several times a week, to almost 25 years during his career. listen to librarians reading aloud novels, The publication of Nielsen’s collected etc. I became fascinated by story telling, works entailed, among other things, the and I loved short elegant openings where translation of Nielsen’s major papers, sev- you immediately felt in the middle of eral of which had monograph size, from events. Like many children and adults all German to English. For the actual transla- over the world, I was deeply fascinated by tion we had highly competent and expedi- the short novels of Hans Christian ent help by the Australian mathematician Andersen: few authors can paint a picture John Stillwell. He even translated a few in words so well. Along a different line, the papers from Danish. British author W. Somerset Maugham The collected works were finally pub- mastered the importance of good open- Vagn Lundsgaard Hansen with one of his four lished in a two-volume set by Birkhäuser in ings and the ability to stimulate your imag- grandchildren during holidays 2000. 18 EMS March 2003 INTERVIEW matics. Many people from all over the make it a very special event. It was clear to world have made valuable and inspired everybody that mathematics is held in high contributions to the presentation of math- esteem in China. This gives renewed ematics for the public, so I felt greatly hon- momentum and hopes for a world-wide oured by this invitation. For the lecture I and bright future for our subject. chose subjects that I find suitable for con- versation on mathematics among people, A selection of works by V. Lundsgaard with my starting point as concrete manifes- Hansen related to this interview tations of mathematics in nature or civili- Geometry in Nature, A. K. Peters, Ltd., 1993. sation: I think that such conversations may Shadows of the Circle – Conic Sections, Optimal prove a good way of raising the public Figures and Non-Euclidean Geometry, World awareness of mathematics. After my lec- Scientific, 1998. ture I was interviewed by journalists from Braids and Coverings – Selected Topics, the leading Chinese press agency, who Cambridge University Press, 1989. wanted to use some of my ideas in future Fundamental Concepts in Modern Analysis, World articles about mathematics. I was certainly Scientific, 1999. confirmed in my hopes that the idea of (ed.) Collected Mathematical Papers of Jakob ‘mathematical conversations’ will catch on. Nielsen, Birkhäuser Verlag, 1986. At a meeting in connection with the World I was thoroughly impressed by the con- ‘Jakob Nielsen and his contributions to topolo- Mathematical Year held during the Third gress. It was amazing to see the Chinese gy’, Chapter 37 in History of Topology (ed. I. European Congress of Mathematics in President, the Vice-Premier of China and M. James), Elsevier Science B.V. (1999). Barcelona, Vagn Lundsgaard Hansen presents the Mayor of Beijing attending the full ‘I am the Greatest’, Mathematics in School 25 (4) a Danish poster picturing the bridge over the opening ceremony. I think all participants (1996), 10-11. Great Belt in Denmark, entitled ‘Mathematics felt really welcome in China, and our ‘The Story of a Shopping Bag’, Mathematical bridges gaps in culture, science and technology’. Chinese hosts did everything they could to Intelligencer 19 (2) (1997), 50-52. (The poster appeared on the back cover of EMS Newsletter 38 (December 2000). The other person in the picture is Kim Ernest Andersen, who designed and implemented the EMS- gallery containing the posters submitted for the Obituary: Carlo Pucci poster competition organised by the EMS in connection with the WMY. Giuseppe Anichini 1995 the committee was formally estab- Carlo Pucci, one of the most distinguished Italian mathematicians of his generation, lished by the Executive Committee. died in Firenze on 10 January 2003, at the age of 77. Among the excellent and energetic mem- Carlo Pucci was the Honorary President of the Italian Mathematical Union (UMI). bers of the committee, I am sure that He was born in Firenze in 1925 and, after graduating under the direction of everybody will allow me to single out Giovanni Sansone, he worked in Rome under the direction of Mauro Picone. From Mireille Chaleyat-Maurel as a quite excep- 1962 until his retirement in 2000 he was full professor in mathematical analysis in tional and dynamical person in this con- Catania, Genova and Firenze. He also worked also in the United States: for two years nection. Working with Mireille is a plea- he was assistant professor in the Institute for Fluid Dynamics, University of Maryland, sure, and we all owe a lot to her for her and was subsequently visiting professor at Rice University, the University of positive and highly creative work in con- Louisiana at Baton Rouge, and the University of California at Berkeley. nection with the WMY. Quite early in the Pucci was a mathematician of remarkable presence and immense energy. He life of the committee, my old friend believed that mathematicians’ jobs could be wholly fulfilling if world-wide connec- Ronnie Brown became a member of the tions could be made as soon as they began their research. So he worked tirelessly to committee, and his extensive experiences see this goal realised. As President of the National Mathematical Committee of the with the popularisation of mathematics Italian Research Council he promoted an impressive programme of fellowships for also became vital to the committee. A spe- young students in mathematics and for visiting professors, in order to establish cial personal benefit for me was that, strong connections between Italian and foreign mathematics researchers. through Ronnie, I became familiar with Among the most striking aspects of his personality was his long-term vision: he was the fascinating symbolic sculptures of the able to see and pursue ideas that would come to maturity only some years later. So, Australian-British artist John Robinson. as President of the UMI and President of the National Institute for Higher During my work with the WMY, I came Mathematics he later had considerable influence on mathematicians and mathemat- to know many wonderful persons with a ical institutions and achieved his aims to a very large extent. deep dedication to mathematics, and the The mathematical work of Carlo Pucci was mainly concerned with partial differen- work has given me many inspiring experi- tial equations. He obtained a celebrated maximum principle (simultaneously and ences. independently discovered by A. D. Alexandrov), where sharp analytic and geometric arguments concur to bring about an appealing result. Together with F. John, M. M. Last year you were an invited speaker at the Lavrentiev and A. N. Tikhonov, he was also a pioneer in investigating the so-called International Congress of Mathematicians ill-posed problems in the sense of Hadamard. His work in this field contributed to in Beijing, where your talk, Popularising establishing the basics of the current theory of these problems. Mathematics: From Eight to Infinity, was Carlo Pucci was, in many respects, an exceptional person. Generous, open and extremely well received. You demonstrated accessible, particularly with his young students, he had many good ideas and initia- once again, that mathematics contains an tives and the talent (and the physical strength) to understand the people who would abundance of concrete topics and results implement them. All his students were delighted and amazed at his availability to that lend themselves directly to mathemati- discuss their mathematical drafts, together and with each of them separately. Many cal conversations. [This article will appear of his students have themselves become well-established mathematicians. in the June issue of the EMS Newsletter.] He grew up very close to his uncle Ernesto Rossi, one of the strongest opponents Could you tell us some of your impressions of the fascist dictatorship in Italy, and this legacy was strongly impressed on Carlo from the Congress? Pucci. During World War II he was active in the Resistance, and subsequently had a It came as a great and unexpected surprise strong sense of civil commitment. In his last years he devoted himself to the Ernesto for me when I was invited to lecture at the Rossi - Gaetano Salvemini Foundation as a historical and cultural heritage of these International Congress of Mathematicians two major Italian personalities from the last century. in Beijing on the popularisation of mathe- Carlo Pucci will be very much missed by his friends and colleagues.

EMS March 2003 19 INTERVIEW

InterviewInterview withwith D.VD.V.. AnosovAnosov interviewer: R. I. Grigorchuk

This interview is in two parts: the second Moscow was rather exceptional, since the part will appear in the June issue. attention of the powers-that-be to science was generally more verbal than real. The Dmitry Anosov was born in 1936 in Moscow. salary was not the same as during the post- He graduated from the Department of war period. However, even before the war Dmitry Anosov Mechanics and Mathematics of Moscow State many talented young people chose a scien- University in 1958, and took postgraduate tific career. For many, science was inter- To a certain extent my interest in mathe- courses at the Steklov Mathematical Institute in esting in itself, but there were at least two matics became apparent in the middle of Moscow in 1961. Since then he has worked in other factors. First, in many other profes- secondary school. But at that time I was that institute, in various positions: he is cur- sions the salaries were also low. Second, more attracted to physics. During the rently head of the Department of Differential for many young people other choices were early post-war years it undoubtedly became Equations. From time to time he has also closed for administrative reasons, or were the dominant part of the natural sciences: worked at the Moscow State University (where unattractive because of ideological or other atomic energy, rockets, radar, and also he is Honorary Professor and head of the pressures. television (this had been invented earlier department of Dynamical Systems) and at At that time there were not enough com- but entered our life in the 1950s – even Moscow Independent University. petent college instructors (the scale of ordinary radio receivers were not wide- He is an expert on dynamical systems and engineering education expanded dramati- spread until the early post-war years). The related areas of the theory of differential equa- cally after the beginning of industrialisa- quality of popular scientific literature in tions and geometry. His best-known achieve- tion), so my father, besides working at the physics and astronomy was quite high at ment was the active role he played in creating AS, taught simultaneously at three other that time. the ‘hyperbolic’ direction of dynamical systems colleges. This was not due to his desire to In 9-10th grades I went to the physical theory. This was officially recognised by the share knowledge (which he satisfied after circle (study group) at the University, State Prize of the USSR in 1976 and unoffi- the war by lecturing on more advanced supervised by G. D. Petrov: I was less inter- cially by the appearance of his name in Anosov subjects to graduate students of the AS ested in the mathematical circles. I reck- systems, flows, diffeomorphisms and foliations, institute), but for extra income. So the oned that the next step after high-school and quasi-Anosov homeomorphisms. He was an family was relatively wealthy, both before maths was higher mathematics which was invited section speaker at the International the war and during the early war years. taught in colleges, and what they did in the Mathematical Congresses in 1966 and 1974. After this, the leadership learned that mathematical circles was not very impor- science was capable of producing valuable tant. I now think I was half-right and half- What are your most important childhood fruit, such as radar (information on atomic wrong, which agrees with R. Courant’s memories? energy became available at that time, but point of view in his book What is I have almost no recollection of the time physically appeared later), and the salary Mathematics? (with H. Robbins). I studied before Hitler’s Germany attacked the and rations of scientists were increased more on my own then. I had average suc- USSR in June 1941 – only a few blurry considerably (the consequences of this, cess in Olympiads, no brilliance: I under- episodes: I cannot say when they took though gradually eaten by inflation, sur- stand that I am not alone in this respect – place. During the war my family suffered vived until the arrival of so-called ‘democ- success in such competitions is not neces- much less than most other people, but the racy’). Because of this, we were lucky to sary to reach the level of an RAS member. profound changes in our lives at the begin- live through the war without misery: we Of course, there were competition winners ning of the war and during evacuation in evacuated to Kazan where we lived in one who later became famous mathematicians Kazan left such a strong imprint that I room in a former university dormitory. at the highest level – such as V. I. Arnold, remember a lot. I was four-and-a-half at Since my parents no longer spent as who was one year younger than me; I did the beginning of the war: later, as I grew, I much time at home and my grandmother not have contact with him then. remembered more. was constantly busy with housekeeping, I In my later grades I gave more attention was urgently taught to read so that I had to mathematics, since I came to under- Tell me about your parents. an occupation. Maybe because of that self- stand that the great book of the universe ‘is My parents were scientists – chemists who study period I acquired a taste for theoret- written in mathematical language’ reached professorial level. They were from ical science. (Galileo). Gradually I became interested in Saratov, and from the 1920s they lived in mathematics itself. Leningrad where they worked mainly at Do you remember Moscow life in the late- the Academy of Sciences (created when the 1930s? How did you enter the Moscow State capital of the Russian Empire was St I don’t remember anything, and could not University? Petersburg). Later they moved with the know much: I know only from the stories of I graduated from high school in 1953 with main body of the Academy to Moscow. older people. The initial ignorance of the a gold medal (high honours) and so need- During this transition, many Academy importance of science had a positive side ed only to pass an interview. If it had gone employees received rather spacious quar- to it – the repression at the end of the badly, I would have had another chance by ters (even by present-day standards) – for 1930s affected others. This was clear in taking the entrance examinations – but it us, it was a three-room apartment for three our apartment building, where some sec- went well. I was interviewed by L. N. persons (the third was my grandmother). tions were occupied by AS employees and Bolshev and V. G. Karmanov, who asked After that, the fresh Muscovites merrily some by the employees of the Federal something mathematical – had I ever been ‘became fruitful and multiplied’ (though Bank, mainly those who worked abroad. interested in something beyond the high- still not with biblical intensity). school curriculum? I remember a question This generosity in accommodating the When did your mathematical talents which sounded like ‘Are there more ratio- Academy employees during the move to become evident? nal numbers or irrational ones?’ Then 20 EMS March 2003 INTERVIEW they proceeded to general questions. I our topological education), Pontryagin’s said that I liked classical music. They book Smooth Manifolds and Their Applications asked whether I liked Prokofiev, and I in Homotopy Theory appeared; its first chap- replied honestly that I liked only the ter was the first ever textbook on smooth Classical Symphony. The interviewers manifolds. (G. de Rham’s book grinned – ‘you will have to grow up’: they Differentiable Manifolds, which came out in were right. 1953 and appeared in Russian in 1956, The year 1953 was very important for could not play such a role: it brought the our country – Stalin died in March, and in reader too quickly to its main subject – the summer his right-hand man Beria was homology theory based on differential arrested (later he was put on trial and forms and currents – without giving the shot). Life became freer, though people in reader time to get used to manifolds. the West would not have considered it free. Maybe de Rham did not have this educa- (This is not only my opinion.) Many years tional goal in mind, while Pontryagin did.) later, A. N. Kolmogorov told Arnold that When Pontryagin’s book appeared, I he ‘got a glimpse of hope’ at that time and hesitated – was it worth buying? Books that it partly stimulated a rush in his scien- Anosov as a student were cheap then in Russia, the price was tific activity in the mid-1950s. not a problem even for a poor student, and The year 1953 is also memorable for I was not poor – my parents had a good Moscow University, because it acquired a Which MSU professors had the most influ- income. But I knew that Pontryagin’s new building – the famous (more than 30- ence on you? achievements in homotopic topology were storey) building that became almost as First was Pontryagin (see below) and his co- surpassed by the French, so how good was much a symbol of Moscow as the Kremlin. workers (not yet professors) Boltyansky, his book? Fortunately, Gamkrelidze came The University was fortunate that I. G. Gamkrelidze and Mishchenko. I have up to me at that moment: he could not Petrovsky had become rector shortly already mentioned Shafarevich, one of the imagine that I doubted the value of the before that: he was quite influential at the best, if not the best, lecturer I have ever book. He thought I had no cash and kind- time and for a few years later. Of course, heard. During my third year a group of ly offered to lend me some money. That the communist party group made many of relatively young mathematicians started a convinced me that the book was worthy the decisions, but from time to time lecture-and-seminar series on new areas of and I bought it. Thanks to Revaz Petrovsky managed to stand his ground: I topology (mainly, homotopic topology): Valerianovich for his advice! think that the highest party leaders trusted these were Boltyansky, Gamkrelidze, During my fourth student year, him and did not have much respect for Onishchik, Postnikov, Shafarevich and Gamkrelidze started a seminar with their party servants. (Unfortunately, he Schwarz. They were joined by E. B. ‘smooth’ orientation. Of special impor- later lost his influence, in the middle of the Dynkin, who did not take part in the edu- tance to me was learning the area that Brezhnev period, and the influence of the cational aspects but studied some things Serge Lang later called ‘the no-man’s land party group grew.) Petrovsky could not with the others, and in particular worked between the great three differential theo- change the situation in social sciences or on a collection of translations, ‘Fibre ries’ (differential topology, differential biology, but could (and did) do things in Bundles and their Applications’, which geometry and ordinary differential equa- other fields. appeared in 1958 and played an important tions). Very quickly I learned to think in role in our country. I never heard of a sim- invariant terms, with the corresponding Tell me about your first two student years? ilar undertaking among MSU mathemati- underlying notions, and to bring to gener- At first I was rather disappointed: I was cians or elsewhere to study a whole field. al position by small perturbations using well prepared and could have been taught Not all of the students who took to the new Sard’s theorem. (Sard’s work appeared faster and more intensively. On the other wind stayed in science, and not all of those during the war and was not known in hand, nobody prevented me from studying who remained worked in algebraic or dif- Moscow for a long time; his theorem was more intensively by myself – quite the ferential topology or in the adjacent area later rediscovered by Dubovitsky, whose opposite. During my freshman year I. R. of algebraic geometry: this was also true of name we attached to it.) Shafarevich started a study seminar in our teachers. But, I think, nobody was Later, at the Steklov graduate school, S. algebra. By the spring, only Yu. I. Manin, hurt by the acquired culture. P. Novikov and I became interested in cal- E. A. Golod and I still attended the semi- The announcement (by A. S. Schwarz?) culus of variations in the large, and we nar: by that time we had reached the ele- of this enterprise for students said some- read the monograph on it by M. Morse. ments of Galois theory. thing like ‘one can study simple properties We later used our acquired knowledge dif- Also, during my freshman year, E. F. of complex spaces or complex properties ferently. For me, the main thing was not Mishchenko supervised recitation sessions of simple spaces’. This phrase irritated P. the calculus of variations in the large itself, in analytic geometry. He told me that S. Aleksandrov, the chair of topology and but rather seeing how a far-reaching there was a famous mathematician, L. S. geometry, who was generally an important mixed analytical and geometrical theory is Pontryagin (I had heard of him indepen- person who had switched to general topol- developed. By that time I had not enjoyed dently), who would lecture to us the follow- ogy. He did not oppose the new areas, but the supervising and directing influence of ing year and would hold a special seminar. neither did he support them, trying senior colleagues, but I had very useful That is where I went. I was grateful to instead to make room for general topolo- contacts with S. I. Alber who then worked Shafarevich for the algebra (later I took gy. Several years later, at an all-union in Gorkii (Nizhnii Novgorod). topics courses from him), but I was more topology conference in Tashkent, he said The middle of the 1950s saw the remark- attracted to analysis, and to some extent to that according to Kolmogorov (a scientist able achievements of A. N. Kolmogorov in geometry. with a wide range) algebraic and differen- the theory of dynamical systems. Many people expressed the opinion that tial topology had not attained as wide an Somewhat later (in 1958-59, when I was a the 1950s to 70s were the blossom time for importance in mathematics in general as graduate student), these were included in a the MSU Department of Mechanics and general topology, in spite of all their topics course that he gave (only once) and Mathematics. This prosperity had no ana- remarkable achievements. To a certain in a related seminar. logue elsewhere in our country, or possibly degree, Kolmogorov was right – continuity In many respects Kolmogorov had his in the whole world; it was manifested in the is encountered more often than (say) some own ‘style’ which made him very different abundance of topics courses and seminars bordisms or others. However, the addition from the rest. In particular, unlike covering all of mathematics. I dived into of integers is encountered still more often. Pontryagin, Gelfand and many others, that sea during my third year, and for the At the beginning, smooth manifolds did including scientists of my generation, first two years was satisfied with what I not play a special role in our education. Kolmogorov did not conduct a permanent described. But in 1955 (coinciding with the start of seminar that would reflect the changes in EMS March 2003 21 INTERVIEW his scientific interests. I think that there in that direction. I have never dealt with which was unsafe at the time. (Aleksandrov was a ‘central’ seminar on probability the- direction in my work, so in this case one and Kolmogorov also tried to help him. ory to which Kolmogorov devoted more should rather talk about impressions All three also tried to help Efremovich, time than to anything else; but after rather than influences. who was not Jewish, so this does not say becoming interested in other things, he The last topics courses in which I had anything about their attitude towards Jews, did not change the direction of that semi- great interest were those run by Arnold but it required the same valour as for nar but rather started a new seminar which and Sinai on KAM and ‘abstract’ ergodic Rokhlin.) I think the latter outweighs. ran for only a year or two. As far as I theory. I took other courses as well, but Apart from these two paragraphs I see remember, the entropy approach in was mostly influenced by those I have no need to discuss LSP’s non-mathematical ergodic theory, which he invented, was not described. activities. In the end, these people are mentioned either in the course or in the worth talking about only from the view- seminar, although some other aspects of point of their scientific and educational ‘abstract’ (purely metric) ergodic theory activities. were considered, such as the spectrum and I was LSP’s undergraduate and graduate dynamical systems with discrete spectrum; student, and then worked in his depart- I think that there was some discussion of ment. I was never as close to him as his systems with unusual spectral properties, three co-workers mentioned above, but it is but I do not remember this well; in any hard to overestimate his influence on me. case, some random processes were consid- However, I think this influence was some- ered as dynamical systems. what unusual. However, another of Kolmogorov’s Pontryagin never taught me systemati- achievements – now called the KAM theo- cally, and apart from the first few months ry – was covered. Strangely, Kolmogorov Anosov as a postgraduate of our acquaintance, not even non-system- never wrote a detailed exposition of these atically. But he offered me several topics results – it was done by Arnold. Of course, to work on, first simple (not far beyond the KAM is difficult to present, and it would Tell us about your teachers. level of exercises), then more and more not have been surprising if it had not I shall talk mainly about Lev Semyonovich difficult: these turned out to be important appeared for several years. Pontryagin Pontryagin. It is well known that he was for my growth. There were also a couple of and P. S. Novikov (my friend’s father) blind – he lost his sight at 13 in an acci- topics that he did not suggest but which I spent several years writing full expositions dent. For a blind person to get higher ‘caught’ in the ambient creative atmos- of their achievements in topology and education is quite a feat, and he became phere around him. The influence of his group theory (with Novikov finishing this one the most important mathematicians of general approach to mathematics may work in collaboration with his student S. I. his time. Of course, we reckon that our have been more important, but that is dif- Adian). But Kolmogorov never wrote a full main work is done in the brain and paper ficult to describe. text on his results in KAM, although he was scribbling only helps, but it is a significant Shortly before I became a student at the not tight-lipped – he wrote several papers help and anyone deprived of it must be MSU, LSP decided to abandon topology on different subjects in the period between under considerable stress. This does not and switch to ordinary differential equa- his first KAM announcements and Arnold’s come for free. Pontryagin was a worka- tions. Actually, ODEs were not something publications. holic, and with time this took its toll. new for him. Many years before that, there Kolmogorov has over 500 publications, Unfortunately, memories of his last years were contacts between Pontryagin and but his high reputation is based on a few are overshadowed by several circum- Andronov (a physicist, at least by educa- ‘pearls’ whose number is naturally smaller. stances. One talks about his anti-Semitism, tion, who majored in physics at the MSU in In the middle of the 1950s he had a rush but not about his trying to judge things the 1920s). Around 1930 Andronov moved of scientific activity – I have already men- that he could not keep track of (and those to Nizhnii Novgorod (then Gorkii), and tioned dynamical systems, but he also sug- were not his private views – he played an the transformation of this city into a signif- gested using entropy notion in the theory active administrative role too). icant centre for mathematics and physics is of functional spaces. (Entropy dimension Undoubtedly, he was used. Several years largely due to him and his co-workers. to some extent was discussed by after his death Shafarevich even remarked (Incidentally, they also established that Pontryagin and Shnirelman, but they had in print that if LSP had lived longer, he Lobachevsky was born in Nizhnii no applications.) His whole entropy enter- would have moved away from ruling Novgorod, but his scientific development prise was new and important. As for KAM, Areopagus. But even during that period started later – there was no university there he may have hoped to obtain other new there were two significant bright moments at that time; after his childhood results in this area and then write about it. in his life. First, he actively fought turning Lobachevsky lived, studied and worked in Curiously, when preparing a full collection the rivers. (A giant hydro-technical project Kazan.) The collaboration between of his works at the end of his life, he was involving transferring water from the Pontryagin and Andronov resulted in four very selective and included only a few northern rivers to Middle Asia and partly papers: two by Pontryagin himself, one a things. to the Volga had been suggested: the eco- joint paper with Andronov, and the last a I was very impressed by Kolmogorov’s nomical soundness of this project was joint paper with Andronov and another lectures and seminars, but I did not under- unconvincing, and the ecological conse- physicist, A. A. Vitt, a student of Andronov. stand many things. His lecturing style was quences would have been catastrophic.) (Vitt was a victim of Stalin’s repression.) difficult for the audience. I don’t know if Second, as head of the commission on sec- A little later he wrote two papers on the he overestimated us or purposefully aimed ondary mathematical education, he helped zeros of quasipolynomials. Formally this is exclusively at the best prepared and capa- to correct the consequences of the careless not ODEs, but the stability of ODEs with ble in the audience. Only later did I reforms of the end of the late-1960s and delay depending on the distribution of remember something I had heard, thought early-1970s. those zeros. However, all these works were it through anew and began to understand. My personal memories are from an ear- episodes for LSP, although they were not I was also very interested in N. V. lier period – we had almost no contact dur- episodic for the theory of ODEs. He now Efimov’s course on differential geometry ing his final years. But I have to say that decided to switch to ODEs completely, in the large: this was mainly on the rigidi- when evaluating the life and career of a since he had no new ideas in topology and ty of surfaces of different types. Efimov’s person, one should take into account his some French papers with very strong new most famous result on the non-existence of whole life, and not only the last years. topological results appeared at that time: complete surfaces in R3 with negative cur- Those who speak of his anti-Semitism dur- the first announcements of these were vature separated away from 0 had not yet ing his last years should remember that he short and the gist of the new methods was been obtained, but Efimov was ‘approach- had several Jewish students, and that fur- difficult to judge. Who knows: if ing’ it and talked about some partial results thermore he tried to help V. A. Rokhlin, Pontryagin could have established contact 22 EMS March 2003 INTERVIEW with French topologists, he might have course was new, certainly in the USSR. (S. removed ‘Vitt’, but forgot to delete the come up with new ideas, or at least com- Lefschetz and V. Gurevich had already comma. Not to encourage politically bined his old ideas with those of the written somewhat similar books that were wrong conclusions, the suspicious comma French. His approach was more geometri- unknown in the USSR. Although these was scraped off with a razor, but if one cal, and we know that more geometrical first attempts to modernise the ODE looks carefully, there is less space after ideas, some going back to LSP’s works, course did not have followers in the West, ‘and’ than before, where there are visible were later added to the French algebraic it was only after Pontryagin’s book traces of scraping. I suspect that those who methods. But he was not permitted to go appeared that the situation started to forgot about the comma were penalized.) to France. change. Lefschetz himself later turned his This book had an extremely profound After his switch to ODEs, LSP had no book into a longer graduate-level text.) influence on me – I had probably not been chance to work with Andronov – the latter Pontryagin carefully prepared his lec- so impressed by any other book. I think died in 1952. But the first topic in ODEs tures and tried to be comprehensible to there were two reasons for this. First, for that LSP started to work on was ‘inherited’ most of his students. Still, from time to the first time I was reading not a text book from Andronov – the theory of singular time his lectures were difficult for quite a but a monograph written by scientists, one perturbations. Many different situations few. It was related in part to LSP’s lack of a luminary and the other an exceptionally arise in this theory. Some require ‘only’ teaching experience – before that, he had gifted educator (besides being a good sci- premises that are easy to guess, but from taught only topics courses in a different entist). Second, the two-dimensional qual- the very beginning Pontryagin concentrat- subject. There are still places in his book itative theory is quite impressive initially. ed on the more difficult question (in which that are worth changing – but these are iso- (Before Pontryagin, there was almost no Andronov was also interested), where the lated shortcomings that could easily have discussion of this field in a regular ODE answer was difficult to guess – the asymp- been removed in subsequent editions; course. It was covered in Poincaré’s collec- totics of solutions of differential equations unfortunately, he did not do it. tion On curves defined by differential equations describing relaxation oscillations close to LSP took a responsible attitude towards – Andronov urged its publishing – which discontinuous. While I was an undergrad- his duties as a professor. For example, contained detailed comments, and in uate student, he offered me a simpler before exams there were review sessions Qualitative theory of Ordinary Differential statement which I managed to prove. during which students asked questions if Equations by Nemytsky and Stepanov. Since Independently, the same was done by L. they had not understood something in the the first book was ‘too special’, I read it Flatto and N. Levinson, whose work was course. Usually this involved straightening only several years later; the second, though published earlier, but I considered a slight- out some issues, but LSP considered it nec- undoubtedly rich in content (for its time) ly more difficult version of the problem. I essary to repeat one or two of his lectures. always bored me, I don’t know why, to the think that they purposely restricted their After a couple of years he got tired of same extent that as the Theory of Oscillations paper to the simpler version, because it teaching a required course. He did not absorbed me.) Later generations of stu- required the same main ideas: if necessary lecture poorly, but refused to teach the dents were not as impressed by the mathe- they could have proved my theorem. I do course and created a new one. matical chapters of Theory of Oscillations, not know anything about Flatto, but From the second half of the 1950s, since elements of the two-dimensional Levinson was a well-known analyst and it Pontryagin worked mainly on optimal con- qualitative theory were soon covered in was an honour to do what he did. Still, my trol and later on differential games. I did many textbooks and courses; after this, the work was a success for an undergraduate not take part in that work, since by then I Theory of Oscillations became a source with a student: it was ‘a sophisticated exercise’ had found my own field. I learned classi- more complete exposition of a subject that was useful for my development. cal ODEs mainly by reading myself – only whose basics were already known. Formally, it did not depend on anyone towards the end was it complemented by I studied many other aspects of the the- else, but in essence it was not based on new the topics courses of Kolmogorov, Arnold ory of ODEs by myself, from the works of ideas and methods. and Sinai, but that was not the classical the- Lyapunov, Perron and Bogolyubov. I Pontryagin lectured on ODEs to my class ory. practised searching the literature on sub- (it was a required part of the curriculum): jects of interest to me, which was also use- this was the first time he had lectured on ful. As I read, I tried to evaluate the work this subject, or had taught a required using Pontryagin’s criteria: is it new in course to a large audience. (Although he principle? or is it a useful refinement of had worked at the University before the known ideas and techniques? or neither? Academy’s move to Moscow, there were I still believe that LSP’s best achieve- probably more students in one lecture hall ments were in topology, and I caught him than in the whole department of mechan- in decline – but the beginning of the ics and mathematics before – and topolo- decline was slight and the level still very gy, which he also taught at the Academy, high. My only critical comment on that was not a required course and did not have period relates less to his scientific activity a large enrolment.) At the same time he than to a certain mood that overcame him. was preparing his well-known ODE text- He used to say that he studied real-life book, and by the end of the school year we problems (which he naively called ‘physi- received a present – mimeographed copies cal’; what kind of physics is it when one of the book. Publishing a book was differ- does not have to know a single fundamen- ent then – now you use a computer to write tal physical law?); it was rather explicit, anything you want and then print it out. although not in the open, that others such The process then was much longer and Anosov lecturing on as Petrovsky, Bogolyubov or Gelfand had required more work, in addition to the complete uniform hyperbolicity previously worked on important applied administrative logistics. Many years later, problems but could not talk about them at when I began lecturing, I sometimes wrote that time: at different times, and to a dif- out my lecture notes, but had only frag- But the first nudge was from LSP, who ferent degree, all three were involved with ments by the end of the course. So, I can- recommended that I read the mathemati- the Soviet atomic project. However, on the not help but admire LSP’s responsibility cal parts of Andronov and Khaikin’s Theory surface everything looked decent. I and ability to work. of Oscillations. (It originally had Vitt as a remember only one criticism of these Today’s ODE courses (at least at major third author, but after he was arrested his remarks of LSP. It was by Kolmogorov, universities) more-or-less follow the high- name disappeared from the first edition. who was also involved with physics and lights established by LSP, which became At first the cover page read ‘A. A. some applications (the theory of shooting; standard. However, upon checking earlier Andronov, A. A. Vitt and S. E. Khaikin’. turbulence, some questions connected to textbooks, it is clear that Pontryagin’s When the cover page was reprinted, they fluid dynamics and some applications of EMS March 2003 23 INTERVIEW statistics of random processes, created by I cannot judge to what degree he felt that dent is the current seminar of MIAN’s DE him and N. Wiener). He said that there is LSP’s shortcomings, which for a while department. a nice model for ordinary differential appeared rather innocently in conversa- equations – the geometrical picture of the tions, but which later became more promi- Who were your student friends? behaviour of trajectories in the phase space nent: I am making the risky assumption Primarily these were the people with whom (Andronov coined the expressive term that the former played the main role at I studied the new field. First was S. P. phase portrait), which carries so much infor- that time. LSP himself, after giving the Novikov. There were others among the mation that there is no need for anything restructured ODE course a couple of times regular participants of our topological else, unlike partial differential equations, and written the corresponding textbook, seminars whose contribution to science which require the knowledge of the physics did not make too much effort to overcome (not necessarily to topology) was real, they originated from. Petrovsky’s guarded attitude. But he had though not as great as Novikov’s: I was far removed from higher circles, achieved his goal – this course, when Averbuch, Vinogradov, Ivanovsky, but I have the impression that Petrovsky offered at a serious level, is now taught in Moishezon, Tyurina, and Fuks. I do not was not particularly enthusiastic about the style of Pontryagin everywhere in the remember how regularly, but Zhizhchenko LSP’s new direction. To some extent, he world. In addition to giving the new and Melnikov also came; Manin and Golod disliked the emergence of a competitor in required ODE course, LSP and his co- participated in one of the study groups, a field that he had ruled earlier (being the workers held an accompanying seminar. but they were attracted to algebra, and university rector, he had no time for This was initially a study group, but later soon got pulled into it. It was only later research, and at best could only follow became a research seminar and moved that I drew closer to Arnold, Sinai and what was happening in mathematics); and from the MSU to MIAN. Its direct descen- Alekseyev.

en the role of mathematics in this interactive process. In order to achieve this, the NewNew rresearesearchch centrcentree inin BerlinBerlin Centre’s research program is application- The German Science Foundation Deutsche tors, many of them with participation from driven, but we do basic research in mathe- Forschungsgemeinschaft (DFG) has established other mathematics departments. In July matics and we envision that it will also have a new research centre in Berlin: 2001 we learned that we were among the a strong impact on the development of Mathematics for key technologies: three finalists, who then had to prepare a many other areas of mathematics. We also Modelling, simulation, and optimisation of detailed proposal (a densely packed book of hope that the Centre’s activities will increase real-world processes. 400 pages). In January 2002 the finalists inner-mathematical, inter-disciplinary and The Centre is funded by DFG with 5 million had to defend their proposals in competi- trans-disciplinary cooperation. euro per year, and is operated and cofi- tion before an international group of The Centre focuses on the mathematical nanced with 3 million euro per year by the reviewers. The final decision in May 2002 fields of optimisation and discrete mathematics, three Berlin Universities, the Free was based on the rule the winner takes all. It numerical analysis and scientific computing, and University (FU), Humboldt University (HU) saw two very strong but disappointed run- applied and stochastic analysis and, building and the Technical University (TU) as lead- ners-up who had spent as much time and on existing cooperations, it will address the ing institution, together with the two energy on their applications as we had. following key technologies: research institutes, the Konrad-Zuse Since the decision was made, the activity • Life sciences (computer-assisted surgery; Zentrum für Informationstechnik (ZIB) and within the Centre has grown immensely. patient-specific therapies; protein data the Weierstrass Institute for Applied The administration of the Centre had to be base analysis; protein conformation Analysis and Stochastics (WIAS). The cen- set up and the facilities for the Centre are dynamics) tre was opened on 20-22 November 2002 at being prepared (it will occupy a large part • Traffic and communication networks (plan- the Technical University of Berlin with a of the mathematics building of TU Berlin). ning of multi-level and multi-layer com- three-day workshop that started with a Furthermore, and most important, about 60 munication networks, planning of the Mathematical firework. This firework, with researchers, 7 assistant professors and 7 full UMTS radio interface, line planning, talks for the general public including 3-D professors, covering the areas of applied periodic time-tabling, and revenue man- mathematical visualisations, drew a spectac- analysis, numerical analysis, stochastics, optimi- agement in public transport) ular audience of more than 1000 people sation, visualisation, discrete mathematics and • Production (shape memory alloys in air- and received a large and enthusiastic echo scientific computing have to be hired. The foils, production of semiconductor crys- from both audience and media. current grant is for four years and it has a tals, methanol fuel cell optimisation, on- maximum lifetime of 12 years, with two line production planning) History of the Centre evaluations on the way. • Electronic circuits and optical technologies In August 2000 the DFG (as a result of fund- (quantum-mechanical modelling of opto- ing obtained through the UMTS licence Mission of the Centre electronic devices, design of nano-pho- auction) started a new programme to estab- Since modern key technologies need more tonic devices, integrated circuits for lish several centres of excellence in research and more complex modelling, simulation future chip generations) in Germany. The first call was open to all and optimisation techniques, and since • Finance (measurement and hedging of fields of research and drew more than innovation cycles in technological develop- risks, interaction models for asset price eighty proposals. In the first round three ment get shorter and shorter, it is essential fluctuation) centres were granted, with the topics Ocean to have flexible mathematical models that • Visualisation (discrete differential geome- rims in Bremen, Functional nanostructures in allow to master complexity, to react quickly, try, image processing). Karlsruhe, and Experimental biomedicine in and to explore new smart options. Such The Centre is not only a mathematical Würzburg. models can be obtained only via abstraction. research institution, but also aims at coop- The second call in early 2001 was more This line of thought provides our global eration with other sciences, engineering specific and was devoted to the topic of vision: innovation needs flexibility, flexibility and economics, and in particular with part- Modelling and simulation in science, engineering needs abstraction, abstraction is mathematics. ners in commerce and industry. and social science. A joint mathematics pro- But mathematics is not only the language of Furthermore, the Centre will also put a posal was written by mathematicians from science, it provides theoretical insight, effi- strong emphasis on changing the public the Berlin universities and research centres, cient algorithms and optimal solutions. awareness for mathematics and will con- and coordinated by Martin Grötschel (TU Thus, key technologies and mathematics tribute to mathematical education at all lev- and ZIB, Chair of the Centre), Volker interact in a joint innovation process. We els. Mehrmann (TU, Vice-Chair of the Centre), think that new products in key technologies The Centre has just begun to design and Peter Deuflhard (FU and ZIB), Hans should carry the stamp ‘Mathematics’ develop its web-presentation; for further Föllmer (HU) and Jürgen Sprekels (HU inside. information see: http://www.math.tu-berlin. and WIAS). There were 14 strong competi- The mission of the Centre is to strength- de/DFG-Forschungszentrum 24 EMS March 2003 SOCIETIES late some students are not returning to Israel, indicating a small brain drain. During the high-tech bubble period, academia lost some manpower, but late- TheThe IsraelIsrael ly it seems to have stabilised. The topics covered in Israel represent all disciplines of modern mathematics – MathematicalMathematical UnionUnion pure and applied, as well as mathematical education. At the last EMS council Mina Teicher meeting in Oslo, the IMU was upgraded to third category (meaning three representatives on the Council). The Israel Mathematical Union (IMU) recipient Avi Wigderson. Three IMU One of the festive events of the math- represents 300 members, most of whom members are recipients of the European ematical life in Israel (from the late are individual members of the EMS. Prize for Young Mathematicians: Leonid 1970s) is the annual Wolf Prize ceremo- Polterovich (at ECM2), Dennis ny, which takes place in the Knesset (the Gaitsgory (ECM3) and Semyon Alesker Israel Parliament). Friedrich (ECM3). About 50 other IMU members Hirzebruch, the first President of the have given plenary and invited address- EMS, received the prize in 1988, and es at various International Congresses of Lennart Carlson, the President of the Mathematics (ICMs) and European scientific committee of 4ECM, received Congresses of Mathematics (ECMs). the prize in 1992. Other mathemati- Every two years new officers of the cians from EMS member states who have IMU are chosen, rotating among the dif- received the prize include Izrail M. ferent research universities. The cur- Gelfand (Russia), Carl L. Siegel rent positions are held by Tel-Aviv (Germany), Jean Leray (France), Henri University faculty members Prof. Cartan (France), Andrei N. Kolmogorov Milman (President), Dan Haran (Russia), Mark Grigor’evich Krein (Secretary) and Gadi Fibich (Treasurer). (Russia), Paul Erdõs (Hungary), Lars The newly appointed positions, from the Hormander (Sweden), Ennio De Giorgi Technion, include Alan Pinkus who will (Italy), John G. Thompson (USA and become the next President, along with UK), Mikhael Gromov (France), Jacques the incoming Secretary Eli Elias and Tits (France), Jurgen K. Moser Budget Officer Eli Aljadeff. Since the (Switzerland), Laszló Lovász (USA and IMU became a member of the EMS, the Hungary), Jean-Pierre Serre (France), following presidents have held office: Vladimir I. Arnold (Russia and France). Yosef Zaks of Haifa University (geome- The central IMU activity is the annual try), Larry Zalcman of Bar-Ilan 2-day meeting, covering many areas University (complex analysis), Steve with invited addresses on ‘hot’ topics, Gelbart of the Weizmann Institute (auto- frequently given by distinguished math- Mina Teicher morphic forms) and Miriam Cohen of ematicians from abroad; the Erodes Ben-Gurion University (algebra). Prize for Young Mathematicians is The body of members includes faculty Despite the small size of the country, awarded during this event. In addition members from the seven research uni- mathematical activity in Israel is very to the annual meetings, the IMU also versities (Bar-Ilan University, Ben- intense. This intensity is evidenced by holds regional specialised workshops. Gurion University, Haifa University, our specialised research institutes (locat- The most recent annual meeting took Hebrew University, Tel-Aviv University, ed in different departments), several place at the picturesque and beautiful the Technion, and the Weizmann hundred graduate students, and five desert location of Mitspe Ramon, not far Institute graduate school), from other mathematical journals published in from the observatory. institutions for higher education in Israel: Israel Journal of Mathematics Israel such as the Open University and (Hebrew University), GAFA (Tel-Aviv Mina Teicher [[email protected]] is undergraduate colleges, many of which University), Journal d’Analyse Professor of Mathematics at Bar-Ilan also conduct research. Teachers’ col- Mathématique (Bar-Ilan University), University, Ramat-Gan 52900, Israel. leges (involved in the training of mathe- Integral Equations and Operator Theory matics teachers for elementary schools) (Ariel College), and Israel Mathematical are also included among those repre- Conference Proceedings (Bar-Ilan sented in the IMU. Graduate students University). In addition, Israel is host to from research universities are also mem- international postdoctoral fellowship bers: many of them are mathematicians programmes, many distinguished lec- (having received their Ph.D. degrees) ture series, visitor programmes, and who are currently employed in Israel by international workshops and confer- the high-tech, banking and aviation ences. industries. The IMU has a high concen- Israeli mathematicians are involved in tration of members from the former many European Networks. On the Soviet Union. It became a member of international scene, several internation- the EMS in 1991. al collaborations exist at governmental Some IMU members are internation- level, with research support and ally recognised mathematicians of the exchange programmes with countries highest level. Included among these are such as Germany, Italy, France, the Wolf Prizewinners Ilya Piatetski-Shapiro USA, India and China. and Saharon Shelah, Turing For the most part, new Ph.D. recipi- F. Hirzebruch receives the 1988 Wolf Prize Prizewinners Michael Rabin and Amir ents may opt to take a 1- or 2-year post- in Mathematics from the President of the Pnueli, Harvey Prizewinners Israel doctoral position in Europe or the USA. State of Israel, the late Chaim Herzog, at the Aumann, Michael Rabin and Hillel Unfortunately, however, there are not Knesset (parliament) in Jerusalem, on 12 Furstenbe, and the Nevanlinna Prize enough positions in academia and as of May 1988. EMS March 2003 25 SOCIETIES SocietySociety ofof Mathematicians,Mathematicians, PhysicistsPhysicists andand AstrAstronomersonomers ofof SloveniaSlovenia Peter Legiša

History of the Society decades: the last revisions were printed just potential theory and analytic functions. The Society was founded in 1949 with before WWII. Moènik, as an administra- When the University of Ljubljana opened three aims: to publish, improve teaching, tor, significantly increased the teaching of just after WWI, he became its first rector. and unify terminology. Slovenian in our schools, then part of the Plemelj won two major prizes for his work, At that time, teachers in our elementary Austrian Empire, which otherwise a German and an Austrian one. These and secondary schools were often qualified favoured the German language. enabled him to build a villa in his home to teach both mathematics and physics. place, the famous lake resort of Bled. Now secondary school teachers, as a rule, Plemelj donated the villa to our Society. specialise. There have accordingly been Ivo Lah (1896-1979) was a demographer recent attempts to break the Society into and statistician and an expert in actuarial two or three parts. But in Slovenia, with mathematics. The Lah numbers in combi- two million inhabitants, we find it more natorics are named after him. rational to work together, at least for now. Plemelj’s student Ivan Vidav (born in This article will, of course, focus on the 1918) made a quantum leap in Slovenian mathematical achievements of the Society. mathematics. He had sixteen PhD stu- Slovenians have the mixed blessing to be dents and managed to direct them into the westernmost South Slavic nation, several fields of mathematics, while doing wedged between Italy in the west and good research himself. (He was still pub- Austria in the north. lishing original work four years ago.) Plemelj and Vidav set very high standards for lecturing at university level and I am proud to say that the tradition goes on. The Institute of Mathematics, Physics and Mechanics (IMFM, www.ijp.si) in Ljubljana is an umbrella organisation for mathematical research. Its 2001 yearbook listed more than a hundred publications in (mostly high-quality) international research journals.

Periodicals Josip Plemelj Since 1951, the Society has published its own magazine, Obzornik za matematiko, fiziko in mehaniko. Six editions every year present survey articles in Slovenian, as well as articles on education and reports on the activities of the Society, sometimes also original scientific work. Most of the 1100 members of our Society are teachers who often complain about the high level of the Two stamps featuring Jurij Vega survey articles. In 1973 the Society started to publish Presek (Intersection), a periodical for young Several distinguished mathematicians of mathematicians, physicists and the past came from Slovenia. Jurij (Georg) astronomers. It was an instant success, Vega (1754-1802) produced improved log- with a circulation of 20,000 every two arithmic tables that were immensely popu- months and special issues as well. lar, with the total number of editions going Although we have managed to keep the into hundreds. His four-volume course in price low and the quality high, the circula- mathematics and mechanics was translated tion has now plummeted to 2600. into several languages and was a source of University lecturers and teaching assistants knowledge, for example, for young János write most of the contents. It is rather dif- Bolyai. Vega was essentially a self-taught ficult to find interesting material for read- mathematician, who through a military ers in elementary schools, and many arti- career managed to advance from a poor cles turn out to be for the age group 17-18. Slovenian peasant family to aristocracy. Next year we plan to celebrate the 250th Books and teaching material anniversary of his birth with several events. Publishing used to be an integral part of Franc Moènik (1814-92) wrote a best- Bled with Plemelj’s villa in the foreground the Society. Now there is a separate pub- selling series of high-quality mathematical lishing house (DMFA-Zaloništvo, textbooks (in German) for elementary and Josip Plemelj (1873-1967) was a first- www.fmf.uni-lj.si/~zaloznistvo/), supervised secondary schools. These texts were trans- class mathematician. He worked in inte- by our Society and the School of lated into many languages and used for gral and differential equations, as well as in Mathematics and Physics (FMF) of the 26 EMS March 2003 SOCIETIES University of Ljubljana. The popular those in the 6th, 7th, and 8th class enter from the government (usually with delays), SIGMA series started with Ivan Vidav’s regional qualifications. The crème de la and most of it is spent on competitions, the Solved and Open Problems in Mathematics, crème – ten per cent of the best – compete lion’s share on the cost of sending a team which is still in print. Most of the 72 books at national level. About half of them win to the Mathematical Olympiad. (about 45 of them still available) are suit- prizes. able for bright students at secondary At high-school level, about 5000 stu- Events schools. Most of these books are mathe- dents participate in a similar three-level Every year the Society holds a meeting, matical and original work. Recently, we competition, but the prizes are more struc- lasting two or three days. We organise it in have had more translations. tured and limited. different regions of the country, so local Even more university textbooks and manuscripts have been printed. The clas- sic one is Vidav’s Higher Mathematics, and the author donated the royalties to the publishing house. Two monographs are in English (J. Vrabec, Bordism, Homology, and Stiefel Whitney numbers and P. Pavešiæ, The Hopf Invariant One Problem). Handbooks and exercise collections for elementary and secondary schools earn a profit. D. Felda’s book 40 National Math Olympiads in Slovenia gives in English the texts of problems in the national competitions, a topic to which we will return.

Education The Society helps to organise seminars and workshops for teachers of mathematics. It presents summer schools for the most gifted pupils, often in Plemelj’s villa at Bled. The Society has actively participated in curriculum changes in secondary schools, ensuring that no hasty decisions were made. For many years the Society provided special courses and lectures for students of The two journals of the Society members can attend it without cost. The secondary schools, given by university lec- meeting includes survey lectures, mostly turers and students. In my earlier years I on elementary mathematics and mathe- attended an excellent course on probabili- matical education, but also on applied ty. The instructor (Prof. R. Jamnik) first mathematics. I listened to several very made clear to us that there would be an interesting talks, given by mathematicians, exam at the end. He adapted to our lower physicists and astronomers to a general level and the course was a remarkable suc- audience. This is definitely one of the cess – it convinced even those who other- advantages of working together. wise did not like mathematics but unex- Each year we reward distinguished pectedly joined the course. The best par- teachers and schools that excel in mathe- ticipants earned books as prizes. matical education. The Society has helped But I also listened to a mathematician to erect monuments or memorial plaques who did not care about the reaction of the to several Slovenian mathematicians. It listeners and was too fast even for the also helps to maintain the memorial room brightest – a very frustrating experience for Vega in his birthplace Zagorica, and an for me and certainly not a good way to exposition on Plemelj in his villa. attract young people to mathematics. Links Competitions For many years the Society has maintained The most popular activities of the Society excellent connections with mathematicians are competitions for pupils and students of in neighbouring Zagreb (Croatia). We secondary schools. These have been going have occasional contacts with colleagues right from the beginning, and have from Skopje (Macedonia) and now again expanded enormously. with colleagues from the (shrunken) In the past, there were debates on the Yugoslavia. (Slovenia was part of impact of competitions. It turned out that Yugoslavia from 1918 to 1990.) some of the best competitors never got a Recently, we started separate competi- In my view Italy and Austria have so far university degree. Quick successes, arising tions for students of technical schools been mainly interested in attracting talent- from their talents, did not prepare them (aged 15-18, about 3000 participants) and ed students from our territory, but recent- for the strenuous work at higher level. for students of vocational schools (aged 15- ly, there has been research cooperation This now seems to be less of a problem, but 17, 1600 competitors). with a centre in Austria (Leoben). Contacts the best competitors do not always choose The 14th competition in Recreational directly across the border are weak: this is mathematics as their field of study. Mathematics attracted several hundred probably linked to the fact that there are Every year, about 60,000 pupils (50 per competitors. It was supplemented by the Slovenian populations in neighbouring cent of those who attend elementary third competition in Space Visualisation. areas of those two countries, a fact that schools) participate in school competitions, In these competitions we collect a fee of some people find hard to admit. If which are now integrated in the European about 1 euro per participant. This enables Slovenia joins the EU next year, we hope Kangaroo. [For further information about us to maintain the on-line registration that the situation will improve. the European Kangaroo, see Paul Jaint’a scheme, print the diplomas, and so on. The homepage of our Society is article in issue 45] About ten per cent of Most of the budget of our Society comes www.dmfa.si. EMS March 2003 27 PROBLEM CORNER PPrroblemoblem CornerCorner ContestsContests frfromom Bulgaria,Bulgaria, PPartart IIII Paul Jainta

The philosophy behind an emphasis on classes that have been established in vari- problem solving is the educational truism ous Bulgarian cities and towns and are that telling is not teaching and listening is frequented by students who are highly not learning. I am a strong advocate of motivated to problem-solving and eager the precept that mathematics is not a mat- to do maths. ter for immediate consumption: one can At least one of the problems in each only derive benefit from this subject if one round is closely connected to the item is doing it! appearing in the journal at the same time. So, it is increasingly important for While working carefully through the arti- teachers and lecturers to offer new oppor- cles the contestants are provided with tunities for youngsters to stimulate their fresh knowledge and some tools necessary interest by coaching them in doing math- for solving the corresponding problem or ematics. A vast supply of ideas, methods a similar one. In addition to the nine and techniques lie dormant in problems questions presented to the different age of Olympiad type. By attacking competi- groups, junior contestants especially are tion problems, students can develop their confronted with a problem that ‘steps out talents for mathematical thinking. of line’. This ‘Tenth Problem’ requires Mathematical talent and problem-solving ingenious ideas and asks participants to ability are needed in today’s world in go exploring. It usually allows challeng- engineering, physics, chemistry and many ing and deep generalisations that can be other sciences. In fact, with the applica- found after some hard work and concen- tions of mathematics in business, commu- trated examination. nications, and the social sciences, there is Apart from individuals, groups of stu- Later, a considerable percentage of hardly a field that does not require a good dents and mathematical circles are those who found their way into one of background in mathematics. encouraged to submit solutions. The these Summer Camps become members This has been known in Bulgaria for teachers in charge of a circle or working- of the Bulgarian team participating in more than 100 years, where they found it group also play another significant part – international Olympiads – and after grad- increasingly important to invest time and for example, they give their young pro- uating from prestigious universities like resources in developing the mathematical tégés a hand when struggling with one of Harvard, Princeton, MIT and others, they skills of a small but particularly talented those fiddly Tenth Problems and provide may start careers as a highly qualified section of its young persons. We can advice in coping with the difficult task mathematicians. The timely motivation of learn a lot about the imaginativeness of writing down solutions to problems: this junior students has doubtless activated the Bulgarian pioneers for encouraging assistance is useful for them, too. So, them towards individual research. particularly gifted pupils and students. In solving a Tenth Problem is an activity that As a kind of levelling rod for the the second part of his series, Prof. Sava involves the whole team; teachers and achievements of students at this early age, Grozdev, from the Institute of Mechanics, pupils together learn new mathematical it is useful to know how they have per- Bulgarian Academy of Sciences, Sofia, facts and are thus stimulated by fruitful formed in the Junior Balkan Mathematics describes the essential role that mathe- ideas and tools. Sometimes, highly com- Olympiad. In all five contests held up to matics journals and summer camps play in plicated tenth problems forge a close now, Bulgaria has been represented by 26 this continual national task of fishing out bond between coaches and their flock – students, and all came back with a medal. those splendid young persons, in order to but even a teacher may have to give up a The other regular guests in the Balkan further their mathematical abilities. particularly stubborn problem. Olympiad are young people from Albania, The ‘Mathematics Plus’ junior contest is Bosnia, Cyprus, Greece, Macedonia, Accompanying Measures (Sava Grozdev) carried out by written communication Moldova, Romania, Turkey and Serbia. The home journal Mathematics Plus between participants and corresponding Since 2001 each participating country has plays a lead in recruiting apt students. Its markers. A special jury grades the papers, put forward a six-person team. main goal is to identify highly talented giving priority to the tenth problem. Already while a senior at school, many boys and girls, and for this purpose the Those students who have worked well on of these students publish interesting trea- journal organises each year a junior con- all problems are invited, with their teach- tises on specialist topics or create original test for pupils from grades 4-7. The trial ers, to a Summer Camp organised every problems. It is not unusual to encounter is held in three rounds, each comprising July. The Camp is free of charge for those an author of several articles and challeng- three questions. Each stage is preceded selected. Some outstanding Bulgarian ing questions in Mathematics Plus who is by two small articles in this journal, mathematicians are regularly asked to lec- still attending school. The Junior contest, addressed first and foremost to those stu- ture on a special topic in this relaxed set- and its counterpart for Senior students, dents who participate in the contest. The ting. These courses are usually enriched appear in the journal as parallel contests. articles feature special topics that are usu- with general challenges and classical Each issue contains six problems for each ally not on the curriculum; for example, mathematical problems, and include curi- age group: these are well known for their squares and square numbers, induction in ous facts connected with the history of increasing level of difficulty, and ‘breathe geometry, the finite element principle, mathematics and the life of famous math- the spirit’ of an Olympiad. Usually, many Euler’s formula, some invariants, and ematicians. The Summer Camp always of the new problems come from the stu- mathematical games. These articles are ends in a festival, when many guests, students. Their brainpower is impressive, as meant to be studied by the young reading dents and teachers, can establish contacts you can see from the questions in the last public, independently or with the help of among themselves, or become friends. Problem Corner (issue 45). parents and teachers, at home or outside Most importantly, during their stay the lessons. Usually, these extra lessons are young mathematicians will grow into the The next six problems have been taken used in mathematics circles or special world of mathematical science and society. from the professionals. 28 EMS March 2003 PROBLEM CORNER

EMS March 2003 29 PROBLEM CORNER

30 EMS March 2003 BOOK REVIEW astronomy. Several made a living in quite different professions, for example as engineers or lawyers or administrators. Like Bell I have tried to bring out the human MathematicalMathematical side, avoiding too much technical detail which can generally be found elsewhere. The general question of whether an BiographyBiography aptitude for the kind of abstract thought required for mathematics is in any sense inherited, and if so how, is an intriguing IOAN JAMES one. There is some evidence in favour; Francis Galton, in Hereditary Genius [5] discusses the case of the Bernoullis, and there It is now over sixty years since Eric Temple the human side, such as the life of are other less striking examples. A possi- Bell set out to write about mathematicians Hamilton by Hankins [6], of Galois by ble reason why a genetic factor could be in a way which would grip the imagination Laura Toti Rigatelli [19], of Courant [17] involved may be found in the medical lit- of the educated public. His immensely and Hilbert [18] by Constance Reid, of erature. Asperger syndrome [8] is a mild readable book Men of Mathematics [4] was Hadamard [14] by Vladimir Maz’ya and form of autism. Asperger people are first published in 1937 and is still in print. Tatyana Shaposhnikova, of Pólya [1] by G. attracted to mathematics; autistic tenden- He was a man of strong opinions, not sim- L. Alexanderson, and of Zariski [16] by C. cies run in families. It would be interest- ply reflecting the prejudices of a bygone Parikh. Some of these books are more ing to try and identify which of the great age, for example: ‘There is no more scholarly than others, but the best have mathematicians of the past were Asperger vicious academic hatred than that of one been carefully researched and.one should people, like Newton, Einstein, Raman- Jew for another when they disagree on not be put off by catchy titles. The biogra- ujan, and possibly Dirac. purely scientific matters. When two intel- phies of Sonya Kovalevskaya by Don The only woman mathematician who lectual Jews fall out they disagree all over, Kennedy [12] and Ann Koblitz [13], that of appears in Men of Mathematics is Sonya throw reserve to the dogs, and do every- Ramanujan [11] by Robert Kanigel, that of Kovalevskaya, who is included in the pro- thing in their power to cut one another’s Stefan Banach [10] by Roman Kaluza, and file of Weierstrass. The prevailing preju- throats or to stab one another in the back.’ those of Abel [21] and Lie [22] by Arild dice against women in science has taken a Moreover, he was not above distorting the Stubhaug are also of this type. The long time to break down, and unfortu- facts in the interests of making a good authors have some mathematical back- nately the process is still not complete. story. Although his book is looked down ground, although not all would claim to be Until the end of the nineteenth century upon by the historians of mathematics, it professional mathematicians: Kaluza, for and even beyond there were all kinds of continues to influence the impression that example, is a journalist and Stubhaug a obstacles which made it difficult for a ordinary mathematicians have of the his- writer. The life [15] of the Nobel Laureate woman to become a scientist. Exceptional tory of their subject. John Nash by Sylvia Nasar is another such determination was required; men were In his introduction Bell begins by example. The author is an economist, now believed to have a monopoly of abstract emphasising that his book is not intended, professor of journalism at Columbia thought. As a result, of my sixty subjects, in any sense, to be another history of University. Bell, of course, was a pioneer only three are women, but there can be no mathematics, and goes on: ‘The lives of of science fiction as well as a professional doubt that many other women had no mathematicians presented here are mathematician. opportunity to develop their mathematical addressed to the general reader and to gifts. others who might wish to see what sort of Sometime ago I began to think about writ- Galton also mentions the common belief human beings the men were who created ing a Men and Women of Mathematics which that the mothers of great men are more modern mathematics.’ He continues: might, I hoped, provide an alternative to influential on their development than the ‘Two criteria have been applied in select- Bell’s book. This work has now appeared, fathers. Gauss, Poincaré and Hilbert ing names for inclusion: the importance under the title Remarkable Mathematicians believed that their mathematical gifts for modern mathematics of a man’s work; [7]. For each of sixty subjects it provides a came from their mother’s side of the fam- the human appeal of the man’s life and brief life which takes account of recent ily rather than the father’s side. character. ... When these criteria clash ... scholarship. They were chosen from the second has been given precedence, as mathematicians born in the eighteenth, we are primarily interested here in mathe- nineteenth and early twentieth centuries. maticians as human beings.’ Among them, twelve different European Mathematical biography is a growing countries are represented, including industry these days. At least fifty of the Russia. France and Germany are very great mathematicians of the past have heavily represented. While Bell does not been the subject of a full-scale treatment, venture outside Europe, I have included usually either a Life and Work or a Life and mathematicians from India and Japan, as Times, and there are many more who merit well as several from the United States. I the attention of a biographer. Most of start with Euler and end with von these books have been written by histori- Neumann, whereas Bell begins in antiqui- ans of mathematics, who tend to write pri- ty and finishes with Cantor. marily for other historians. These seem to After digesting the relevant literature I me too specialised to appeal to the ordi- chose the subjects of the profiles with an nary mathematician, but others have been eye to diversity and contrast. Most of written for a rather wider readership. For them made important discoveries, but I example, we have the biography of included some who contributed in other Cauchy [3] by Bruno Belhoste, which com- ways, for example Mittag-Leffler, Courant bines a good account of his life with an and Veblen. The majority spent at least evaluation of his contribution to the devel- some time teaching, with various degrees opment of mathematics; such books are of of success; several were the authors of suc- interest to anyone with some knowledge cessful textbooks. In the eighteenth cen- of mathematics and its cultural history. tury, when there were hardly any universi- There are also a number of biographies ty posts for mathematicians, some occu- which avoid technicalities and emphasise pied chairs in other subjects, such as EMS March 2003 31 BOOK REVIEW Regrettably, far too little is known about important I am thinking of combining the of Sonya Kovalevskaya, Ohio Univ. Press, the mothers of the great mathematicians, most interesting profiles from the two Athens OH, 1983. although some of them were clearly books into a third one in which mathe- 13. Ann Koblitz, A Convergence of Lives, remarkable women. The mother of Galois maticians and physicists are treated Birkhäuser Verlag, Basel, 1983. was described as ‘intelligent, lively, head- together. 14. Vladimir Maz’ya and Tatyana strong, generous and eccentric’, the moth- Shaposhnikova, Jacques Hadamard, a er of Ramanujan as ‘shrewd, cultured and References Universal Mathematician, History of deeply religious’, and the mother of. 1. G.L. Alexanderson, The Random Walks of Mathematics 14, American and London Kolmogorov as ‘liberal and independent’. George Pólya, Math. Assoc. of America, Math. Societies, Providence RI, 1998. Others are simply stated to have been well- Washington DC, 1999. 15. Sylvia Nasar, A Beautiful Mind, Faber and to-do, or from a wealthy family, or to have 2. A.S. Alexandrov, Pages from an autobiog- Faber, London, 1998. been well educated. Often we just know raphy, Russian Math. Surveys I 34 (1979), 16. C. Parikh, The Unreal Life of Oscar Zariski, their names, sometimes not even that. 267-304; II 35 (1980), 315-358. Academic Press, San Diego CA, 1991. Mathematical autobiography seems to 3. Bruno Belhoste, Augustin-Louis Cauchy, 17. Constance Reid, Courant, Springer Verlag, be quite a recent phenomenon, although Springer Verlag, Berlin, 1991 (originally Berlin, 1996 (originally published under various novels of Sonya Kovalevskaya are published in French). another title). based to a large extent on her own life. 4. E.T. Bell, Men of Mathematics, Victor 18. Constance Reid, Hilbert, Springer Verlag, Another Russian who gave a vivid account Gollancz, London, 1937. Berlin, 1970. [2] of his life story is P. S. Alexandroff. 5. Francis Galton, Hereditary Genius, 19. Laura Toti Rigatelli, Evariste Galois (1811- Other important examples are those of Macmillan, London, 1869. 1832), Birkhäuser Verlag, Basel, 1996. Laurent Schwartz [20] and André Weil 6. T.L. Hankins, Sir William Rowan Hamilton, 20. Laurent Schwartz, Un Mathématicien aux [23]. The idiosyncratic autobiography by Johns Hopkins Univ. Press, Baltimore, Prises avec le Siècle, Editions Odile Jacob, Norbert Wiener [24], [25] should also be 1980. 1997. mentioned. As Hans Freudenthal com- 7. Ioan James, Remarkable Mathematicians, 21. Arild Stubhaug, Niels Henrik Abel and his mented: ‘Wiener never had the slightest Cambridge Univ. Press, Cambridge, and times, Springer Verlag, Berlin, 2000 (origi- idea of how he appeared in the eyes of Math. Assoc. of America, Washington DC, nally published in Norwegian). others.’ An autobiography is no substitute 2002. 22. Arild Stubhaug, The Mathematician Sophus for a biography. 8. Ioan James, Singular Scientists, J. Roy. Soc. Lie, Springer Verlag, Berlin, 2002 (origi- Medicine, 2003. nally published in Norwegian). A companion volume to Remarkable 9. Ioan James, Remarkable Physicists, 23. A. Weil, Souvenirs d’Apprentissage, Mathematicians, entitled Remarkable Cambridge Univ. Press, Cambridge, 2003. Birkhäuser Verlag, Basel, 1991. Physicists [9], will follow shortly. Fourier 10. R. Kaluza, Through a reporter’s eyes: The. life 24. Norbert Wiener, Ex-Prodigy – My Childhood and Laplace appear in both books; of of Stefan Banach, Birkhäuser Verlag, and Youth, Simon and Schuster, New York, course, many physicists contributed great- Basel,1966 (originally published in Polish). 1953. ly to mathematics, and mathematicians to 11. R. Kanigel, The Man who knew Infinity, 25. Norbert Wiener, I am a Mathematician – the physics. Because the interaction between Charles Scribner’s Sons, New York, 1991. Later Life of a Prodigy, Doubleday, New the two branches of science has been so 12. Don. H. Kennedy, Little Sparrow: a portrait York, 1956.

HELSINKI UNIVERSITY OF TECHNOLOGY Institute of Mathematics Two Professors of Mathematics Helsinki University of Technology invites applications for two positions as Professor in Mathematics at the Insitute of Mathematics, Faculty of Engineering Physics and Mathematics. Helsinki University of Technology is located in Espoo, about 8 km from downtown Helsinki, the capital of Finland. When appointing a professor of the state university system of Finland, special emphasis is given to both research and teaching competence and scientific leadership skills. Proficiency in Finnish, Swedish or English is required. Since the positions are full-time jobs, residence in the Helsinki area is necessary. The applicants are required to a have demonstrated scientific competence in the following fields: Position 1: Analysis (interpreted widely) or geometry Position 2: Stochastic analysis and some other central subfield of mathematical analysis For more details on the particulars, see the announcements (in English) on the web site http://www.hut.fi/Yksikot/Hallitus/Virat/index.html The applications should be addressed to the Council of Helsinki University of Technology and sent to: Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland. The deadline for the applications will be around 10 April 2003; see the above website for precise information. Informal inquiries may be made to Position 1: Prof. Juhani Pitkäranta: e-mail, [email protected] Position 2: Prof. Stig-Olof Londen: e-mail, [email protected]

32 EMS March 2003 NEWS (Australia), Z. N. Zahreddine (UAE), V. I. Zhukovskii (Russia). NONLINEARNONLINEAR DYNAMICSDYNAMICS Submission of manuscripts: Authors are invited to submit articles for publication. Instruction for contributors are on the ANDAND SYSTEMSSYSTEMS THEORTHEORYY website: http://www.sciencearea.com.ua A new International Journal of Research and Surveys Subscription Information: Nonlinear Dynamics and Systems Theory (ISSN 1562- 8353) 2003, Vol. 3 (approx. 300pp.). This new mathematical journal is pub- Sivasundaram (USA), V. W. Spinadel Annual subscription rate: Institutional: lished under the auspices of the S. P. (Argentina), Sree Hari Rao (India), N. M. US$278 or 300 euros; Individual: US$99 Timoshenko Institute of Mechanics of the Stavrakakis (Greece), R. Toscano (Italy), or 100 euros. Orders should be sent to National Academy of Sciences (NAS) of F. E. Udwadia (USA), T. Vincent (USA), V. the Editor-in-Chief or the Managing Ukraine and the Laboratory for Industrial V. Vlasov (Russia), Weiyong Yan Editor. and Applied Mathematics (LIAM) at York University (Toronto, Canada). Its aim is to publish original research articles of CIME Courses 2003 excellent quality in the broad area of non- linear dynamics and systems theory 6-13 July: Stochastic Methods in Finance, Bressanone, Bolzano including the following topics: (Joint course with the European Mathematical Society) Analysis of uncertain systems; bifurca- Course directors: tions and instability in dynamical behav- Profs. Marco Frittelli (Univ. di Firenze) and Wolfgang Runggaldier (Univ. di iours; celestial mechanics, variable mass, Padova). rockets; control of chaotic systems; con- Lectures: trollability, observability, and structural Kerry Back (St. Louis): Partial and asymmetric information. properties; deterministic and random Tomasz Bielecki (Northeastern Illinois): Stochastic methods in credit risk modeling, valu- vibrations; differential games; dynamical ation and hedging systems on manifolds; dynamics of sys- Christian Hipp (Karlsruhe): Finance and insurance tems of particles; Hamilton and Lagrange Shige Peng (China): Nonlinear expectations and risk measures. equations; hysteresis; identification and Walter Schachermayer (Vienna): Utility maximization in incomplete markets adaptive control of stochastic systems; modelling of real phenomena by ODE, 14-21 July: Hyperbolic Systems of Balance Laws, Cetraro, Cosenza FDE and PDE; non-linear boundary prob- Course director: lems; non-linear control systems, guided Prof. Pierangelo Marcati (Univ. de L’Aquila) systems; non-linear dynamics in biological Lectures: systems; non-linear fluid dynamics; non- A. Bressan (Trieste): Viscosity solutions of systems of conservation laws linear oscillations and waves; non-linear C.M. Dafermos (Providence): Conservation laws on continuum mechanics stability in continuum mechanics; non- D. Serre (Lyon): Shock profiles in scalar conservation laws smooth dynamical systems with impact or M. Williams (North Carolina): Stability of multidimensional viscous shocks discontinuities; numerical methods and K. Zumbrun (Indiana): Planar stability criteria for multidimensional viscous shock Waves simulation; optimal control and applications; qualitative analysis of systems with 1-6 September: Mathematical Foundation of turbulent Viscous Flows, Martina after effect; robustness, sensitivity and dis- Franca, Taranto turbance rejection; soft computing: artifi- Course directors: cial intelligence, neural networks, fuzzy Profs. M. Cannone (Univ. de Marne-la-Vallée) and T. Miyakawa (Kobe Univ.) logic, genetic algorithms, etc.; stability of Lectures: discrete systems; stability of impulsive sys- P. Constantin (Chicago): TheNavier-Stokes equations of viscous fluids and questions of tur- tems; stability of large-scale power sys- bulence theory tems; stability of linear and non-linear G. Gallavotti (Rome): Incompressible fluids and strange attractors control systems; stochastic approxima- A. Kazikhov (Novosibirsk): The theory of strong approximation of weak limits via the tions and optimisation; symmetries and method of averaging with applications to Navier-Stokes equations conservation laws. Y. Meyer (Paris): Size estimates on solutions of nonlinear evolution equations and conse- The Editor-in-Chief is A. A. Martynyuk quences [[email protected]], S. P. S. Ukai (Yokohama): The asymptotic analysis theory of fluid equations. Timoshenko Institute of Mechanics, NAS of Ukraine, Nesterov Str., 3, MSR 680, 2-10 September: Symplectic 4-Manifolds and Algebraic Surfaces, Cetraro, Cosenza Kiev-57, Ukraine. The Managing Editor Course directors: is I. P. Stavroulakis [[email protected]], Profs. Fabrizio Catanese (Bayreuth) and Gang Tian (M.I.T.) Department of Mathematics, University of Lectures: Ioannina, 451 10 Ioannina, Greece. The B. Siebert and Gang Tian (Bochum and M.I.T.): Pseudo holomorphic curves and sym- Editorial Board is N. V. Azbelev (Russia), plectic isotopy Chen Han-Fu (China), G. Dauphin- M. Manetti (Rome): Smoothing of singularities and deformation and differentiable type of Tanguy (France), Duan Li (Hong Kong), surfaces J. H. Dzhalalow (USA), M. Fabrizio (Italy), D. Auroux and I. Smith (M.I.T. and Cambridge): Lefschetz pencils, branched covers and H. I. Freedman (Canada), G. Georgiou symplectic invariants (Cyprus), L. Hatvani (Hungary), N. A. P. Seidel (London): Lagrangian spheres and Dehn twists in dimension 4 Izobov (Belarussia), D. Ya. Khusainov F. Catanese (Bayreuth ): Classification and deformation types of complex and real mani- (Ukraine), T. Kuepper (Germany), V. B. folds Larin (Ukraine), G. Leitman (USA), S. Leela (USA), O. S. Limarchenko CIME can offer some fellowships. An on-line application form appears on the page (Ukraine), V. G. Miladzhanov for each CIME course: website (Uzbekiston), J. S. Muldowney (Canada), C.I.M.E. courses are made possible thanks to the generous support received from: E. Noldus (Belgium), V. N. Pilipchuk - Istituto Nazionale di Alta Matematica (USA), M. D. Shaw (USA), P. D. Siafarikas - Ministero Affari Esteri, Dir. Gen. Per la Promozione e Cooperazione Culturale (Greece), D. D. Siljak (USA), S. - Ministero dell’ Istruzione, dell’Università e della Ricerca Scientifica e Tecnologica EMS March 2003 33 CONFERENCES and A. Zuk Local organisers: T. Ceccherini-Silberstein, A. Machi, F. Scarabotti and F. Tolli Proceedings: The conference proceedings FForthcomingorthcoming conferconferencesences will be published in a special issue of the International Journal of Algebra and compiled by Vasile Berinde Computation. Deadline for submission is 1 October 2003. Location: Hotel Serapo, Spiaggia di Serapo, 04024 Gaeta Please e-mail announcements of European confer- Information: e-mail: [email protected] Grants: support for a limited number of ences, workshops and mathematical meetings of website: : http://main.amu.edu.pl/~ta2003 participants interest to EMS members, to one of the following [For details, see EMS Newsletter 44] Deadlines: deadline for abstract submission addresses: [email protected] or vasile_berinde was 1 March @yahoo.com. Announcements should be written 12-17: 23rd International Seminar on Information: in a style similar to those here, and sent as Stability Problems for Stochastic Models, [email protected]; [email protected] Microsoft Word files or as text files (but not as TeX Pamplona, Navarra, Spain website: http://www-old.math.kth.se/math/ input files). Space permitting, each announce- Information: e-mail: [email protected] users/gaeta/ ment will appear in detail in the next issue of the website: http://www.unavarra.es/stochastic Newsletter to go to press, and thereafter will be [For details, see EMS Newsletter 46] 1-7: Spring School in Analysis: Function briefly noted in each new issue until the meeting Spaces and Applications, Paseky nad takes place, with a reference to the issue in which 25-31: Workshop on Singularity Theory, Jizerou, Czech Republic the detailed announcement appeared. Edinburgh, UK Information: Organisers: International Centre for e-mail: [email protected] website: http://www.karlin.mff.cuni.cz/ April 2003 Mathematical Sciences Information: e-mail: [email protected] katedry/kma/ss/jun03/ss.htm website : http://www.ma.hw.ac.uk/icms/ [For details, see EMS Newsletter 46] 27-May 3: Spring School on Analysis: meetings/2003/singth/index.html Variational Analysis, Paseky nad Jizerou, 2-6: Workshop on Derived Categories, Czech Republic 26-30: Fifth International Conference on Edinburgh, UK Information: Sampling Theory and Applications Organisers: International Centre for e-mail: [email protected] (SampTA03), Strobl, Austria Mathematical Sciences website: http://www.karlin.mff.cuni.cz/ Information: web site: www.univie.ac.at/ Information: e-mail [email protected] katedry/kma/ss/apr03/ss.htm NuHAG/SampTA03/ website: http://www.ma.hw.ac.uk/icms/ [For details, see EMS Newsletter 46] [For details, see EMS Newsletter 45] meetings/2003/dercat/index.html

13-22: Poisson Geometry, Deformation 28-June 20: Bimestre Intensivo: June 2003 Microlocal Analysis and Related Subjects, Quantisation and Group Representations Torino, Italy (PQR2003), Brussels, Belgium Topics: short courses and specialist talks on 1-6: International Conference on Group Information: e-mail: [email protected]; the following topics are scheduled: Theory, Gaeta, Italy website: http://homepages.ulb.ac.be/~ Perturbative methods in non-linear analysis; Dedicated to Slava Grigorchuk on the occa- pqr2003/ Pseudo-differential methods for evolution sion of his 50th birthday [For details, see EMS Newsletter 46] equations; Quantization and harmonic Theme: combinatorial, geometric, and numerical analysis; Elliptic and hypoelliptic dynamical aspects of infinite groups 18-19: Two-day Colloquium in honour of equations. Aim: presentation of recent developments Enrico Magenes, Pavia, Italy Scientific Committee: P. Boggiatto, I. concerning combinatorial, geometric and Topic: On the occasion of the 80th birthday Fujita, T. Gramchev, G. Monegato, A. dynamical aspects of group theory of Professor Enrico Magenes, his former stu- Parmeggiani, J. Pejsachowicz, L. Rodino, A. Scope: to bring together leading experts dents at the University of Pavia are organis- Tabacco. and younger researchers to discuss recent ing a two-day colloquium in his honour in Sponsor: INdAM (Istituto Nazionale di Alta developments Pavia. The programme consists of seven lec- Matematica), Italy. Topics: geometric group theory; ergodic tures by the following speakers: C. Baiocchi Location: Department of Mathematics, theory; groups acting on trees and bound- (Rome); J. M. Ball (Oxford); L. A. Caffarelli University of Torino; Department of aries; random walks; amenability; growth of (Texas); G. Geymonat (Montpellier); P.-L. Mathematics, Politecnico of Torino. groups, languages, and automata; groups Lions (Paris); C. Verdi (Milano); A. Visintin Information: e-mail: [email protected] and fractals; L2-cohomology; bounded coho- (Trento). website http://www.dm.unito.it/convegnisem mology; branch groups; groups generated The Colloquium at the University of Pavia inari/indam/bimestri.htm by finite automata; calculus of spectra; prob- or at one of the University Colleges (to be lems of Burnside type; combinatorics of announced later) will take place from 18 June at 3 pm to 19 June at 6 pm. May 2003 words. Main speakers: D. Anosov (Moscow); G. Deadline: Those interested in participating Baumslag (New York); M. Burger (Zürich); should register by 15 April. 2-3: X Encuentro de Topologia, Bilbao, H. Furstenberg (Jerusalem); E. Ghys (Lyon); Information: Spain R. Grigorchuk (Texas and Moscow); M. e-mail: [email protected] Information: e-mail: [email protected], Gromov (Paris); F. Grunewald (Düsseldorf); phone/fax: +39 0382 505620 / +39 0382 website: http://www.ehu.es/xet P. de la Harpe (Geneva); V. Jones 505602 [For details, see EMS Newsletter 46] (Berkeley); A. Lubotzky (Jerusalem); W. website: http://www.imati.cnr.it/~magen80/ Lück (Münster); G. Margulis (Yale); A. eng.html 11-16: International Conference on Ol’shanskii (Vanderbilt Moscow); G. Pisier mail address: Prof. Marco Luigi Bernardi, General Control Problems and (Texas and Paris); S. Sidki (Brasília); A. Dipartimento di Matematica ‘F. Casorati’, Applications (GCP-2003), Tambov, Russia Valette (Neuchâtel); A. Vershik (St. Università di Pavia, Via Ferrata n.1, I-27100 Information: e-mail: [email protected], Petersburg); E. Zelmanov (San Diego and Pavia, Italy [email protected] Yale); website: http://www.opu2003.narod.ru Format: plenary talks, invited talks [For details, see EMS Newsletter 44] Sessions: plenary lectures and parallel ses- 18-28: Instructional Conference in the sions Mathematical Analysis of Hydrodynamics, 11-18: Conference on Topological Languages: English and French Edinburgh, UK Algebras, their Applications, and Related Organisers: L. Bartholdi, T. Ceccherini- Organisers: International Centre for Topics, Bedlewo, Poland Silberstein, Tatiana Smirnova-Nagnibeda Mathematical Sciences 34 EMS March 2003 CONFERENCES Information: Call for papers: If you wish to present a I. Skrypnyk (Kyiv), M. Tajiri (Osaka), P. e-mail: [email protected]: contributed presentation, please submit an Winternitz (Montreal,), Yehorchenko (Kyiv), http://www.ma.hw.ac.uk/icms/meetings/ abstract according to the web instructions R. Zhdanov (Kyiv) 2003/hydro/index.html Programme committee: L. Schumaker Deadline: for registration 22 May (USA), P. Constantini (Italy), J. H. Miller Information: 19-22: 66th Workshop on General Algebra (Ireland), Z. Tutek (Croatia), L. Sopta e-mail: [email protected] / 66. Arbeitstagung Allgemeine Algebra (Croatia), R. Scitovski (Croatia), K. Veselic website: http://www.imath.kiev.ua/ (AAA66), Klagenfurt, Austria (Germany), A. Mikelic (France) ~appmath/conf.html Topics: universal algebra, classical algebra Organising committee: M. Marusic, M. or mirror http://www.bgu.ac.il/~alexzh/ and applications of algebra Rogina, S. Singer, J. Tambaca (all from appmath/conf.html Format: invited talks and contributed pre- Croatia) sentations Proceedings: to be published by Kluwer 24-27: Days on Diffraction ’03, St Sessions: plenary lectures and parallel ses- publ. co. Petersburg, Russia sions Location: Island Brijuni, near Pula (Croatia) Information: Registration: online registration form avail- Grants: none so far e-mail: [email protected], able by the end of February 2003 Deadlines: for registration and abstracts, 30 website: http://mph.phys.spbu.ru/DD Organisers: H. Kautschitsch, W. More and April; for manuscript 31 October 31 [For details, see EMS Newsletter 45] J. Schoißengeier Information: e-mail: [email protected] Proceedings: it is intended to publish the website: http://www.math.hr/~rogina/ 25-28: International Congress proceedings of the conference as Volume 15 ApplMath03 ‘Mathematics in the XXI Century. The in the series Contributions to General Algebra. Role of the Mathematics Department of All papers will be refereed. 23-27: Workshop on Extremal Graph Novosibirsk University in Science, Location: University of Klagenfurt, A-9020 Theory (Miklos Simonovits is 60), Lake Education, and Business’, Novosibirsk Klagenfurt, Austria Balaton, Hungary Akademgorodok, Russia Grants: probably support for participants Information: e-mail: [email protected], Information: e-mail [email protected], from countries in a difficult economic situa- website: http://www.renyi.hu/~extgr03 website: http://www-sbras.nsc.ru/ws/ tion [For details, see EMS Newsletter 45] MMF-21/index.en.html Information: e-mail: [email protected]; [For details, see EMS Newsletter 46] web site: www.uni-klu.ac.at/AAA66 23-27: Equations aux derivees partielles et quantification, Colloque en l’honneur de 25-28: 7th WSEAS CSCC International 20-27: Intermediate problems of model Lous Boutet de Monvel Multiconference on Circuits; Systems; theory and universal algebra, Novosibirsk, Location: Institut de Mathématiques de Communications and Computers, Corfu Russia Jussieu, Paris Island, Greece Information: web site: WWW2.nstu.ru/deps/ Information: website: http://www.institut. Information: website: http://www.wseas.org/ algebra/erlogol math.jussieu.fr/congres-lboutet/ conferences/2003/corfu [For details, see EMS Newsletter 46] 23-28: Tools for Mathematical Modelling 25-28: Current Geometry 2003, Naples, 21-28: X International Summer Conference St Petersburg, Russia (MATHTOOLS Italy on Probability and Statistics (ISCPS) and ‘2003) Subject: Current geometry 2003, the IV edi- the Seminar on Statistical Data Analysis Information: tion of the international conference on prob- (SDA 2003), Sozopol, Bulgaria e-mail: [email protected], lems and trends of contemporary geometry. Topics: Stochastic processes, limit theorems, website: www.neva.ru/journal Invited Speakers (provisional): E. Arbarello financial mathematics, combinatorial analy- Mailing address: Lidiya Linchuk, MATH- (Rome), M. Berger (Paris), P. Griffiths sis, theoretical and applied statistics, applica- TOOLS’2003, Dept. of Mathematics, State (Princeton), A. Sossinski (Moscow), A. tions in industry, economics, biology and Technical University, Polytechnicheskaya st. Vinogradov (Salerno) education of statistics 29, St Petersburg, 195251, Russia Scientific Committee: E. Arbarello (Rome), Organisers: Institute of Mathematics and [For details, see EMS Newsletter 46] F. Baldassarri (Padova), U. Bruzzo (Trieste), Informatics of the Bulgarian Academy of C. Ciliberto (Rome), A. Collino (Torino), M. Sciences, Faculty of Mathematics and 23-29: The Fifth International Conference Cornalba (Pavia), C. De Concini (Rome), B. Informatics of Sofia University and the ‘Symmetry in Nonlinear Mathematical Dubrovin (Trieste), L. van Geemen (Pavia), Bulgarian Statistical Society. Physics, Kyiv (Kiev), Ukraine P. Griffiths (Princeton), V. Kac (Boston), K. Organising committee: N. Yanev (chair of Topics: Classical, non-classical, conditional, O’Grady (Rome), C. Procesi (Rome), J. ISCPS), D. Vandev (chair of SDA 2003), E. approximate and other symmetries of equa- Stasheff (Chapel Hill), A. Vinogradov Pancheva, L. Mutafchiev, P. Mateev, M. tions of mathematical physics, Symmetry in (Salerno). Bojkova (secretary), E. Stoimenova. quantum mechanics, Quantum field theory, Organising Committee: A. De Paris Location: Hotel Dolphin just on the beach Gravity, Fluid mechanics, Mathematical biol- (Naples), G. Rotondaro (Naples), G. of the gulf of Sozopol ogy, Mathematical economics, Symbolic Sparano (Salerno), A. Vinogradov (Salerno), Information: computations in symmetry analysis, R. Vitolo (Lecce). website: http://stochastics.fmi.uni-sofia.bg Supersymmetry and its generalisations, Sponsors: Istituto Italiano per gli Studi Representation theory, q-algebras and quan- Filosofici, Naples; Università degli studi di 22-25: Conference on Applied Mathematics tum groups, Dynamical systems, Solitons Salerno; Gruppo Nazionale per le Strutture and Scientific Computing and integrability, Superintegrability and sep- Algebriche, Geometriche e le loro (ApplMath03), Brijuni, Croatia aration of variables Applicazioni; Dipartimento di Matematica Theme: Numerical analysis and differential Scientific committee: A. Nikitin and A. ed Applicazioni dell’Università degli Studi di equations in applied mathematics Samoilenko (Co-Chairs, Institute of Napoli ‘Federico II’ Aim: exchange of ideas, methods and prob- Mathematics, Kyiv), J. Beckers (Liège), G. Deadline: 15 May lems between various disciplines of applied Bluman (Vancouver), J. Carinena Information: e-mail: [email protected] or mathematics (Zaragoza), P. Clarkson (Canterbury), E. [email protected] Scope: to present the state of the art in the Corrigan (York), N. Debergh (Univ. of website: http://www.diffiety.ac.ru/conf/ field Liege, Belgium), H.-D. Doebner (Technical curgeo03 Topics: Splines and wavelets with applica- Univ. of Clausthal, Germany), G. Gaeta or http://www.diffiety.org/conf/curgeo03 tions to CAGD, CAD/CAM, computer graph- (Milan), G. Goldin (Rutgers), B.K. Harrison (mirror) ics and differential equations (Utah), N. Ibragimov (Blekinge), V. Main speakers: L. Schumaker (USA), P. Kadyshevsky (Dubna), J. Krasil’shchik 29- July 5: Workshop on Physics and Costantini (Italy), J. J. H. Miller (Ireland) (Moscow), A. Klimyk (Kyiv), M. Lakshmanan Geometry of Three-dimensional Quantum Format: keynote lectures, invited talks and (Tiruchirappalli), P. Leach (Durban), W. Gravity, Edinburgh, UK contributed presentations Miller (Minneapolis), J. Niederle (Prague); Organisers: International Centre for Sessions: plenary lectures and two parallel P. Olver (Minneapolis), G. Pogosyan Mathematical Sciences sessions (Yerevan, Cuernavaca and Dubna), Information: e-mail: [email protected] EMS March 2003 35 CONFERENCES website: http://www.ma.hw.ac.uk/icms/ Lecturers: V. Drensky (Bulgarian Academy Main speakers: J.-P. Allouche (France), Ch. current/index.html of Sciences); E. Formanek (Pennsylvania Bachoc (France), M. Bhargava (USA), Ch. State University) Breuil (France), J. Brüdern (Germany), A. 30-July 4: EMS School on Dynamical Topics: Structure theorems of Kaplansky, Lauder (UK), K. Soundararajan (USA), S. Systems, Porto, Portugal Posner and Artin; ring of generic matrices; Wewers (Germany), U. Zannier (Italy). Theme: Dynamical systems generic division ring and its relation with Call for papers: participants are invited to Aim: A one-week training programme on the theory of central simple algebras; struc- present a contributed talk of 20 minutes; dynamical systems and ergodic theory, lead- ture of the centre of the generic division abstract submission via Altas Mathematical ing to an understanding of recent develop- ring; Amitsur-Levitzki theorem; construction Conference Abstracts (http://atlas-confer- ments in these areas of central polynomials for matrices; polyno- ences.com/), deadline 31 May Topics: Quantitative recurrence and dimen- mial identities of matrices and their relation Programme committee: E. Bayer Fluckiger sion theory; tessellations; reconstruction: with invariant theory; Nagata-Higman theo- (Switzerland), P. Debes (France), J.-M. (numerical) methods for the investigation of rem; Shirshov theorem; Regev theorem Deshouillers (France), G. Frey (Germany), R. recurrent orbits and attractors from their Coordinator: Ferran Cedó Heath-Brown (UK), H. W. Lenstra time series; deterministic products of matri- Scientific Committee: Pere Ara, Dolors (Netherlands), P. Sarnak (USA), R. ces Herbera Tijedeman (Netherlands) Main speakers: L. Barreira (Portugal), J.-M. Organising Committee: Rosa Camps, Organising committee: S. Frisch, A. Gambaudo (France), F. Takens Ferran Cedó Geroldinger, P. Grabner, F. Halter-Koch, C. (Netherlands), M. Viana (Brazil) Grants: a limited number of grants for regis- Heuberger, G. Lettl, R. Tichy (Graz) Format: Four intermediate-level courses tration and accommodation for young scien- Proceedings: special issue of Journal de Sessions: Five one-hour sessions tists and scientists from less favoured coun- Théorie des Nombres de Bordeaux Organising committee: J. Alves, V. Araújo, tries Location: Karl-Franzens Universität Graz M. Carvalho, F. Moreira, J. Rocha (Portugal) Deadlines: applications for financial sup- Deadlines: for early registration (at lower Sponsors: EMS port, 25 April; registration and payment, 31 rates) 30 April; for registration: 15 June; for Location: Department of Pure Mathematics, May submission of abstracts: 31 May Faculty of Sciences, University of Porto - Rua Information: e-mail: [email protected] Information: e-mail: [email protected] do Campo Alegre, 687, 4269-007 Porto, website: http://www.crm.es/PI-rings website: http://ja03.math.tugraz.at/ Portugal Grants: Expected, but not yet confirmed, 3-8: Wavelets and Splines, St Petersburg, 9-12: XV Italian Meeting on Game Theory financial support from UNESCO. Russia and Applications, Urbino, Italy Information: e-mail: [email protected] Theme: wavelets and splines as tools for Information:e-mail: [email protected], website: http://www.fc.up.pt/cmup/sds approximation theory and applications website: www.econ.uniurb.it/imgta Aim: to exchange information on many [For details, see EMS Newsletter 46] July 2003 problems related to the wavelet and spline theory 13-28: VI Diffiety School in the geometry Topics: wavelets and wavelet methods, sig- of Partial Differential Equations, Santo 1-5: EuroConference VBAC 2003, Porto, nal processing, spline theory and its applica- Stefano del Sole (Avellino), Italy Portugal Dedicated to Andrei Tyurin tions, related topics Theme: two series of courses, one for begin- Topics: the meeting will cover a range of Main speakers: B. Kashin (Russia), A. Ron ners and one for veterans, will be given. The topics in the area of vector bundles on alge- (USA), L. Schumaker (USA), P. Wojtaszczyk beginners’ courses consist of a general intro- braic curves, with special emphasis on mod- (Poland), Yu. Brudnyi (Israel), N. Din duction, analysis on manifolds and observ- uli spaces and topology (Israel), A. Pinkus (Israel), M. Unser ables, introduction to differential calculus in Main speakers: J. Andersen (Aarhus), S. (Switzerland) commutative algebras. Detailed pro- Bradlow (Urbana-Champaign), V. Balaji Format: plenary 60- and 45-minute lectures, grammes have been published on our web (Chennai), W. Goldman (Maryland), T. 20-minute presentation and posters site. The veterans’ courses will discuss mod- Hausel (Austin), L. Jeffrey (Toronto), L. Sessions: plenary sessions, parallel sessions, ern geometric and homological methods in Katzarkov (Irvine), F. Kirwan (Oxford), M. special session on bivariate splines PDEs (including the elements of secondary Reid (Warwick), M. Thaddeus (Columbia). Call for papers: an electronic copy of the calculus) and their applications to integrable Scientific Committee: L. Brambila-Paz, O. abstract should reach the organising com- systems and equations of mathematical Garcia-Prada, P. Gothen, D. Hernandez mittee before 1 May. The abstract should be physics. We will also organise a scientific Ruiperez, F. Kirwan, H. Lange, P. Newstead LaTeX-formatted in the style Article, should session on the research interests of the par- (Chair), W. Oxbury, E. Sernesi, C. Sorger not exceed one page, and should contain ticipants and to discuss starting pro- Organisers: Carlos Florentino title, names of the authors, official address grammes, intended to involve interested ([email protected]) and Peter Gothen and e-mail address participants into our research projects ([email protected]). Organisers: St Petersburg branch of Steklov Lecturers and tutors of the School: A. De Sponsors: European Commission, High- Mathematical Institute and St Petersburg Paris (Napoli), S. Igonin (Moscow), J. Level Scientific Conferences, Contract State University Krasil’shchik (Moscow), A. Verbovetsky HPCF-CT-2001-00248; Research Training Programme committee: A. Averbuch (Moscow,), A. Vinogradov (Salerno), M. Networks EAGER and EDGE; Centro de (Israel), O. Davydov (Germany), Yu. Vinogradov (Diffiety Institute), R. Vitolo Matematica da Universidade do Porto; Demjanovich (Russia), R. DeVore (USA), L. (Lecce) Centro de Matematica e Aplicacoes Gori (Italy), D. Leviatan (Israel), V. Organising committee: D. Catalano (Instituto Superior Tecnico, Lisbon); Malozemov (Russia), I. Novikov (Russia), A. Ferraioli, A. De Paris, C. Di Pietro, G. Fundacao para a Ciencia e a Tecnologia Petukhov (USA), V. Zheludev (Israel), V. Manno, R. Piscopo, G. Rotondaro, A. (Portugal) (*); Reitoria da Universidade do Zhuk (Russia) Vinogradov, R. Vitolo. Porto (*); Departamento de Matematica Organising committee: M. Skopina (Chair, Sponsors: Diffiety Institute (Russia), Istituto Pura, Faculdade de Ciencias, Universidade Russia), S. Kislyakov (Vice-Chair, Russia), V. Italiano per gli Studi Filosofici, Municipality do Porto; (*) to be confirmed. Malozemov (Russia), A. Petukhov (USA) of Santo Stefano del Sole (AV), Italy Deadlines: to give a talk and/or apply for Location: Euler International Mathematical Deadline: 10 June financial support, registration deadline was Institute, Pesochnaya nab.-10, 197022 St Participation fee: 100 euro, to cover lodg- 1 March; other registration 15 April Petersburg ing and living expenses Information: website: http://www.math. Deadlines: for registration, 1 March; for Information: e-mail: [email protected]; ist.utl.pt/~cfloren/VBAC2003.html abstracts, 1 May website: http://www.diffiety.ac.ru or Information: e-mail: [email protected] http://www.diffiety.org. 1-10: PI-rings: structure and combinatorial website: http://www.pdmi.ras.ru/EIMI/ aspects (summer course), Bellaterra, 2003/ws 14-18: International Conference on Barcelona (Catalonia) Algebras, Modules and Rings, Lisboa, Aim: to introduce the students in the struc- 6-12: Journées Arithmétiques XXIII, Graz, Portugal [in memory of António Almeida tural and combinatorial theory of algebras Austria Costa, on the centenary of his birth] satisfying polynomial identities (PI-algebras) Topics: all branches of number theory Information: e-mail: [email protected]; 36 EMS March 2003 CONFERENCES web site: http://caul.cii.fc.ul.pt/lisboa2003/ creative education in mathematics and infor- 5-10: Workshops Loops ’03, Prague, Czech Subscribe to the conference mailing list at matics of gifted students Republic http://caul.cii.fc.ul.pt/alg.announce.html Topics: see the website Theme: lectures on quasigroups, loops and [For details, see EMS Newsletter 46] Proceedings: to be published before the Latin squares conference Lectures and Lecturers: Loop rings (E. 20-27: Hodge Theory in a New Century: A Programme Committee: President: P. Goodaire); self-distributive quasigroups, tri- Euro Conference celebrating the Centenary Vlamos (Greece); Scientific secretary: E. linear constructions and cocyclic modules (T. of Sir William Hodge (1903-1975), Velikova (Bulgaria); Members: H. Meissner Kepka, P. Nemec); Moufang loops and 3- Edinburgh, UK (Germany), A. Agnis (Latvia), A. Warren nets (G. Nagy, P. Vojtechovsky); latin trades Organisers: International Centre for (Australia), J. Becker (USA), F. Bellot- and Hamming distances (A. Drapal); auto- Mathematical Sciences Rosado (Spain), V. Berinde (Romania), S. mated reasoning in loop theory (J. D. Deadlines: Registration 18 April; financial Bilchev (Bulgaria), M. Bartolini Bussi (Italy), Phillips); introduction to smooth loops (M. support, passed C. Daniel (New Zealand), J.-C. Deledicq Kinyon). Information: e-mail: [email protected] (France), S. Dimitrova (Bulgaria), S. Format: four 90-minute lectures each day website: http://www.ma.hw.ac.uk/icms/ Dodunekov (Bulgaria), I. Ganchev Programme and Organising Committee: D. meetings/2003/HODGE/index.html (Bulgaria), A. Gardiner (UK), M. Georgieva Bedford (UK), O. Chein (USA), A. Drapal (Bulgaria), E. Gerganov (Bulgaria), D. (Secretary, Czech Rep.), M. Kinyon (USA), 21-25: W³adys³aw Orlicz Centenary Grammatikopoulos (Greece), K. Grigorova G. Nagy (Hungary), M. Niemenmaa Conference and Function Spaces VII, (Bulgaria), S. Grozdev (Bulgaria), M. Isoda (Finland), H. Pflugfelder (Honorary Chair, Poznañ, Poland (Japan), S. Kantcheva (Bulgaria), P. USA), J. D. Phillips (USA), V. Shcherbacov Topics: Banach space, geometry and topolo- Kenderov (Bulgaria), K. Kreitht (USA), C. (Moldova), P. Vojtechovsky (USA) gy of Banach spaces, operators and interpo- Lozanov (Bulgaria), K. Manev (Bulgaria), A. Local Organising Committee: A. Drapal lations in Banach spaces, Orlicz spaces and Momchilova (Bulgaria), O. Mushkarov (Chair), S. Holub (social programme), P. other function spaces, decomposition of (Bulgaria), D. Pavlov (Bulgaria), N. Rajkov Jedlicka (visas), T. Kepka (finances), P. function, approximation and related topics (Bulgaria), N. Rovoz (Russia), I. Sharygin Nemec (accommodation), D. Stanovsky Main speakers: (Russia), E. Silver (USA), A. Soifer (USA), E. (website, abstracts), P. Vojtechovsky (website, Conference in Honour of Orlicz: G. Bennet Stoyanova (Australia), J. (Bulgaria), P. registration, abstracts) (USA), J. Diestel (USA), P. Domañski Taylor (Australia), I. Tonov (Bulgaria), A. Sponsors: Charles University and the Czech (Poland), F. Hernandez (Spain), N. Kalton Ulovec (Austria), E. Vlamou (Greece) University of Agriculture (USA), B. Kashin (Russia), H. König Organising Committee: B. Tomov Location: Czech University of Agriculture, (Germany), S. Konyagin (Russia), J. Kurzweil (President); E. Velikova, S. Chernev, S. Prague (Czech Republic), A. Pinkus (Israel), K. Bilchev (Vice-presidents); Members: R. Notes: see also Loops ’03 Urbanik (Poland), P. Wojtaszczyk (Poland); Alexieva; G. Atanasova; K. Bankov; M. Deadlines: for registration: 20 June Function Spaces VII: J. Appell (Germany), D. Beikov; A. Bojadzhiev; P. Bonchev; E. Buhm Information: Pallaschke (Germany), L. Persson (Sweden), (Germany); M. Dikova; S. Dimitrov; J. e-mail: [email protected] B. Sims (Australia), T. Sukochev (Australia), Donkers (Netherlands); M. Drakakakis website: http://www.karlin.mff.cuni.cz/~loops H. Triebel (Germany) (Greece); G. Dushkov; V. Evtimova; A. /workshops.html Call for papers: for an oral 20-minute com- Gardiner (UK); A. Georgiev; M. Georgieva; munication, submit before 31 March an V. Gocheva; D. Grammatikopoulos (Greece); 10-17: Loops ’03, Prague, Czech abstract of up to 200 words (.doc or .rtf P. Hristova; V. Iliev; V. Jordanov; E. RepublicTheme: quasigroups, loops, latin extension) using the form at or mail to: Kalcheva; J. Kandilarov; M. Karailieva; R. squares, and related topicsAim: to highlight Faculty of Mathematics and Computer Kasuba (Lithuania); M. Kezas (Greece); N. new results in quasigroup theory, and to fos- Science, Adam Mickiewicz University, Knoche (Germany); A. Kopankova; T. ter connections to combinatoricsMain speak- Umultowska 87, 61-614 Poznan, Poland, Kopcheva; M. Kunchev; M. Lambrou ers: Galina B. Belyavskaya (Moldova), M. with postscript “Orlicz100”. (Greece); M. Makiewicz (Poland); D. Kikkawa (Japan), Programme committee: Milanova; T. Mitev; A. Momchilova; E. A. Kreuzer (Germany), K. Kunen (USA), C. .for the Conference in Honour of Orlicz: Z. Perzycka (Poland); M. Petkova; N. C. Lindner (USA), G. L. Mullen (USA), D. A. Ciesielski (Poland), L. Drewnowski (Poland), Popivanov; M. Popova; A. Poulos (Greece); Robinson (USA), J. D. H. Smith (USA) W. Johnson (USA), F. Hernandez (Spain), J. E. Rappos (Greece); P. Rashkov; T. Format: standard; contributed talks 30 or 15 Lindenstrauss (Israel), N. Kalton (USA), J. Rashkova; E. Rashkova; R. Russev; A. minutes long Musielak (Poland), G. Pissier (France), A. Smrikarov; N. Strateva; J. Svrcek (Czech Programme and Organising Committee: as Pe³czyñski (Poland), P. Ulyanov (Russia); Republic); M. Teodosieva; V. Tsonev; S. for previous conference (above) for Funcion Spaces VII: J. Musielak, H. Tsvetanova; M. Todorova; A. Ulovec Local Organising Committee: as for previ- Hudzik and L. Skrzypczak (all Poland) (Austria); V. Vaneva; V. Velikov; P. Vlamos ous conference (above) Organising committee: Z. Palka (Chair), B. (Greece); V. Voinohovska; A. Vrba (Czech Sponsors: Charles University and Czech Bojarski (Vice-Chair), S. Janeczko (Vice- Republic). University of Agriculture Chair), L. Skrzypczak (secretary), P. Organisers: Univ. of Rousse (Bulgaria), Proceedings: will be published in Domañski , H. Hudzik, J. K¹kol, I. Union of Bulgarian Mathematicians Commentationes Mathematicae Universitatis Kubiaczyk, M. Masty³o, P. Pych-Tyberska, S. (Rousse), ‘V-publications’ (Greece), Vlamos Carolinae, and in Quasigroups and Related Szufla, R. Urbañski, J. Werbowski, A. Preparatory School (Greece), Research Systems Waszak, W. Wnuk (all from Poland) Center for Culture and Innovation (Greece), Location: Czech University of Agriculture, Proceedings: to be published World Federation of National Mathematics Prague Location: the main building of the Faculty Competitions (Australia), Ministry of Notes: see also Workshops Loops ‘03 of Mathematics and Computer Science, Education and Science (Bulgaria), Deadlines: for registration and abstracts: 20 Adam Mickiewicz University, Poznan Mathematical High School (Rousse), Univ. June; for survey papers: 15 April; for pro- Deadlines: for abstracts, 31 March; for reg- of Veliko Turnovo (Bulgaria) ceedings papers: 10 October istration, 31 May Location: University of Rousse, Bulgaria Information: Information: e-mail: [email protected] Grants: there will probably be support for e-mail: [email protected] website: httm://orlicz.amu.edu.pl participants from countries in a difficult eco- website: http://www.karlin.mff.cuni.cz/~loops nomic situation, young gifted and PhD stu- August 2003 dents 11-15: Workshop on Finsler Geometry and Deadlines: for registration, 30 June; for Its Applications, Debrecen, Hungary abstracts, 30 April Theme: Finsler geometry, spray geometry, 3-9: Third International Conference: Information: e-mail: conf_orgcom@ Lagrange geometry, their generalisations Creativity in Mathematics Education and ami.ru.acad.bg or [email protected] and applications in physics, biology, control the Education of Gifted Students, Rousse, website: www.cmeegs3.rousse.bg, theory, finance, psychometry, etc. Bulgaria. www.ami.ru.acad.bg/conference2003/ Advisory Board: P. Antonelli (Edmonton); Aim: to formulate the problem and define www.nk-conference.ru.acad.bg G. S. Asanov (Moscow); D. Bao (Houston); S. globally the directions of the developing of S. Chern (Tianjin); P. Foulon (Strasbourg); EMS March 2003 37 CONFERENCES R. S. Ingarden (Torun); R. Miron (Iasi); G. Paris, France ing journals have accepted to publish select- Patrizio (Firenze); Z. Shen (Indianapolis); H. Information: ed Proceedings of ICCMSE 2003: Shimada (Sapporo); Z. I. Szabo (New York); e-mail: editions.europeenne @wanadoo.fr Computational Materials Science (Elsevier L. Tamassy (Debrecen). [For details, see EMS Newsletter 46] Science), Journal of Supercomputing (Kluwer), Local organisers: S. Bacso, L. Kozma, and J. Journal of Mathematical Chemistry (Kluwer), Szilasi (Debrecen) 2-6: Barcelona Conference on Asymptotic Communication in Mathematical and in Information: e-mail: [email protected] Statistics, Bellaterra, Barcelona, Catalonia Computer Chemistry (MATCH), Journal of website: http://www.math.klte.hu/finsler/ Information: e-mail: [email protected] Computational Methods in Sciences and website: http://www.crm.es/bas2003 Engineering (JCMSE) (Cambridge 18-22: ENUMATH 2003, The European [For details, see EMS Newsletter 46] International Science Publishing), Conference on Numerical Mathematics and Mathematical and Computer Modelling (Elsevier Advanced Applications, Prague, Czech 12-16: International Conference of Science), Communications in Nonlinear Science Republic Computational Methods in Sciences and and Numerical Simulation (Elsevier Science) Theme: numerical mathematics with appli- Engineering (iccmse 2003), Kastoria, Location: Kastoria, Greece cations Greece Grants: No grants available at this time Aim: analysis of numerical algorithms as Theme: computational methods in sciences Deadlines: registration 30 April; abstracts well as their application to challenging sci- and engineering passed entific and industrial problems Aim and Scope: In recent decades many sig- Information: [email protected] Main speakers: A. Bermudez (Spain), R. nificant insights have been made in several website: http://www.uop.gr/~iccmse/ or Blaheta (Czech Republic), T. Gallouet areas of computational methods in sciences http://kastoria.teikoz.gr/~iccmse/ (France), J. Haslinger (Czech Republic), R. and engineering. New problems and Hiptmair (Germany), T. J. R. Hughes (USA), methodologies have appeared. There is a 15-21: First MASSEE Congress, Borovetz, J. Rappaz (Switzerland), A. Russo (Italy), V. permanent need in these fields for the Bulgaria Schulz (Germany), A. Tveito (Norway) advancement of information exchange. This Aim: to revive the traditional collaboration Format: invited talks and contributed pre- undoubtedly beneficial practice of interdisci- in mathematics and informatics (computer sentations plinary and multidisciplinary interactions science) among south-east European coun- Sessions: there will be plenary lectures, should be expressed by an appropriate con- tries mini-symposia and contributed presenta- ference on such computational methods. Topics: I. Mathematical structures: logics tions ICCMSE 2003 aims at playing the above and foundations; algebra; topology; analysis; Call for papers: to present a contributed role and for this reason the aim of the con- differential equations; geometry; stochastics presentation, please submit an extended ference is to bring together computational and probability theory; other related topics abstract of up to one page in TeX or LaTeX scientists and engineers from several disci- II. Applications of mathematics and infor- Organisers: Charles University Prague, plines in order to share methods, method- matics (computer science): mathematical Faculty of Mathematics and Physics, Institute ologies and ideas modelling; operations research; wavelets of Chemical Technology Prague, Topics: these include (but are not limited analysis and image processing; computation- Department of Mathematics to) computational mathematics, computa- al and numerical analysis; other related top- Programme Committee: F. Brezzi (Italy), M. tional physics, computational chemistry, ics Feistauer (Czech. Rep.), R.Glowinski computational engineering, computational III. Mathematical foundations of informatics (France/USA), R. Jeltsch (Switzerland), Yu. mechanics, computational finance, computa- (computer sciences): theory of computing; Kuznetsov (Russia/USA), J. Periaux (France), tional medicine, computational biology, discrete mathematics in relation to computer R. Rannacher (Germany). computational economics, high performance science; computing methodologies and Scientific Committee: O. Axelsson computing, mathematical methods in sci- applications; algorithms; data mining; math- (Netherlands), C. Bernardi (France), ences and engineering, industrial mathemat- ematical linguistics; other related topics C.Canuto (Italy), M. Griebel (Germany), R. ics, etc. IV. History and education in mathematics Hoppe (Germany), G. Kobelkov (Russia), M. Main speakers: H. Ågren (Sweden), J. Vigo- and informatics: didactics of mathematics Krizek (Czech Republic), P. Neittaanmaki Aguiar (Salamanca); D. Belkic (Stockholm); and informatics (blackboard techniques and (Finland), O.Pironneau (France), A. E. Brändas (Uppsala); J. C. Butcher hypermedial methods); mathematical her- Quarteroni (Italy/Switzerland), C. Schwab (Auckland); S. C. Farantos (Greece); U. itage of south-east Europe; detecting and (Switzerland), E. Suli (Great Britain), W. Hohm (Braunschweig); A. Q. M. Khaliq developing mathematical talent; attracting Wendland (Germany) (Illinois); G. Maroulis (Patras); A. Mylona- talent to science; other related topics Organising Committee: V. Dolejsi, M. Kosma (Ioannina); S. Wilson (UK) Format: The congress will incorporate a Feistauer, J. Felcman, P.Knobloch, K. Format: Plenary lectures (by invitation); series of mini-symposia that emphasise top- Najzar, E. Plandorova, J. Segethova (Czech. original papers (selection based on extended ics of specific interest for the region: Rep.) abstracts of 3-4 A4 pages); posters (selection Organiser: the Mathematical Society of Proceedings: to be published similar to original papers) South-East Europe (MASSEE): a recently Location: Institute of Chemical Technology Sessions: to be announced registered organisation comprising mathe- Prague Call for papers: send your abstract or matical societies from Albania, Bulgaria, Grants: probable support for participants description of session to [email protected] Bosnia-Herzegovina, Cyprus, Greece, from countries in a difficult economic situa- Organisers: European Society of Macedonia, Moldova, Romania and tion and young mathematicians Computational Methods in Sciences and Yugoslavia Deadlines: for registration, 30 April; for Engineering (ESCMCE), Department of Location: Hotel Samokov, at the heart of abstracts, 31 March International Trade Technological the famous summer and winter resort of Information: Educational Institution of Western Borovetz (55km south-east of Sofia) e-mail: [email protected] Macedonia, Greece Information: website: website: http://www.karlin.mff.cuni.cz/~enu- Programme (Scientific) committee: H. http://www.math.bas.bg/massee2003/ math/ Agren, H. Arabnia (Georgia, USA), J. Vigo- Aguiar, D. Belkic, K. Belkic (Southern 16-20: Barcelona Conference on Set 18-22: 7th International Symposium on California), E. Brandas, J. C. Butcher, A. Q. Theory, Bellaterra, Barcelona, Catalonia Orthogonal polynomials, Special Functions M. Khaliq (Illinois), G.Maroulis, S. Wilson, J. Information: e-mail: [email protected], and Applications, Copenhagen, Denmark Xu (Pennsylvania) web site: http://www.crm.es/set-theory Information: e-mail: [email protected], Organising committee: Th. Monovasilis, [For details, see EMS Newsletter 46] website: http://www.math.ku.dk/conf/ Eleni Ralli, Secretary of ICCMSE, I. opsfa2003 Sinatkas, E. Siskos, Th. Themelis, K. Tselios, 17-19: Conference on Computational [For details, see EMS Newsletter 46] N. Tsounis Modelling in Medicine, Edinburgh, UK Sponsors: European Regional Development Organisers: International Centre for September 2003 Fund, Region of Western Macedonia, Greece Mathematical Sciences Proceedings: Extended abstracts will be Information: e-mail: [email protected] published in a special volume of World website: http://www.ma.hw.ac.uk/icms/ 2-5: Symposium on Cartesian Set Theory, Scientific Publishing Company. The follow- current/index.html 38 EMS March 2003 RECENT BOOKS Anosov diffeomorphisms and geodesic flows on Riemannian manifolds. The last two chapters are based on Pesin’s results, and form the RecentRecent booksbooks heart of the book. Local stable manifolds are constructed in Chapter 4, where their absolute edited by Ivan Netuka and Vladimír Souèek continuity (in the sense of Anosov) is proved. This is one of the main tools for the ergodic Books submitted for review should be sent to the fol- main results on de Rham cohomology of dif- theory of smooth dynamical systems, and plays lowing address: Ivan Netuka, MÚUK, Sokolovská ferential modules. The authors use a new def- an important role in investigations of ergodic 83, 186 75 Praha 8, Czech Republic. inition of relative algebraic de Rham cohomol- properties of invariant hyperbolic measures in ogy with compact support and prove that it Chapter 5. K. Alster, J. Urbanowicz and H. C. Williams coincides with the Dwork algebraic dual theo- The book contains many technically rather (eds.), Public-Key Cryptography and ry. The final result of the book is a complete complicated results and is written for well-pre- Computational Number Theory, Walter de proof of general non-archimedean compari- pared readers (such as advanced graduate stu- Gruyter, Berlin, 2001, 331 pp., DM 256, ISBN 3- son theorem for de Rham cohomology. As a dents working in dynamical systems) with a 11-017046-9 corollary, it is shown that the functor of p-adic good knowledge of ODEs, differential topolo- These proceedings are dedicated to the mem- analytification of connections is fully faithful. gy and measure theory. Such a reader will ory of Rejewski, Rózycki and Zygalski, who The book will be of interest to specialists in surely benefit by studying these lectures. broke the military version of Enigma in 1933 arithmetic algebraic geometry, and may also (jmil) and gave its reconstructed version to the be used as an introduction to the topics British and French in 1939. The book con- described above. (jbu) E. R. Berlekamp, J. H. Conway and R. K. tains their photographs, but no paper describ- Guy, Winning Ways for Your Mathematical ing their activity. There are 20 papers in the G. E. Andrews, R. Askey and R. Roy, Special Plays, 1, 2nd ed., A K Peters, Natick, 2001, 276 proceedings, relating to various aspects of the Functions, Encyclopedia of Mathematics and its pp., US$49.95, ISBN 1-56881-130-6 scope of the conference. Applications 71, Cambridge Univ. Press, 1999, This first volume of a four-volume series is an Buchmann and Hamdy survey IQ cryptog- 664 pp., £55, ISBN 0-521-62321-9 elementary introduction to the theory of com- raphy, and Schnorr surveys the security of DL- An introductory chapter presents many facts binatorial games, elementary in the sense that cryptosystems and signatures against generic on gamma and beta functions, which form the concepts, such as games, values, etc., are attacks. Patarin presents the concept of secret necessary basic tools for further treatment of defined naively rather than rigorously. public-key schemes, where (in the case of special functions, including a short informa- The book contains 8 chapters. Chapter 1 encryption) anybody can encrypt, but where tion on their finite field analogues. Later (in introduces certain games and calculates their both the key to decipher and the exact algo- Chapter 8), the Selberg multi-dimensional ver- values in complicated positions. Chapter 2, rithm to decipher are secret. There is also a sions of beta integrals (including its finite field among others, introduces the game of Nim 30-page carefully written overview of the XTR analogue) are described. The next two chap- and the values of its positions – nimbers. public key system by Lenstra and Verheul. ters describe properties of the basic case of Chapter 3 continues the exposition of value Kucner and Kutylowski present a stochastic hypergeometric series p+1Fp (mostly for p = 1 arithmetic, studying nimber addition and method of testing against stealing attacks by or 2). A detailed study of Bessel functions introducing the values of ↑ (up) and ↓ (down). manufacturers of cryptographic devices. S. appears in Chapter 4. The following three Chapter 4 illustrates these ideas with a series of Müller is concerned with security proofs based chapters are devoted to properties of various examples: Dowson’s chess, Treblecross etc. on the factorisation problem in the sense of orthogonal polynomials, and Chapter 9 stud- Chapter 5 introduces switch values, their tem- IND-CCA (the indistinguishability-chosen ies spherical harmonics (including the relation perature and their arithmetic, while Chapter 6 cipher text attack). Jacobson, Scheidler and of special functions to representation theory). shows how to deal with hot and big games. Williams investigate key exchange protocols Chapter 10 introduces a q-generalisation of Chapter 7 discusses various versions of that use real quadratic fields. Hoffstein and hypergeometric series, and includes q-versions Hackenbush in more detail, and Chapter 8 Silverman describe optimisation for NTRU, of the gamma and beta functions, the q-bino- introduces the atomic weight of all-small which is a cryptosystem based on ring theory. mial theorem, Ramanujan formulas and a games and related concepts. Each chapter Niederreiter exhibits in a short survey several treatment of elliptic and theta functions. ends with references to further reading. interactions of cryptography and the theory of Relations to the theory of partitions form the The book introduces numerous games with error-correcting codes. subject of Chapter 11. The final chapter is colour illustrations. It does not assume any The other papers are more or less purely devoted to identities of the Rogers-Ramanujan particular mathematical knowledge on part of mathematical. Couveignes discusses connec- type. There are six appendices summarising the reader, but requires a certain degree of tions between algebraic groups and the dis- various tools used in the book. Each chapter is abstract thinking and patience. (ab) crete logarithm, while Teske surveys algo- followed by a number of exercises. rithms to compute discrete logarithms. The book is full of beautiful and interesting F. Borceux and G. Janelidze, Galois Theories, Elliptic and hyperelliptic curves are the subject formulae, as was always the case with mathe- Cambridge Studies in Advanced Mathematics 72, of contributions by Enge, Galbraith, Müller matics centred around special functions. It is Cambridge Univ. Press, 2001, 341 pp., £50, ISBN and Pethö. The remaining three papers deal written in the spirit of the old masters, with 0-521-80309-8 with number theory: te Riele discusses the size mathematics developed in terms of formulas. This book is based on a French manuscript, of solutions n or the inequality ϕ(an + b) < There are many historical comments in the written by the first author as a record of his ϕ(an), a and b coprime, Kubiak develops a pro- book. It can be recommended as a very useful ideas; it is largely completed by results of the cedure which speeds up the extended binary reference. (vs) second author and his coauthors. gcd algorithms, and Dilcher surveys computa- The authors briefly introduce the reader to tional and theoretical work done in the areas L. Barreira and Y. B. Pesin, Lyapunov classical Galois theory and its tools, formulated of Fermat and generalised Fermat numbers, Exponents and Smooth Ergodic Theory, in modern mathematical language. The rest Wieferich and Wilson primes, and Fermat and University Lecture Series 23, American Math. of the book aims to provide deeper insight into Wilson quotients for composite moduli. (ad) Society, Providence, 2001, 151 pp., US$29, ISBN more advanced parts, such as the Galois theo- 0-8218-2921-1 ry of Grothendieck. The reader will find here Y. André and F. Baldassarri, De Rham This is a book on smooth dynamical systems a well organised proof of the Galois theorem. Cohomology of Differential Modules on with a hyperbolic structure, written by two The next part focuses on infinitary Galois the- Algebraic Varieties, Progress in Mathematics 189, experts; in particular, several crucial results ory. The true core of the book consists of the Birkhäuser, Basel, 2001, 214 pp., DM 118, ISBN were proved by the second author. The classi- categorical Galois theory of commutative rings 3-7643-6348-7 cal theorems of Lyapunov and Perron on the (Stone duality, Pierce representation of a com- The main topic of this book is the theory of stability of non-autonomous systems of ODEs mutative ring, the adjoint of the spectrum differential modules on algebraic varieties. have started investigations into the Lyapunov functor, descent morphisms, etc.). The tech- The book offers fundamental results on direct exponents and their regularity. niques of the second author are also used in images of regular differential modules by a The story is described in Chapters 1 and 2 – the chapter on covering maps. The conclud- smooth morphism (proofs of finiteness, base including, for example, the multiplicative ing chapter is devoted to thenon-Galoisian change, regularity and monodromy theorems). ergodic theorem of Oseledets. Chapter 3 is Galois theory, where the reader will find the There is also an algebraic treatment of the the- devoted to two main examples of (non-uni- famous Joyal-Tierney theorem. The book is ory of regularity and irregularity in several form) hyperbolic systems, which stimulated the carefully arranged and can be useful to any- variables, leading to elementary proofs of development of hyperbolic theory, namely body interested in algebraic methods. (lbe)

EMS March 2003 39 RECENT BOOKS C. J. Budd and C. J. Sangwin, Mathematics I. Chiswell, Introduction to Lambda Trees, tion theory. Galore, Oxford Univ. Press, 2001, 254 pp., World Scientific Publishing, Singapore, 2001, 315 The main part of the book contains contri- £14.95, ISBN 0-19-850769-0 and 0-19-850770- pp., £48, ISBN 981-02-4386-3 butions from J.-L. Lions; A.B. Aleksandrov, S. 4 In a connected graph there is a natural dis- Janson, V.V. Peller and R. Rochberg; J. Arazy The aim of this book is to enthuse, inspire and tance function, the minimum number of edges and H. Upmeier; J. Brandman, J. Fowler, B. challenge young people in mathematics. The in a path connecting given vertices. If the Lins, I. Spitkovsky and N. Zobin; M.J. Carro material in this book is not covered by a typi- graph is a tree, this distance has certain specif- and J. Martín; M. Cotlar and C. Sadosky; D. cal school syllabus. The main ideas are acces- ic properties. Generalising them to distances Cruz-Uribe, SFO and M. Krbec; M. Engliš; T. sible to children from the age of eleven, while with values in a general ordered abelian group Figiel and N. Kalton; V. Gol’dshtein and M. some parts of the book should interest and L (instead of the group of integers), one Troyanov; S. Kaijser and P. Sunehag; D. challenge older school and university students, obtains the notion of a L-tree. Part of the book Lukkassen and G.W. Milton; V.G. Maz’ya and as well as their teachers and parents. The (less than a quarter) is devoted to an analysis of I.E. Verbitsky; C. Michels; E. Nakai; L. Pick; book consists of eight independent chapters, the notion and properties of L-trees as metric S.Yu. Tikhonov; H. Triebel; and a list of the 73 each formulating problems motivated by real spaces. Most of the text is concerned with their talks given at the conference. The topics cov- life and developing mathematical ideas that isometries, group actions on L-trees in general, ered by these contributions range from inter- can be used to solve them. Many exercises are and actions of special groups; in conclusion, polation theory, through function spaces, to included. Rip’s theorem is discussed. applications in operator theory. (lp) In Chapter 1 mazes and labyrinths are stud- The book is divided into six chapters. ied. After some short historical remarks, con- Chapter 1 introduces basic notions. Chapter 2 O. Debarre, Higher-Dimensional Algebraic nections to graph theory, the problem of the is devoted to the definition and basic proper- Geometry, Springer, New York, 2001, 233 pp., 16 bridges of Königsberg and the general method ties of L-trees, and to R-trees (which play an fig., DM 96, ISBN 0-387-95227-6 for solving all mazes are described. Chapter 2 important role in the theory). Chapter 3, pre- This book describes certain topics on the links group theory to study of patterns in danc- sents some basic facts on isometries of L-trees progress in classifying algebraic varieties of ing, bell-ringing and knitting. Chapter 3 con- (special features of individual isometries and dimension at least 3. The first two chapters are tains some results in trigonometry. In Chapter their pairs, group actions as group of isome- devoted to the standard definitions and results 4 some interesting mathematical theorems tries, etc.). Chapter 4 is concerned with more on nef, big and ample Cartier divisors and (mostly expressions of ð) are mentioned, with involved questions of group actions. Some spe- spaces of morphisms of a fixed algebraic curve some examples of magic tricks and the mathe- cial action groups are introduced and to a fixed algebraic variety. Chapters 3, 4 and matics behind them. Chapter 5 shows how analysed, and the spaces of actions on R-trees 5 deal with various aspects of the geometry of mathematics can apply to a problem of the are discussed. Chapter 5 is devoted to actions smooth algebraic varieties with many rational best design of castles: ideas on the isoperimet- of free groups. Finally, Chapter 6 contains a curves – in particular, uniruled or rationally ric inequality are presented, and the book thorough discussion of Rip’s theorem (charac- connected varieties. It is proved, for example, looks at properties of later designs of castles terising finitely generated R-free groups) that that Fano varieties are rationally connected. and more modern fortifications. Chapter 6 can be approached using isometry groups on Chapters 6 and 7 take a first step toward the deals with codes, ciphers and the mathematics R-trees. Mori minimal model programme of classifying used to break the codes: the Caesar and In the quarter-century since L-trees (and algebraic varieties, proving the cone and con- Viginère ciphers are mainly discussed, with Tits’ R-trees) were introduced, the theory has traction theorems. (pso) some remarks about modern methods based developed considerably. This monograph is on prime factorization. Chapter 7 studies ways timely and useful. (ap) P. Dolbeault, A. Iordan, G. Henkin, H. Skoda of representing numbers, with properties of and J.-M. Trépreau (eds.), Complex Analysis different number bases (including negative M. Cwikel, M. Engliš, A. Kufner, L.-E. and Geometry: International Conference in ones). Chapter 8 introduces the properties of Persson and G. Sparr (eds.), Function Spaces, Honor of Pierre Lelong, Progress in Mathematics logarithms. (ab) Interpolation Theory and Related Topics, 188, Birkhäuser, Basel, 2000, 241 pp., DM 118, Walter de Gruyter, Berlin, New York, 2002, 462 ISBN 3-7643-6352-5 I. Chavel, Isoperimetric Inequalities: pp., EUR 138, ISBN 3-11-017117-1 This is a collection of 18 papers written in hon- Differential Geometric and Analytic Interpolation theory is an important field of our of the 85th birthday of Pierre Lelong. The Perspectives, Cambridge Tracts in Mathematics functional analysis, which can be, roughly meeting, organised on this occasion in Paris, 145, Cambridge Univ. Press, 2001, 268 pp., £50, speaking, divided into its classical and modern was also the closing conference for the ISBN 0-521-80267-9 parts. The main landmarks of the classical European network ‘Complex analysis and ana- The classical isoperimetric inequality com- interpolation theory are the 1926 M. Riesz’s lytic geometry’. pares the volume V(Ω) of a domain Ω in Rn convexity theorem, furnished later with the The first contribution (by H. Skoda) and the surface area A(∂Ω) of its boundary. celebrated complex-variable proof of O. describes the main topics of Lelong’s research, There are several ways of interpreting the Thorin (1939/48), and the 1939 theorem of J. and includes his complete bibliography. quantity A(∂Ω) – Hausdorff measure, perime- Marcinkiewicz. Modern interpolation theory, Further papers are written by J. Siciak, J.-P. ter and Minkowski area – and the correspond- whose foundations were laid in the early 1960s, Demailly, G. Bassanelli, M. Christ, K. ing approaches to the proof of the isoperimet- has several fathers, including E. Gagliardo, A. Diederich and T. Oshawa, K. Diederich and J. ric inequality are presented. The Faber-Krahn Calderón, J.-L. Lions, S. G. Krein and J. McNeal, G. Herbort, U. Hiller, S. Webster, C. inequality on the smallest eigenvalue for the Peetre. The last of these, Prof. Jaak Peetre of Laurent-Thiébaut and J. Leiterer, T.C. Dinh, Laplace operator is deduced: among domains Lund, reached his 65th birthday on 29 July P. Dingoyan, E. Mazzilli, E. Bedford and M. with equal volumes, the minimum is attained 2000, and a delightful conference was held in Jonsson, G. Tomassini, F. Berteloot and J. for a ball. After this, the author turns to gen- Lund a month later. The special spirit of this Duval, C. Epstein and G. Henkin. At the end eralisations to manifolds. He develops the meeting can be felt from the conference web- is a list of ten open problems in the field, for- method of discretization and studies also site. mulated by participants at the meeting. The isoperimetric constants for graphs, and relates This book, containing the conference pro- book will be of interest to mathematicians isoperimetric inequalities, Nirenberg-Sobolev ceedings, is organised equally well. It has an working in the field. (vs) inequalities, Nash-Sobolev inequalities and interesting introductory part, consisting of the Faber-Krahn inequalities. Then he studies Editors’ preface, an opening address by H. L. T. Fernholz, S. Morgenthaler and W. the large time heat diffusion on manifolds: the Wallin from which the reader can learn inter- Stahel (eds.), Statistics in Genetics and in the method of proof again uses a discretisation. esting facts (such as Peetre’s impressive per- Environmental Sciences, Trends in Mathematics, The book is very useful in two ways. First, it sonal record in marathon races), a picture of Birkhäuser, Basel, 2001, 183 pp., DM 130, ISBN nicely explains the story of the classical Peetre in his rose garden, a beautiful article 3-7643-6575-7 isoperimetric inequality, a result with a big dis- ‘Jaak Peetre, the man and his work’ by M. This book is a collection of twelve papers, proportion between the ease of formulation Cwikel, L.-E. Persson, R. Rochberg and G. based on contributions to the 1999 Workshop and difficulty of the proof. It is very useful that Sparr, giving a comprehensive review of on Statistics and Science, held at the Centro the reader can compare different approaches. Peetre’s work (including an unbelievable list of Stefano Franscini in Ascona. It provides fur- Second, it presents a topical and interesting 289 publications), and an essay ‘On the devel- ther proof of the crucial role of statistics in part of global analysis on manifolds, relating opment of interpolation – instead of a history modern genetics and environmental science, the asymptotic behaviour of the isoperimetric three letters’, edited and/or translated by and will be useful for anyone interested in sta- inequality for large domains and large-time Peetre, including letters by O. Thorin, A. tistical applications or methodology in this heat diffusion. This second part contains deep Zygmund and M. Cotlar that give a very inter- area of research. The articles range from results obtained by the author. (jama) esting insight to the beginnings of interpola- applied statistics to theoretical results with tied

40 EMS March 2003 RECENT BOOKS connection to environmetrics. ics and scientific computing. (mfei) topological space constructed as the spectrum The book starts with three articles on of A. applied stochastical genetics. This part covers S. Feferman, J. W. Dawson, Jr., S. C. Kleene, The book is divided into four parts, com- quantitative genetics, with applications to plant G. H. Moore, R. M. Solovay and J. van prising 14 chapters. The first part contains a breeding, DNA microarray analysis after stan- Heijenoort (eds.), Kurt Gödel: Collected summary of the basics of C*-algebras, such as dardisation, and variance component estima- Works, Vols. I and II, Oxford Univ. Press, 2001, the Gelfand-Naimark theorem, the Tannaka- tion with an uncertain link between individuals 473 and 407 pp., each volume £26.50, ISBN 0- Krein reconstruction theorem, Serre-Swan cat- and their parents. The next four articles pre- 19-514720-0 and 0-19-514721-9 egorical equivalence between vector bundles sent non-trivial statistical applications in chem- These two volumes present a comprehensive and projective modules over unital commuta- istry. The authors face problems of censored edition of all Kurt Gödel’s published works in tive algebras, K-theory and its Bott periodicity data and severe outliers, when estimating the period 1929-74. The first volume covers for C*-algebras, Morita equivalence of C*-alge- chemical concentration, risk under low dose the period 1929-36 and begins with his disser- bras, etc. The second part contains some con- exposure, age-dependent risk of carcinogene- tation, previously available only through the structions of universal algebras that are behind sis, and atmospheric chemistry. The applied University of Vienna. Each article or group of the real analysis foundations of non-commuta- part of the proceedings concludes with an articles is preceded by an introductory note tive geometry – in particular, universal forms analysis of the problem of small objects on the placing it into historical context and clarifying and connections, cycles and their Chern char- Earth’s orbit. The last four papers can be clas- it. The members of the editorial board, and acters, together with Hochschild cohomology. sified as theoretical: written with applications some outside experts, are the authors of these The third part is devoted to ingredients of to the environmental sciences in mind, these notes. Each article originally written in non-commutative Spin geometry, built upon articles deal mainly with multivariate data and German is printed with an English translation. the notion of a spectral triple. The fourth part robust techniques. Here one can find treat- The first volume starts with Solomon discusses possible applications of this machin- ments of robust principal components, robust Feferman’s bibliographical essay on Gödel’s ery in the realm of mathematical and theoreti- inverse regression, regression depth or τ-esti- life and work. In each volume, there are exten- cal physics, including descriptions of non-com- mate for linear regression. sive lists of references, as well as interesting mutative gauge theories and perturbative The book provides a sample of possible photographs. quantum field theories. The book contains applications of statistics for statisticians inter- The books are carefully and beautifully pro- proofs of almost all assertions, as well as many ested in how their methods are used. Others duced and offer rich material, illuminating not explicit examples illustrating the theoretical from different areas can learn how to use sta- only the outstanding work of Gödel, but also developments described. (pso) tistics in their work. (dh) the whole mathematical logic of the twentieth century, including some philosophical and his- M. R. Grossinho, M. Ramos, C. Rebelo, L. H. Freistühler and G. Warnecke (eds.), torical aspects. Some questions from physics Sanchez, Eds., Nonlinear Analysis and its Hyberbolic Problems: Theory, Numerics, are also discussed. (jmlc) Applications to Differential Equations, Progress Applications, 8th Internat. Conference in in Nonlinear Differential Equations and Their Magdeburg February/March 2000, Vols. I, II, M. Gardner, Gardner’s Workout: Training the Applications 43, Birkhäuser, Boston, 2001, 380 International Series of Numerical Mathematics, Mind and Entertaining the Spirit, A K Peters, pp., DM 188, ISBN 0-8176-4188-2 and 3-7643- 140/141, Birkhäuser, Basel, 2001, 472 and 469 Natick, 2001, 319 pp., US$35, ISBN 1-56881- 4188-2 pp., EUR 80 each volume, ISBN 3-7643-6709-1 120-9 The book contains many of the talks delivered and 3-7643-6710-5 This is a remarkable book. It is a collection of at the Autumn School on Non-linear Analysis The book, in two volumes, is the Proceedings 41 articles that the author wrote for academic and Differential Equations, held at the CMAF, of the Eighth International Conference in journals and popular magazines. It also con- University of Lisbon, in 1998. The school con- Magdeburg, in 2000. It contains about one tains ideas of the author on ‘how to teach math sisted of short courses and a seminar. hundred refereed papers presented at this to pre-college students without putting them to The first part of the book contains the fol- conference. Most of these are concerned with sleep’. Let us pick out a few characteristic lowing short courses: An overview of the non-linear hyperbolic equations of conserva- points. method of lower and upper solutions for ODEs tion laws. • There is an old picture of a baker, who (C. De Coster and P. Habets); On the long- The papers can be divided into three baked a square cake and sold a quarter of it. time behaviour of solutions to the Navier- groups. Those from the first group are con- Four hungry kids enter the shop to buy the rest Stokes equations of compressible flow (E. cerned with such theoretical aspects of hyper- of it. Could they tell how to cut it into four Feireisl); Periodic solutions of systems with p- bolic problems as the existence and uniqueness pieces of the same size and shape? Laplacian-like operators (J. Mawhin); of solutions, asymptotic behaviour, large-time • Another problem: ‘Cut an equilateral trian- Mechanics on Riemannian manifolds (W. M. stability or instability of waves and structures, gle into three similar parts, no two congruent’ Oliva); Twist mappings, invariant curves and various limits of solutions, the Riemann prob- is easily solved. It is probably unique, though parabolic differential equations (R. Ortega) lem, etc. In particular, non-linear conservation no proof is known. and Variational inequalities, bifurcation and laws are treated. One can see a considerable • One afternoon, while sitting in a car waiting applications (K. Schmitt). The second part progress in mathematical theory on the one for my wife to finish supermarket shopping, I contains 21 contributions from various topics, hand, but the results published here indicate located a pencil and paper and drew on the related in one way or another to either ordi- that mathematicians are struggling with a sheet the unique lo shu, or magic square made nary or partial differential equations. The top- number of difficult open problems. The sec- with distinct digits 1-9. … Back home I began ics in the ODE part include spectral theory for ond group of papers is devoted to numerical experimenting… (How typical of a married the 1-dimensional p-Laplacian, application of a analysis of hyperbolic problems – for example, mathematician!). time-map in boundary-value problems, non- development of numerical schemes, investiga- It remains for the reader to find a lonely linear oscillations, non-linear resonance, and tion of their stability and convergence. These island, an unlimited quantity of paper and an more. The topics in the PDE part include sym- papers study finite differences, finite element eternal pencil, together with this book. It will metries of positive solutions to equations and finite volume schemes, investigate surely produce a paradise for anybody who involving the higher-dimensional p-Laplacian, schemes with special properties, and pay atten- wants to enjoy the pleasure of the creative work bifurcation theory and its applications to the tion to adaptivity, domain decomposition, in his brain. (lbe) Monge-Ampère operator, application of the multi-resolution and artificial dissipation. The dual method to the Tricomi problem, the tele- third group of articles is oriented to a wide J. M. Gracia-Bondía, J. C. Várilly and H. graph equation, an abstract concentration- range of applications, such as one-phase and Figueroa, Elements of Noncommutative compactness method, and degree and index multiphase flow, shallow water problems, high- Geometry, Birkhäuser Advanced Texts, Birkhäuser, theories on the Nielsen numbers. In both speed flow, relativistic magnetohydrodynam- Boston, 2001, 685 pp., DM 138, ISBN 0-8176- parts, problems from the calculus of variations ics, low Mach number flow, elasticity, thermo- 4124-6 and 3-7643-4124-6 and optimal control appear naturally – for dynamics, electromagnetic fields, etc. The branch of mathematics now called non- example, in Lipschitz regularity of minimisers The books contain a large amount of mater- commutative geometry is a far-reaching gener- (ODE part) or optimal control for some elliptic ial and give an excellent overview of the con- alisation of the Gelfand-Naimark theorem stat- equations of logistic type (PDE part). Finally, temporary state of art in the area of hyperbol- ing that, for a commutative C*-algebra A, there we mention the dynamics of delayed systems ic problems. They will be of interest to is an isometric *-isomorphism between the which appears in connection with asymptotic researchers and students of applied and algebra A and the set of continuous functions expansion and Hopf bifurcation. (lp) numerical mathematics, computational fluid on the set of characters of A. In a sense, any dynamics and computational physics, scientists non-commutative C*-algebra gives rise to an P. Hájek (ed.), Gödel ‘96, Lecture Notes in and engineers engaged in applied mathemat- algebra of functions on a non-commutative Logic 6, A K Peters, Natick, 1996, 322 pp.,

EMS March 2003 41 RECENT BOOKS US$50, ISBN 1-56881-153-5 author’s book Operator theory in function spaces tions of quadratic forms in wireless communi- This volume contains the proceedings of a con- (Marcel Dekker, New York 1990). cation problems: the bridge between the two ference held in Brno on the 90th anniversary The exposition is beautifully organised and subjects are orthogonal designs (known also as of the birth of Kurt Gödel. It is divided into very lucid and well written. Although some space-time block codes), and Hurwitz’ famous two parts: the first, ‘Invited papers’, contains 9 important topics close to the spirit of the book theorem of classifying normed algebras (reals, papers, and the second part, ‘Contributed have been omitted (such as the recent proof of complex numbers, quaternions, and octo- papers’, has 13 papers. The contributions the so-called Korenblum conjecture), the book nions) finds its way into applied mathematics! reflect many areas substantially influenced or is surely indispensable for anyone actively J. A. Thas focuses on the most important touched by Gödel’s work. They mainly illumi- working in the area of Bergman spaces, while results on partial m-systems and m-systems of nate or develop some of Gödel’s results and making good reading for any mathematical finite classical polar spaces. L. A. Goldberg’s ideas concerning mathematical logic and the analyst. (meng) contribution is concerned with the computa- foundations of mathematics. Some contribu- tional difficulty of three problems: for a per- tions discuss aspects of his results and opinions H. Heuser, Lehrbuch der Analysis, 1, 14. mutation group acting on a finite set, to count in physics, as Ellis’s ‘Contributions of K. Gödel Auflage, B.G. Teubner Verlag, Stuttgart, 2001, the orbits exactly and approximately, and to to Relativity and Cosmology’ and Stöltzner’s 643 pp., EUR 29,90, ISBN 3-519-52233-0 choose an orbit uniformly at random. M. ‘Gödel and the Theory of Everything’. Other This outstanding textbook covers all basic top- Aigner ‘surveys in a leisurely pace’ connections contributions refer to Gödel’s philosophical ics of first-year mathematical analysis at uni- of the Penrose polynomial, developed as a tool opinions, as, for example, ‘Gödel’s Ontological versities: differential and integral calculus, and for attack on the 4-colour problem, to graph Proof Revisited’ by Anderson and Gettings. related topics such as sequences, series, and an theory, binary space, Tutte polynomial, Gauss The authors of invited papers are S. Feferman, introduction to differential equations. Besides problem, Hopf algebras, and invariants in knot M. Baaz, G.F.R. Ellis, B.A. Kushner, C. the theory, the book offers numerous applica- theory. (mkl) Parsons, P. Pudlák, W. Sieg and J. Byrnes, G. tions in physics, chemistry, biology, agricul- Takeuti and M. Yuasumoto, and A. Wisser. A ture, technics, medicine, psychology, warfare, J. Hong and S.-J. Kang, Introduction to wide area of Gödel’s work is covered, and the etc. The purpose is to show how powerful a Quantum Groups and Crystal Bases, Graduate contents could inspire a large community of mathematical approach is and how rich the Studies in Mathematics 42, American Math. Society, researchers. (jmlc) applications can be, as well as to show what a Providence, 2002, 307 pp., USD$49, ISBN 0- stimulating influence these sciences can have 8218-2874-6 V. P. Havin and N. K. Nikolski (eds.), for mathematics. There are about 1000 exer- This book deals with some aspects of quantum Complex Analysis, Operators, and Related cises and problems in the text (the more diffi- groups, defined as the spectra of no-commuta- Topics, Operator Theory Advances and Applications cult ones are marked), some of them solved at tive Hopf algebras given by one-parameter 113, Birkhäuser, Basel, 2000, 408 pp., DM 198, the end of the textbook. deformations of universal enveloping algebras ISBN 3-7643-6214-6 The three chapters on applications are real- of Kac-Moody algebras. In the first part, the This book is dedicated to the memory of a ly worth while: it is easy to have run through Lusztig representation theory of deformed uni- famous analyst, S. A. Vinogradov. The first ‘dry’ theory without a single application. A versal enveloping algebras is recalled. paper (by V. P. Havin and N. K. Nikolski) question then arises, as to whether readers can Chapters 4 and 5 develop the theory of crystal describes Vinogradov’s life and mathematical apply anything from what they have just bases, following the combinatorial approach of work and includes his complete list of publica- learned. The depth, width, skill and refine- Kashiwara and geometric approach of Lusztig. tions. The next two papers are English trans- ment make this book highly valuable, not only The next chapters discuss the structure of crys- lations of two of his articles (summaries of the for students of pure mathematics and students tal graphs of finite-dimensional integrable rep- main results of his Ph.D. and doctoral theses). of other areas that need it, but also for profes- resentations of deformed universal enveloping There are 27 contributed papers from various sional mathematicians and lecturers who can algebras via semistandard Young tableaux. branches of real, complex and harmonic analy- find here a lot of inspiration. Of course, we The final three chapters describe a connection sis, using points of view and methods from can hardly expect less from a book that has between representation theory of deformed functional analysis and operator theory. There attained its fourteenth edition and has thereby universal enveloping algebra of affine algebras are both survey papers and research papers, proved beyond any doubt its high standard and solvable lattices and vertex models. (pso) and one short paper is of a personal character. and popularity. (jdr) (vs) A. A. Ivanov and S. V. Shpectorov, Geometry J. W. P. Hirschfeld (ed.), Surveys in of Sporadic Groups II: Representations and H. Hedenmalm, B. Korenblum and K. Zhu, Combinatorics, 2001, London Mathematical Amalgams, Encyclopedia of Mathematics and its Theory of Bergman Spaces, Graduate Texts in Society Lecture Note Series 288, Cambridge Univ. Applications 91, Cambridge Univ. Press, 2002, Mathematics 199, Springer, New York, 2000, 286 Press, 2001, 301 pp., £27.95, ISBN 0-521- 286 pp., £50, ISBN 0-521-62349-9 pp., 4 fig., DM 109, ISBN 0-387-98791-6 00270-2 This is the second half of a two-volume set, Although Bergman spaces (spaces of square- This volume contains nine invited talks pre- which contains the proof of the classification of integrable holomorphic functions) resemble sented at the 18th British Combinatorial the flag-transitive P- and T- geometries. The the familiar Hardy space on the unit circle, Conference, held at the University of Sussex in geometries involved are those in the sense of they are much less manageable and their theo- July 2001. It also contains a memoir of C. Tits: an incidence system of subsets of different ry is still far from being complete. This book Nash-Williams, who died in January 2001, writ- types. deals exclusively with the Bergman space on ten by J. Sheehan, and the list of Nash- The existence of the geometries was estab- the unit disc and presents an exposition of the Williams’s publications. Four survey articles lished in the first volume of the treatise. The current state of the theory, including several deal with graph theory and matroids, three main theorem of the second volume consists in recent advances that took place in the 1990’s. with combinatorial designs and finite geome- the proof that the amalgam of maximal para- After introducing the basic tools and con- tries, one with computational Pólya theory, and bolics obtained from a flag-transitive automor- cepts (Bergman projections, the Berezin trans- one with the Penrose polynomial. phism group of a P- geometry or T-geometry is form, Carleson measures), the main topics dis- B. Mohar surveys classical and recent results isomorphic (as an amalgam) to the amalgam of cussed are the factorisation theory and zero related to graph minors and graphs on sur- maximal parabolics obtained from one of the divisors on the Bergman space (due to the first faces. M. Molloy discusses progress on two known cases. The book is written with obvious α author), zero sets and the growth spaces A- problems in random structures: how many care and the arguments are usually not difficult (due to the second author), interpolation and edges must be added to a random graph until to follow. The authors have also taken care sampling (the work of Seip and others), invari- it is almost surely k-colorable, and the analo- with summaries and overviews that ease under- ant subspaces of higher index and the gous question for satisfiability in the random k- standing of the general strategy of the proof. Beurling-type theorem of Aleman, Richter and SAT problem. J. Oxley writes on the interplay The only deficiency worth mentioning seems Sundberg, the construction of invertible non- between graphs and matroids (2-connected- to be the index, which contains too few items: cyclic functions (after Borichev and the first ness, removable circuits, minors and infinite it also contains no list of symbols, which means author), and the solution of the domination antichains, branch-width). D.R. Woodall that a considerable amount of time can be problem via weighted biharmonic Green func- describes results on list colorings: in the first wasted searching for the first appearance of a tions with respect to log-subharmonic weights. part he surveys mostly proper colorings, and in symbol or a notation convention. (ad) (This last result, due to Hedenmalm, the second part he gives a number of new Jakobsson and Shimorin, appears here for the proofs and conjectures on improper list color- T. Iwaniec and G. Martin, Geometric Function first time in full.) The authors deliberately ings. I. Anderson discusses results on combi- Theory and Non-linear Analysis, Oxford abstain from treating the operator-theoretic natorial designs with cyclic structure. A. R. Mathematical Monographs, Clarendon Press, aspects, thus avoiding overlap with the third Calderbank and A. F. Naguib describe applica- Oxford, 2001, 552 pp., £75, ISBN 0-19-850929-4 42 EMS March 2003 RECENT BOOKS Geometric function theory studies mappings f method of unitary dilatations. This theory and much preparation (for instance, using specific from an open set Ω in Rn to Rn. If f has inte- its later extensions to functional models (done examples instead of general notions), and has grable Jacobian J(x, f) and satisfies the distor- by Sz.-Nagy with C. Foias) provide one of the added three appendices on the homology of tion inequality |Df|n ≤ K(x) J(x, f) a.e., where K main research directions in modern operator discrete groups, classifying spaces and K-theo- is a non-negative finite measurable function theory. Other papers are devoted to further ry, and étale cohomology. Each chapter is fol- and Df is the weak gradient in the sense of parts of operator theory, such as operator lowed by exercises (some quite difficult). The Sobolev, then f is said to be a mapping of finite inequalities and orderings, spectral theory, bibliography has 134 items up to the year distortion. Such mappings appear naturally as Banach algebras and their applications to 2000. This book represents a very good intro- minima of various variational problems, or ele- physics, stochastic processes and system theo- duction into contemporary research in this ments of classes of deformations. Their topo- ry. Several papers emphasise the connections interesting field. (jiva) logical and geometric behaviour recalls the between complex function theory and operator behaviour of holomorphic functions. The first theory. I. Lasiecka and R. Triggiani, Control Theory historical step towards this theory was the gen- This book is oriented mainly to experts, but for Partial Differential Equations: Continuous eralisation from conformal to quasiconformal its scope is wide enough to show the richness of and Aproximation Theories II. Abstr. mappings. In the 1960s, Reshetnyak devel- problems and methods of operator theory to Hyperbolic-like Systems over a Finite Time oped the theory of quasiregular mappings other interested readers. (jmil) Horizon, Encyclopedia of Mathematics and its (mappings with bounded distortion). His class Applications 75, Cambridge Univ. Press, 2000, pp. of mappings allows branching, and thus pro- E. Kleinert, Units in Skew Fields, Progress in 645-1067, £60, ISBN 0-521-58401-9 vides a joint generalisation of the theory of Mathematics 186, Birkhäuser, Basel, 2000, 79 pp., This is the second part of an intended three- holomorphic functions and the quasiconformal DM 68, ISBN 3-7643-6293-6 volume treatise on the state-space approach to theory. Geometric function theory is now a sig- This book presents the theory of arithmetic quadratic optimal control theory for linear nificant part of analysis, with links to many groups. In particular, it includes a treatment partial differential equations in Hilbert state other parts of mathematics (differential geom- of unit groups of orders in skew fields, which spaces. While the first volume was devoted to etry, global analysis on manifolds, topology, are finite-dimensional and central over the parabolic-like equations yielding analytic semi- partial differential equations, calculus of varia- rational field. The goal is, in the author’s groups in abstract formulations, this second tions, and harmonic analysis). words, ‘to stimulate the interest in the topic by volume considers autonomous hyperbolic The book begins with an overview of the the- presenting a synopsis of methods and results’. equations and the Petrovski-type equations, ory. After some preliminary material, the The book starts with a description of skew and the finite-time horizon case (the infinite authors prove the generalised Liouville theo- fields, which are considered in the subsequent horizon will appear in Volume 3). A semi- rem, and then study continuity and its modulus theory. The necessary theorems on simple group approach to a control problem depends for mappings of finite distortion. The part on algebras over global fields are stated but not on regularity properties of the input-state map compactness of families of mappings of finite proved. The exposition proceeds with Hey’s – the trace regularity in the authors’ terminol- distortion is related to polyconvex calculus of theorem and Weyl’s reduction theory. The fol- ogy. variation, with results important in the theory lowing chapters touch several features of the The first chapter of this volume (actually of elasticity. As a preparation for further treat- studied groups, such as Zariski-density, the Chapter 7, since the numbering is through the ment, large parts of the theories of differential finiteness theorem of Margulis and Kazhdan’s whole treatise) contains various formulations of forms, Beltrami equations, and Riesz trans- property. The final chapters use crossed prod- this hypothesis. Chapters 8-10 study the forms are developed. The authors present the ucts and results by Tits to construct important resulting differential Riccati equation, giving Hardy estimate of the Jacobian and the examples and show some methods for finding pointwise feedback synthesis of an optimal Gehring result on reverse Hölder estimates. units. The main open problems are discussed. control, within three different frameworks, After an excursion to theory of non-linear The book is not of an introductory character, which differ by continuity or discontinuity of elliptic PDEs, they return to the theory of map- and will be appreciated mainly by researchers the input-state map and the observation oper- pings of bounded distortion and prove their in arithmetic groups and neighbouring areas. ator. These special cases come from different properties (openness, discreteness, positivity of (rb) hyperbolic-like equations: typically, Neumann the Jacobian, branching behaviour, removable boundary control and Dirichlet boundary singularities, and theorems of Picard and K. P. Knudson, Homology of Linear Groups, observation for the second-order hyperbolic Montel type). Progress in Mathematics 193, Birkhäuser, Basel, equations (Chapter 8), a coupled system of a The approach of the authors is entirely ana- 2001, 192 pp., DM 118, ISBN 3-7643-6415-7 wave equation and a Kirchhoff equation with lytical, relying on methods of PDE theory, geo- This is a highly specialised monograph point control (Chapter 9), Dirichlet boundary metric measure theory, the theory of function designed for researchers and postgraduate stu- control for the second-order hyperbolic equa- spaces and harmonic analysis. They skip the dents preparing themselves for work on the tion and the Schrödinger equation (Chapter method of moduli of curve families, which is homology of linear groups. It is well known 10). Like the first volume, this part is mainly well covered by other books. This book dis- that the main impetus for this study were the based on numerous results of the authors, on cusses all important results of the theory. higher algebraic K-groups of rings introduced both abstract and concrete equations. Notwithstanding, most of the material is new, by D. Quillen. The reader will find much important infor- at least in the degree of generality or in the In Chapter 1 the author presents results, mation on various aspects of semigroup theory methods of proof. This book makes life easier now already considered classical, on the coho- and on the regularity of solutions of hyperbol- for all mathematicians interested in quasicon- mology of the general linear groups: these are ic equations. Most of the proofs are carefully formal theory and all its generalisations, analy- linked with famous mathematicians like A. presented, but some preliminary knowledge of sis of mappings between Euclidean spaces or Borel, Dwyer, Friedlander, Lichtenbaum and PDE techniques (such as interpolation theory) manifolds, and all related areas. Even special- Quillen. Chapter 2 deals with stability results is needed. A review of the first volume ists in quite distant fields can find inspiration concerning the homology of general linear appeared in EMS Newsletter 38. (jmil) by studying the far-reaching methods here. groups: t he main result here is the important The book is well written and may comfortably theorem of W. van der Kallen. Chapter 3 then P. Lounesto, Clifford Algebras and Spinors, be read by advanced students. (jama) concentrates on the description of low-dimen- London Mathematical Society Lecture Note Series sional homology (up to dimension 3). The 239, Cambridge Univ. Press, 1997, 306 pp., L. Kérchy, C. Foias, I. Gohberg and H. main theme of Chapter 4 is groups of rank £27.95, ISBN 0-521-59916-4 Langer (eds.), Recent Advances in Operator one. Finally, Chapter 5 is a survey on results This is the second edition of a book that first Theory and Related Topics, Operator Theory concentrated around the Friedlander-Milnor appeared in 1997. It offers a systematic and Advances and Applications 127, Birkhäuser, Basel, conjecture (homology of algebraic groups detailed treatment of many topics connected 2001, 669 pp., DM 330, ISBN 3-7643-6607-9 made discrete). with Clifford algebras and the corresponding A conference in memory of B. Sz.-Nagy (1913- Reading this book requires a lot of prerequi- spinor spaces. Different parts of the book can 98) was held in Szeged in August 1999. This sites, especially from algebraic topology, group be used for different purposes. volume in the Birkhäuser series on operator cohomology, algebra and algebraic geometry. The first chapters are suitable for beginners, theory contains 35 articles, partly proceedings On the other hand, the author has succeeded starting with repetitions of complex numbers, and partly research papers by the conference in writing a lively text and has tried his best to vectors, scalar products, bivectors, exterior participants. One special article, by L. Kérchy make the reading easier, so that a reader with product and quaternions. Relevant topics and H. Langer, briefly describes the scientific possible gaps in his knowledge can proceed from theoretical physics are reviewed in the results of Sz.-Nagy, who was one of the further and is ready to learn more in order to next few sections (electromagnetic theory, spe- founders of modern operator theory. A third understand this book. He also advises a read- cial relativity, the Dirac equation, various types of the papers describe the current state of the er how to understand some notions without too of spinors, Fierz identities). Real Clifford alge-

EMS March 2003 43 RECENT BOOKS bras are introduced in the second half of the tions are discussed. There are many pho- tributes very well to this aim. (vs) book, where all their basic properties are tographs, tables, documents and a detailed bib- shown, including a discussion of Witt rings and liography. This is a really valuable book. (jfi) F. Schweiger, Multidimensional Continued Brauer groups. Matrix realisations of Clifford Fractions, Oxford Univ. Press, 2000, 234 pp., algebras, periodicity questions and the use of J. Oikkonen and J. Väänänen (eds.), Logic £70, ISBN 0-19-850686-4 Clifford numbers in the Vahlen description of Colloquium ‘90, Lecture Notes in Logic 2, A K This is a well-written monograph, written by conformal maps form the next topic. The Peters, Natick, 1993, 305 pp., US$50, ISBN 1- one of the leading experts in the field. It con- book ends with a short summary of basic facts 56881-132-2 tains a study of the properties of multidimen- from Clifford analysis, the Chevalley construc- This volume contains the proceedings (includ- sional continued fractions, which can be tion of Clifford algebras (including characteris- ing invited speakers) of the 1990 European described by fractional linear maps, together tic 2) and relations between octonions and tri- Summer Meeting of the Association for with their relations to other fields of mathe- ality. Symbolic Logic, held in Helsinki. There are matics and its applications. The author The first part of the book is elementary and eighteen papers, some of them devoted to new describes individual algorithms (due to Jacobi- can be used for undergraduate study, while the or generalised logic foundations, intuitionistic, Perron, Güting, Brun, Selmer, Poincaré, etc.) second part is more advanced and can be modal and temporal logic. Among the others and studies their periodicity and convergence warmly recommended to students or are Hintika’s ‘New foundations for mathemati- properties. There is an interesting discussion researchers interested in the topic. (vs) cal theories’ and Gabbay’s ‘Labelled deductive on the Schweiger generalisation of the Kuzmin systems: a position paper’. Other papers cover theorem to higher dimensions. The book ends K. Matsuki, Introduction to the Mori Program, further branches of mathematical logic, such as with chapters on the dimension of exceptional Universitext, Springer, New York, 2002, 478 pp., model theory, proof theory, computability the- sets (a generalisation of Good’s theorem) and 61 fig., EUR 74,95, ISBN 0-387-98465-8 ory and set theory, including Buchler and some applications. It can be warmly recom- The aim of this book is to introduce the Mori Newelski’s ‘On the geometry of U-rank 2 type’ mended to all readers interested in this diffi- programme, which can be regarded as an and Cooper’s ‘Definability and global degree cult theory. (bn) effective approach toward the biregular and/or theory’. The papers cover a wide spectrum of birational classification framework of higher- topics. (jmlc) S. Yu. Slavyanov and W. Lay, Special dimensional algebraic varieties. The first part Functions. A Unified Theory Based on of the book is devoted to the Enriques classifi- J.-P. Pier (ed.), Development of Mathematics Singularities, Oxford Mathematical Monographs, cation of algebraic surfaces in the framework of 1900-1950, Birkhäuser, Basel, 1994, 729 pp., Oxford Univ. Press, 2000, 293 pp., £65, ISBN 0- the Mori programme. Unlike algebraic curves, DM 118, ISBN 3-764-32821-5 and 0-817- 19-850573-6 in the case of algebraic surfaces there are many 62821-5 There are various ways of treating a very broad non-singular representatives in each birational To write comments on the history of mathe- field of special functions in a systematic way. equivalence class. The operations of blowing matics in the second half of the 20th century is This book uses the classifications based on sin- up and blowing down lead in two complex a difficult task, due to the enormous growth in gularities of the corresponding differential dimensions to the machine of the minimal the number of working mathematicians. The equation, and is written in a very nice and sys- model programme, producing either a mini- aim of this book is to contribute to such a pro- tematic way. mal surface or a ruled surface. The important ject with a collection of essays on evolution in Basic facts about linear second-order ordi- characterisation of the minimal model is that certain fields. nary differential equations with polynomial its canonical divisor is nef. Various features of A few contributions are devoted to the foun- coefficients in the complex plane are the Mori programme in dimension 3 or higher dation of mathematics, set theory, logic and explained in the first part of the book. This are discussed in the rest of the book. Here the topology and their applications in various includes a discussion of regular and irregular classification naturally and inevitably forces the parts of mathematics (J.-Y. Girard, J.-P. singularities, confluence and reduction extension of category of the non-singular vari- Ressayre, B. Poizat, F.W. Lawvere and S. processes, and a generalised Riemann scheme eties to the varieties with some specific singu- Sorin). Papers by E. Fouvry, M. Waldschmidt, for description of type of the considered equa- larities. The most important are the notions of J.-L. Nicolas and C. Ciliberto discuss topics tion. The next two chapters form the core of canonical and terminal singularities, together from number theory and its applications. the book, where the authors treat the classical with their logarithmic generalisations. The Graphs and their applications in other fields hypergeometric class of equations and the relation between any two of various minimal are discussed by C. Berge. Riemannian geom- Heun class of equations. A number of applica- models is that they are connected by a etry is the topic of a paper by M. Berger. A tions to problems in physics is given in Chapter sequence of flops, the codimension 2 opera- paper by M.-F. Roy surveys results in real alge- 4. In the final chapter, the authors show that tions with close connection to flips. (pso) braic geometry. Various versions of K-theory Painlevé equations of different types are Euler- are discussed by M. Karoubi. Two papers by V. Lagrange equations for quantum systems E. Menzler-Trott, Gentzens Problem. Arnold are devoted to the local theory of criti- described by different types of Heun equa- Mathematische Logik im cal points of functions and to dynamical sys- tions. Nationalsozialistischen Deutschland, tems. Relations between thermodynamics and The main aim of the book is to be a tool for Birkhäuser, Basel, 2001, 411 pp., EUR 43, ISBN chaotic dynamical systems are studied by V. practical use for applied mathematicians, 3-7643-6574-9 Baladi. B. Mandelbrot discusses questions in physicists and engineers. It offers a very sys- This is the most extensive and detailed biogra- fractal geometry. A review by J. Dieudonné is tematic treatment, without too many proofs, phy of Gerhard Gentzen (1909-45), based on devoted to mathematics during the last 50 and can be complemented by software that is an enormous number of documents, extracts years in France, while one by V. M. Tikhomirov available separately. The book has a lot of from correspondences, personal recollections discusses Moscow mathematics in this period. helpful pictures, diagrams and tables. (vs) and communications, reviews of Gentzen’s A paper by M. Smorodinsky treats questions in papers, and Gentzen’s reviews of papers of information theory, and I. Chalendar and J. I. J. Sobey, Introduction to Interactive other logicians – all carefully reproduced and Esterle discuss some questions in functional Boundary Layer Theory, Oxford Applied and commented on. It also partially elucidates his analysis. Fourier analysis is treated by P.L. Engineering Mathematics 3, Oxford Univ. Press, last days: his arrest in May 1945 in Prague and Butzer, J.R. Higgins and R.L. Sten, and 2000, 332 pp., £45, ISBN 0-19-850675-9 his death in prison in August 1945. The devel- wavelets by S. Jaffard. PDEs are discussed by J. This book is devoted to a better understanding opment of his proof theory and natural deduc- Sjöstrand and R. Temam (microlocal analysis, of the laminar steady plane flows of a tion are discussed at length. The book also Navier-Stokes equations). The calculus of vari- Newtonian fluid in the presence of the bound- contains three Gentzen’s lectures on the con- ation is the topic of a paper by F.H. Clarke. ary. Due to two-dimensional geometries, the cept of infinity, the consistency of mathematics, Several complex variable theory and plurisub- flow is described by the stream function which and the foundations of mathematics (pub- harmonic functions are discussed by P. is then constructed via asymptotic expansions lished, but not easily available), and an Dolbeault and C. Kiselman. Random process- (matched asymptotic analysis techniques). In Appendix gives a concise introduction to the es, branching processes, Brownian motion, particular, the triple deck method proves to be proof theory, written by Jan von Plato. All this random walks, statistics and stochastic analysis a useful tool in understanding the behaviour of is embedded in the general political and ideo- are treated by P.-A. Meyer, M. Yor, J.-F. Le fluid near the points of laminar separation. logical situation in Germany during the Gall, Y. Guivarc’h, K.D. Elworthy, G.R. The following special flowsare studied in national-socialistic regime. The history of the Grimmett, L. Le Cam and B. Prum. The book detail: flow around a flat plate (infinite or relationship between logic and mathematics on concludes with interviews with A. Douady, M. finite), external flow about a circular cylinder, one hand, and politics and ideology on the Gromov and F. Hirzebruch, and various bibli- and flows in (symmetric and asymmetric) chan- other, is carefully described and well docu- ographic and other data. It is important to nels; the historical development of each prob- mented, and general philosophical implica- know our own history, and this book con- lem is underlined. From the point of view of

44 EMS March 2003 RECENT BOOKS mathematical analysis of fluid mechanics equa- The book under review has no such weakness, said this, a reader who is willing to put in some tions, the content of the book is closely related and in my opinion the way the material is pre- effort will obtain an explanation of the ideas, to an interesting open problem: whether in two sented is ‘limiting’ in the following sense: if any methods and main results in Fourier analysis spatial dimensions the solutions of the Navier- mathematical author were given the same during the last three decades, including the Stokes equations subjected to the no-slip amount of information to be covered, it would ground-breaking duality result of C. boundary conditions converge, as the viscosity be a very hard challenge (if not impossible) to Fefferman. In an introductory section, there is vanishes, to the solution of Euler equations write a better text. The mathematical ideas are a graphical description of the cross-depen- with zero normal component of the velocity on exposed in a witty, reader-friendly, narrative dence of the sections, as well as advice as to the boundary. This book provides various style which makes reading of the book a very which of the sections might be safely skipped physical/engineering/historical insights on this pleasant experience. All the important results, by the reader. The book has 28 sections, an topic. (jomal) deep as they are, are followed by a thorough appendix, and an impressive list of references, discussion of the subject, putting it into histor- including an (even more impressive) list of sig- R. P. Stanley, Enumerative Combinatorics, 2, ical context and revealing plenty of links to nificant contributions by the author, published Cambridge Studies in Advanced Mathematics 62, other, often seemingly distant, areas – links in first-class journals. The introduction is well Cambridge Univ. Press, 1999, 581 pp., £45, ISBN that would probably be overlooked otherwise. written, giving a perfect description of what 0-521-56069-1 Occasionally, alternative proofs are given in should be expected from the subsequent text, The book is a continuation of Volume 1 (1986), order to improve the reader’s insight into the and also presenting a brief and very useful starting with Chapter 5 (Trees and the compo- subject. The historical context is often com- introduction to the world of Hardy spaces. sition of generating functions) and continuing plemented by a touch of geography; the author The first thirteen chapters contain several with Chapter 6 (Algebraic, D-finite, and non- has an impressive knowledge of both western characterisations of the Hp spaces, including commutative generating functions) and and eastern, mainly Russian, literature. The those involving certain special convolution Chapter 7 (Symmetric functions). The final reader can thus learn more about the well- operators, culminating with the perhaps most chapter has two appendices on Knuth equiva- known fact that many important results pub- notorious one (on the real line), which involves lence, jeu de taquin, and the Littlewood- lished in Russian journals passed unnoticed, the Hilbert transform. Within the material lie Richardson Rule (by S. Fomin) and the charac- only to be rediscovered independently in the deep sophisticated methods developed since ters of GL(n, C)). Each chapter has its own set West a few years later. These parts of the book the 1970’s, including the arguments, now con- of exercises with solutions – altogether 261 of are of independent interest, even for a non- sidered classical, which employ all kinds of them, but in fact many more when subexercis- mathematician. variations on maximal operators, atomic es are counted. The references to these and The main theme of the book is a constructive decomposition, Hardy-Littlewood-Fefferman- the bibliographies to the chapters constitute a approach to function spaces (here called the Stein inequalities, good λ-inequalities, subhar- giant survey of the literature on enumerative ‘Weierstrassian approach’) and its applications. monicity of functions, basic concepts of the combinatorics. Some parts of the book might be considered a Littlewood-Paley theory, and much more. The What else can be added to the comments continuation of the author’s earlier book characterization of a Hardy space on a real line upon this excellent book? Perhaps a quotation Fractals and Spectra, but in general the book is by the Hilbert transform is a point of departure from G.-C. Rota’s foreword: ‘Every once in a self-contained. As the author assures us in the for the analysis that follows, aimed (among long while, a textbook worthy of the name preface, the four chapters of the book are plenty of other things) at a generalisation of comes along; (...) Weber, Bertini, van der devoted to the study of links between quarko- this result to a higher-dimensional situation: Waerden, Feller, Dunford and Schwartz, nial decompositions of functions on one side, this material can be found in the subsequent Ahlfors, Stanley.’ The paperback edition con- and three other contemporary topics (sharp fourteen sections (14-27). The last eight sec- tains a new short section with errata and inequalities and embeddings, fractal elliptic tions (21-28) contain the main results of the addenda to some of the exercises. (mkl) operators, and regularity theory for certain book, connected with the decomposition of semi-linear equations) on the other. The BMO due to Fefferman and Stein. The author J. Tanton, Solve this: Math Activities for author states that the book is based on recent gives a constructive proof of this result that Students and Clubs, Classroom Resource research carried out by him and his co-work- enables him to obtain surprisingly deep exten- Materials, Math. Assoc. of America, Washington, ers. One would have therefore thought that sions. (lp) 2001, 218 pp., £20.95, ISBN 0-88385-717-0 the book is more a scientific monograph than, This is a collection of problems and exercises say, a textbook for Ph.D. students, but the book V. I. Voloshin, Coloring Mixed Hypergraphs: from recreational mathematics, and is divided is so well written that it can also be a good aid Theory, Algorithms and Applications, Fields into three parts. Thirty chapters in Part I con- for an interested reader who might not be an Institute Monographs 17, American Math. Society, tain many funny and interesting problems, expert in the field of function spaces but who is Providence, 2002, 181 pp., $49, ISBN 0-8218- from sharing a pile of candies, via ‘interesting’ willing to spend a little effort to study this won- 2812-6 surfaces and turning one’s T-shirt inside out derful and interesting book. (lp) This book is a collection of results (obtained with one’s hands clasped together, to map mostly by Vitaly Voloshin himself) on a new colouring and chessboard problems. Parts II A. Uchiyama, Hardy Spaces on the Euclidean type of hypergraph colouring, the so-called and III then contain hints, solutions, further Space, Springer Monographs in Mathematics, ‘mixed hypergraphs’. A proper vertex-colour- thoughts and further reading on the problems Springer, Berlin, 2001, 305 pp., DM 171, ISBN ing of a given mixed hypergraph must respect of Part I. This book is accessible to anyone 4-431-70319-5 two types of opposite constraints: some of the interested in recreational mathematics. (ab) This book is based on a typewritten manuscript edges must not be monochromatic, while some completed by Akihito Uchiyama in 1990. The of the edges must not be rainbow. H. Triebel, The Structure of Functions, author died prematurely in 1997 before he Mixed hypergraphs were introduced by the Monographs in Mathematics 97, Birkhäuser, Basel, could publish the material, and several of his author in 1992, and since then the field has 2001, 422 pp., DM 196, ISBN 3-7643-6546-3 friends and colleagues then proceeded with grown significantly and many interesting con- For more than the past three decades, books by the publication. Through their efforts the nections to other colouring problems have Prof. Hans Triebel of Jena have been land- book is now available for a broad mathematical been discovered; the last chapter of the book is marks of the theory of function spaces, differ- public. devoted to these connections. In some aspects, ential operators and interpolation, which An excellent preface should not be skipped colouring mixed hypergraphs is analogous to nobody seriously interested in the area could by the reader. It is a witty, moving and clever- the usual colouring, while in others it is com- possibly dream of overlooking. They formed ly written essay which takes us to early-1980s pletely different – for example, there exists a an important part of the literature that I was Chicago when Fourier analysis was undergoing mixed hypergraph on six vertices that can be advised to study as a research student almost a stormy development and an impressive coloured with two and four colours but has no twenty years ago, and still appear among the group of the world’s top superstars in the area proper coloring with exactly three colours. recommendations to my own students nowa- were gathered there (A. Calderón, A. The field is developing so rapidly that the days. These books have always been well Zygmund, R. Fefferman, F. Browder, W. author could not include some recent results, known for the precise way in which they are Beckner, to name just a few). The description and several problems listed as open have since written, for the incredible amount of informa- of the atmosphere is very convincing. been solved. tion they contain, and for the original style of The book is devoted to the study of Hardy The book is self-contained and very read- exposition (recall the ‘Steps’ of proofs, to name spaces by real-variable methods. The text is able. It is clearly organised: each of the twelve just one example). Over the years, I have seen clearly meant more as a scientific monograph chapters is devoted to a single concept or a sin- only one objection that could possibly be made than, say, as lecture notes for beginners: the gle class of mixed hypergraphs. Anybody inter- about the author’s style, that certain parts of exposition is rather technical and does not ested in graph or hypergraph colouring will one book or another are a bit difficult to read. contain too much verbal explanation. Having find this book interesting. (dkr)

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