Finnish Mathematical Society

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 STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 32 DK2800 Lyngby, Denmark e-mail: [email protected] June 1999 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University Reymonta 4 30-059 Krakow, Poland EMS News ...... 2 e-mail: [email protected] KATHLEEN QUINN Editorial by EMS Vice-President, Luc Lemaire ...... 3 Open University [address as above] Note from the Editor ...... 4 e-mail: [email protected] SPECIALIST EDITORS Introducing the Committee : part 2 ...... 5 INTERVIEWS Steen Markvorsen [address as above] EMS Executive Committee Meeting ...... 6 SOCIETIES Krzysztof Ciesielski [address as above] Ian Stewart: Making the Magical Maze ...... 7 EDUCATION Vinicio Villani Interview with Helmut Neunzert (Kaiserslautern) ...... 10 Dipartimento di Matematica EMS Summer Schools : Call for proposals ...... 11 Via Bounarotti, 2 56127 Pisa, Italy 1999 anniversaries: Felix Klein, Sophus Lie and Wolfgang Krull ...... 12 e-mail: [email protected] MATHEMATICAL PROBLEMS Letters ...... 14 Paul Jainta Werkvolkstr. 10 Societies: Finnish Mathematical Society ...... 16 D-91126 Schwabach, Germany e-mail: [email protected] Societies: Polish Mathematical Society ...... 17 ANNIVERSARIES June Barrow-Green and Jeremy Gray Problems Corner ...... 19 Open University [address as above] Forthcoming Conferences ...... 23 e-mail: [email protected] and [email protected] and Book Review ...... 28 CONFERENCES Kathleen Quinn [address as above] Recent Books ...... 29 RECENT BOOKS Ivan Netuka and Vladimir Souèek Mathematical Institute Designed and printed by Armstrong Press Limited Charles University Unit 3 Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK Sokolovská 83 phone: (+44)-23-8033 3132; fax: (+44)-23-8033 3134 18600 Prague, Czech Republic Published by European Mathematical Society e-mail: [email protected] and [email protected] ISSN 1027 - 488X ADVERTISING OFFICER Martin Speller NOTICE FOR MATHEMATICAL SOCIETIES Department of Mathematics Labels for the next issue will be prepared during the second half of August. Glasgow Caledonian University Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, Glasgow G4 0BA, Scotland P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: [email protected] e-mail: [email protected] OPEN UNIVERSITY PRODUCTION INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, TEAM Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: Daniel Dubin, Kathleen Quinn, Liz Please include the name and full address (with postal code), telephone and fax number (with coun- Scarna try code) and e-mail address. The annual subscription fee (including mailing) is 60 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS June 1999 1 EMS NEWS EMS News: Committee and Agenda EXECUTIVE COMMITTEE PRESIDENT (1999–2002) EMS Agenda Prof. ROLF JELTSCH Seminar for Applied Mathematics 1999 ETH, CH-8092 Zürich, Switzerland e-mail: [email protected] 28 June – 6 July VICE-PRESIDENTS EMS Summer School, jointly with CIME, at Martina Franca (Italy) in Prof. ANDRZEJ PELCZAR (1997–2000) Pure Mathematics: Iwahori-Hecke algebras and representation theory Institute of Mathematics Jagellonian University contact: V. Baldoni (Rome), e-mail: [email protected] Raymonta 4 15 August PL-30-059 Krakow, Poland Deadline for submission of material for the September issue of the EMS e-mail: [email protected] Prof. LUC LEMAIRE (1999–2002) Newsletter Department of Mathematics contact: Robin Wilson, e-mail: [email protected] Université Libre de Bruxelles C.P. 218 – Campus Plaine 6 – 21 September Bld du Triomphe EMS Summer School at Heidelberg, Freiburg, Karlsruhe, Stuttgart, B-1050 Bruxelles, Belgium e-mail: [email protected] Tübingen (Germany) and Zürich (Switzerland) in Applied Mathematics: SECRETARY (1999–2002) Numerical simulation of flows Prof. DAVID BRANNAN Department of Pure Mathematics organiser: University of Heidelberg The Open University contact: Gabriel Wittum, e-mail: [email protected] Walton Hall 30 September Milton Keynes MK7 6AA, UK e-mail: [email protected] Deadline for submission of proposals for the 2001 EMS Summer Schools TREASURER (1999–2002) contact: Rolf Jeltsch, e-mail: [email protected] Prof. OLLI MARTIO Department of Mathematics 9 – 10 October P.O. Box 4 Executive Committee Meeting, hosted by the ETH, Zürich (Switzerland) FIN-00014 University of Helsinki Finland 15 November e-mail: [email protected] ORDINARY MEMBERS Deadline for submission of material for the December issue of the EMS Prof. BODIL BRANNER (1997–2000) Newsletter Mathematical Institute contact: Robin Wilson, e-mail: [email protected] Technical University of Denmark Building 303 December DK-2800 Lyngby, Denmark e-mail: [email protected] Second announcement of the Third European Congress of Mathematics Prof. DOINA CIORANESCU (1999-2002) (3ecm), Barcelona (Spain) Laboratoire d’Analyse Numérique contact: S. Xambó-Descamps, e-mail: [email protected] Université Paris VI 4 Place Jussieu website: www.iec.es/3ecm/ 75252 Paris Cedex 05, France e-mail: [email protected] 3 – 4 December Prof. RENZO PICCININI (1999–2002) Diderot Mathematical Forum, Mathematics and music, in Lisbon Dipto di Matem. F. Enriques (Portugal), Paris (France) and Vienna (Austria) Universit à di Milano Via C. Saldini 50 contact: Mireille Chaleyat-Maurel, e-mail: [email protected] I-20133 Milano, Italy e-mail: [email protected] 2000 Prof. MARTA SANZ-SOLÉ (1997–2000) Facultat de Matematiques 25 – 26 March Universitat de Barcelona Gran Via 585 Executive Committee Meeting, hosted by the Polish Mathematical E-08007 Barcelona, Spain Society and the Institute of Mathematics of the Polish Academy of e-mail: [email protected] Sciences, Bedlevo, near Poznañ (Poland) Prof. ANATOLY VERSHIK (1997–2000) P.O.M.I., Fontanka 27 3 – 7 July 191011 St Petersburg, Russia e-mail: [email protected] ALHAMBRA 2000: a joint mathematical European-Arabic conference in EMS SECRETARIAT Granada (Spain), promoted by the European Mathematical Society and Ms. T. MÄKELÄINEN the Spanish Royal Mathematical Society Department of Mathematics P.O. Box 4 contact: Ceferino Ruiz, e-mail: [email protected] FIN-00014 University of Helsinki website: www.ugr.es/~ruiz/ Finland tel: (+358)-9-1912-2883 10 – 14 July fax: (+358)-9-1912-3213 Third European Congress of Mathematics (3ecm) in Barcelona (Spain) telex: 124690 e-mail: [email protected] contact: S. Xambó-Descamps, e-mail: [email protected] website: http://www.emis.de website: www.iec.es/3ecm/ 2 EMS June 1999 EDITORIAL Editorial by EMS Vice-President Luc Lemaire The 5th RTD Framework Programme of the European Commission

The EMS and the EU that level requires some European invest- it is expected that the following will At the end of this editorial, you will find a ment, but not so much as to make it a become so during 1999: Iceland, practical guide to the various ‘Calls for hopeless task. The EMS must and will con- Liechtenstein, Norway (as EFTA–EEA Proposals of the European Commission’ tinue to play its role in that endeavour. members), and Bulgaria, the Republic of (Networks, Marie Curie Fellowships, Cyprus, the Czech Republic, Estonia, Conferences, ...), but before getting there I Hungary, Latvia, Lithuania, Poland, would like to describe briefly some interac- Romania, Slovakia and Slovenia (as candi- tions between the EMS and the European dates for EU membership). For Institutions over the years. Switzerland, the negotiations are finalised. At the founding meeting of the EMS in For these countries, applications are 1990, the Council created a Committee for evaluated in the same way as for the others, relations with the European Union (which but granting of the contract is conditional was the European Community at the time), on the agreement’s coming into force recognising the importance of interaction before the contract’s commencement. with that institution. I happened to be pre- Other countries can participate without sent as representative of the Belgian EU funding on a project by project basis, if Mathematical Society, and an Italian col- they contribute to the level of the proposal league suggested that it might be conve- (for all this, see the website http://www. nient if somebody living in Brussels were to cordis.lu/fp5/src/3rdcountries.htm). be a member of that Committee. This off- Marie Curie Fellowships hand remark was for me like a small per- These come in six categories. turbation of a chaotic system: being the (1) Individual Fellowships only Brussels-based member of the These fellowships are awarded to young Council on that day sent me to a quickly post-doctoral researchers for high-level increasing involvement with the EMS and training in an institution established in a the EU. country other than their own. Both the fel- Common aims low and the institution must belong to the It is quite natural that the EMS looked for EU or to an Associated State. For the fel- such an interaction with the EU. Indeed, The Calls for Proposals, a practical guide low, it could be by nationality or by resi- both aim at adding a European dimension The Calls for Proposals can be found on dence for at least five years. The age limit to national programmes, without replacing the web server of the European for the fellow is 35 (except for some specif- them. Thus all programmes of the DGXII Commission’s DGXII. In the middle of the ic cases such as military service or child (in charge of research at the EU) must home page, you can find a list of subjects care). involve more than one member state, so as that evolves quite rapidly, and the most Such an appointment would be for a not to repeat simply what individual states important one at this stage for mathemat- duration of 12 to 24 months. The propos- do. Likewise, the EMS does not replace the ics is the Improving Human Potential al must be introduced by the candidate 52 regional societies that it represents. Programme Call for Proposals – and include the agreement of the host The action of the EMS towards the EU 16.03.1999. Clicking there, you find a list institution, a work project and a letter of (accomplished by many people over many of eight subprogrammes. Clicking on each recommendation. Personally, I think the years) aims at establishing a two-way com- of these, you’ll find a long array of docu- panel examining the application would be munication: on the one hand to inform ments to download, sometimes with rather happy to have 2 or 3 letters instead of one. mathematicians of the EU programmes, cryptic titles: Guide for proposers, infor- It is obvious that to prepare such an appli- and on the other to inform the EU officials mation, proposal forms, guidelines, cation, serious contacts must have been of the specifics of mathematical research in annexes, guide for evaluators, call for pro- established between the fellow and the sci- Europe. posals, call text, work programme, ... entist in charge in the host institution, in Altogether there are a few hundred pages order to write a good project. A declaration of the EMS of reading, luckily with some tables of con- The first deadline for applications has On that last point, the EMS has prepared a tents. You really should browse through already passed, but others will follow more detailed declaration (to be found on the those, fishing for relevant information. or less every six months (in March and website http://www.emis.de/etc/declaration. Here is a brief summary of programmes September until March 2002). The precise html), showing the specific needs of mathe- that may concern mathematicians directly. dates can be checked in the Guide for matical research in the context of the EU Proposers or the Work Programme on aims of economic and sociologic develop- Member States and Associated States http://www.cordis.lu. Watch out because the ment. The specific purpose of that declara- First, a major new aspect of the pro- deadlines are strict, and because it takes tion was to influence the structure of the gramme: it will not be restricted to the fif- some time to prepare a good proposal – Fifth RTD Framework Programme of the teen countries of the European Union, but both from the scientific and administrative EU which started recently. This text is will involve the Associated States, namely points of view (two months is certainly not however still of interest, since the argu- those outside the EU who have a participa- too much). ments it presents are quite general and tion agreement in the research pro- (2) Return Fellowships apply to other decision-making bodies. grammes. These states contribute to the These fellowships are to help Marie Curie European research in mathematics is at research budget and their citizens can be fellows from a less favoured region (LFR) the highest level, both in the West and in full partners in the programme. to return to a LFR in their own country at the East of the continent. To maintain it at So far, Israel is an Associated State, and the end of their two years fellowship. The EMS June 1999 3 EDITORIAL duration of a return fellowship is limited to this programme to further develop the Raising Public Awareness 12 months. level of Zentralblatt-MATH, as a unique The objective of this programme is to (3) Experienced Researchers’ Fellowships European tool for all mathematicians. The bridge the gap between science and the These fellowships can be awarded to high aim of the application is a general public, thereby enabling citizens to under- level researchers for transfer of knowledge improvement of access, search facilities stand the effects of scientific research on between industry and academia or towards and global production of the reviews. The their lives. This will be done through four institutions in a LFR of the Community, first deadline for applications has passed. types of action (an indicative timetable is for a period between 3 and 12 months. given on Cordis): High-level Scientific Conferences (4) Industry Host Fellowships – cooperative networks to promote best This obviously concerns most of us. The Here, registered companies apply to practice in the raising of public awareness variety of allowable conferences has become host institutions, and then choose of science increased, and we find the following cate- and appoint postgraduate and postdoctor- – round table meetings gories: al fellows to work in their research groups. – the organisation of a ‘Science and Euroconferences (up to 5 days and up to 100 Appointments are in two stages, and for Technology Week’ participants) the moment the call is open for companies. – provision of science-related information Euro Summer Schools (training for young Those selected will be able to call for appli- via electronic networks and other means. researchers for up to 2 weeks and up to 80 cations from fellows later. As we all know, a number of mathemati- participants – these may be held at any (5) Development Host Fellowships cians around the world have in recent time of the year!) These fellowships are awarded to institu- decades begun a great effort to popularise Euroworkshops (up to 2 weeks and up to 30 tions in a LFR, who (when selected) can their science, realising that it is both neces- participants) call for applications by fellows. sary and possible – in particular, to encour- Large conferences (funding being reserved (6) Stays at Marie Curie Training Sites age gifted young students to enter mathe- for young researchers, in conferences of This scheme will support short stays by matics programmes. Most of the activities more than 100 participants). young researchers pursuing doctoral stud- planned for Mathematical Year 2000 go in Ph.D. Euroconferences (completely organ- ies in training sites in a country other than this direction. In fact, the EMS has sent an ised and handled by young scientists) their own. Again, the potential sites will application to the EU, in the framework of Eurotron Conferences (meetings in apply to the EU, and those selected will be the Science Week that will take place dur- Cyberspace via the internet). able to choose the visitors. ing year 2000, in particular to support a The deadlines for the reception of propos- For the last two categories, a call for campaign of mathematical posters in the als are 1 February 2000, 2001 and 2002. proposals is announced in June, with a public transportation system of many deadline of 13 October 1999 (to be con- European cities. firmed). This call concerns the potential training sites; the fellows apply later. Research Training Networks A Research Network consists of at least five Note from the Editor groups in at least three different states, proposing a programme of joint research and training of doctoral and postdoctoral Thankyou to those of you who wrote to me concerning fellows. The idea is to have a fairly expen- the new format of the Newsletter. Please continue to send sive project, where typically each group me comments for improvement and suggestions for will fund a fellow for the entire time. The upper financial limit is 1.5 million euros! items to include. I am particularly keen to receive sug- However, there is no minimum, and we gestions for feature articles and for interviews. shall observe in the first round of applica- The articles on the Turner Collection in the last issue tions (for which the deadline has past) whether smaller sums are sometimes allo- produced a lively postbag. Please send me letters on cated. anything that you think would be of interest to EMS The only other call for proposals is readers. announced for June 2000, with a deadline of 4 November 2000 (to be confirmed). In the next issue I should like to start a ‘Personal col- This seems far away, but to set up a good umn’ containing items of a personal nature – promo- Network project takes time and many pre- tions, awards, brief obituaries, and so on. Please could liminary contacts. Important criteria in the choice will be you send me items for inclusion. I have started to build scientific level (of course), actual plans for up a list of ‘country representatives’ who can help with interactions and training contents of the this task. If you would like to be such a representative, project. please contact your local society and let me know. Access to Research Infrastructure I should also like to start a series on ‘Looking back’, A research infrastructure is here a top-level European facility to which researchers of in which distinguished retired mathematicians are all countries would want to gain access. interviewed about their mathematical life, their The programme aims both at directly achievements, colleagues, and views about how the sub- funding the visit of scientists, and at research and development of the infra- ject has developed. Please send me suggestions for pos- structure to improve access. sible interviewers and interviewees. The EMS, together with a number of Robin Wilson partners, has introduced an application in

4 EMS June 1999 EMS NEWS Introducing the Committee : part 2

Olli Martio (Treasurer) received his Ph.D. from the University of Helsinki in 1967, and became an associate professor there in 1972, a professor at the University of Jyvaskyla in 1980, and since 1993 has been Head of the Mathematics Department at Helsinki. He has been a visiting professor in the U.S.A., Norway and Spain, and has been an editor of Mathematica Scandinavica and Acta Mathematica; he currently edits the Finnish journal Ann. Acad. Sci. Fenn. Math. His research interests include function theory (quasi-conformal maps), non-linear potential theory and associated partial differential equations. He has organised several conferences and edited nine international conference proceedings. In addition to holding various positions in the Finnish Mathematical Society, he has been 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 EU Scientific Panels for Mathematics. He is an honorary doctor of the Linköping Institute of Technology and the University of Volgograd.

Doina Cioranescu is directeur du recherche at the Centre National de la Recherche Scientifique (CNRS), Laboratoire d’Analyse Numérique Paris VI from 1981. She graduated from the University of Bucharest in partial differential equations in 1966, and became associate researcher at the CNRS in 1971, receiving her Doctorat d’État in 1978 at Université Paris VI. Her research interests are mainly concentrated on the modelling of non-Newtonian fluids, homogenisation theory (in particular applied to perforated domains and reticulated structures), and control problems in heterogeneous media. She has been involved in several international scientific projects, including being scientific coordinator of the CE Eurohomogenisation Science programme. Since 1997 she has been a member of the management committee of the French Society of Applied Mathematics.

Renzo Piccinini received his Ph.D. in algebraic topology from the University of Wisconsin (Madison, USA). He is currently professor of mathematics at the Università di Milano-Bicocca in Milan, having formerly been a professor of mathematics in Newfoundland. He has also been a long-term visitor in Lille, Zürich and Munich. In 1969–70 he was Secretary-General of the Sociedade Brasiliera de Matematica. While in Canada he became Vice-President of the Canadian Mathematical Society (1977–79), Editor-in-Chief of the Canadian Mathematical Bulletin (1980–83) and President of the Canadian Mathematical Society (1983–85). He is currently Executive Vice- President of the Istituto Nazionale di Alta Matematica (Rome).

Anatoly Vershik is a professor in the mathematics department at St Petersburg State University, where he has been since 1962. He travels widely, having recently held visiting appointments in France, Israel, Austria, the USA, the UK, Canada, Italy, Switzerland and Sweden. His fields of research range from ergodic theory and representation theory to combinatorics, differential and convex geometry, probability theory and mathematical programming. He was an invited speaker at the International Congresses of Mathematics in Vancouver (1974) and Zürich (1994), on dynamical systems and combinatorics, respectively. He is a member of the editorial board of many journals, including Russian Mathematical Surveys, Functional Analysis and its Applications, Dynamical Systems and Control Theory, and Algebras and Representation Theory. He is currently President of the St Petersburg Mathematical Society.

Andrzej Pelczar (Vice-President) received his Ph.D. from the Jagiellonian University, Kraków, Poland, in 1964. He has held various positions at this university, including Professor of Differential Equations (since 1981), Director of the Institute of Mathematics (1981–84 and 1987–90), Vice-Rector (1984–87) and Rector of the University (1990–93). He has held visiting positions in France and Nigeria. He was President of the Polish Mathematical Society from 1987–91, was one of the founder members of EUROSCIENCE, and is currently Chairman of the General Council of Higher Education in Poland. He has been on the Executive Committee of the EMS since 1993.

EMS June 1999 5 EMS NEWS mat from previous issues, and agreed to EMS Executive Committee Meeting circulate complimentary copies of the next few issues fairly widely in order to encour- in Barcelona, Spain, 17 – 18 April 1999 age mathematicians to join the EMS. The question of whether EMS should A weekend meeting, hosted by the Institut Centre, where all the activities of 3ecm will become a publishing house was discussed, d’Estudis Catalans, was held in Barcelona take place. The visitors expressed their and a small committee was set up to inves- on 17-18 April 1999. Committee members appreciation and satisfaction with the tigate the options. present were Rolf Jeltsch, Andrzej Pelczar, arrangements proposed. Barcelona is an Luc Lemaire, David Brannan, Olli Martio, attractive historical city with excellent air Summer Schools and Diderot Fora Bodil Branner, Doina Cioranescu, Renzo and rail connections throughout Europe, Financial support to the two 1999 EMS Piccinini, Marta Sanz-Solé and Anatoly and the city centre has easy rail and bus summer schools was agreed, to be used as Vershik. Others present by invitation were: access from the airport. It is an excellent a guarantee to support students. Two pro- Tuulikki Mäkeläinen, Jean-Pierre venue for the congress!] posals for Summer Schools in 2000 were Bourguignon, Carles Casacuberta, Mireille A bid for the 2004 European Congress approved – one in Saint-Flour (P. Bernard) Chaleyat-Maurel, Berndt Wegner, Sebastià of Mathematics (ECM4) has been received; and one in Edinburgh (E. Somersalo). A Xambó-Descamps and Manuel Castellet a Site Committee was appointed to inspect call for proposals for EMS Summer (President of the Institut d’Estudis the venue and report to the October Schools to be held in 2001 should be in the Catalans). Executive Committee meeting. June Newsletter (see page 11) and EMIS. It Among the items discussed were the fol- was felt important that summer schools lowing: Projects should move around Europe. The Committee discussed the project Progress reports were received on the Officers’ reports MPRESS (Mathematical PREprint Server Diderot Mathematical Fora on The Treasurer reported that the reserves System) in which a search engine looks at ‘Mathematics and Music’ and on had reached a very satisfactory level (about mathematics preprints held on different ‘Telecommunications’. Planning for these 100000 euros), so that some would be servers, and a project EMPRESSA to col- is progressing well, and bids for external invested in longer-term funds. The budget lect and make available articles of general funding are in hand. Possible future for each of 1999 and 2000 was agreed. The interest to member societies themes for Diderot Mathematical Fora financial statement for the year 1998 was The EMS has signed a contract with the include mathematics and medicine, safety accepted and signed. 1000 euros were European Commission on the project in cars, and mathematics and risk. given to the Committee for the Support for ‘Reference levels in school education in Eastern and Central European mathematics’. (An account of this project Future Committee meetings Mathematicians to support attendance at will appear in a forthcoming Newsletter.) The next meeting of the Executive the EMS lectures in 1999. The Committee approved a Memorandum Committee will be in Zürich on 9 – 10 The fees for several member societies of Understanding between various October 1999. The following meeting will were waived or reduced for one year, in prospective partners covering the be in Bedlewo (near Poznañ) in Poland on view of their financial situation. Jahrbuch project. 25 – 26 March 2000. Arrangements were agreed for GAMM And finally ... individual members to join EMS directly Bids It was agreed to bid to the EU programme The Executive Committee expressed its for a trial period. heartfelt thanks to the local Catalan organ- The International Mathematical Union on ‘Public Understanding of Science’ for cooperation networks to compare good isers for a smooth organisation and hospi- is considering the EMS application for tality enjoyed by all. affiliate IMU membership. practice in the public understanding of sci- The Publicity Officer reported on the ence. A bid for cooperation between the present state of the plans for the year EMS and UNESCO-Venice for summer 2000. There will be a new resolution of schools had been made. UNESCO on WMY2000 at the UNESCO By the end of May, Zentralblatt-MATH Journal of the European would finish a project to prepare scanned General Conference in November. (The Mathematical Society EMS has a poster competition in progress page images of back numbers for the inter- for WMY2000.) net. An application to the EU 5th The first issue of this EMS journal Jean-Pierre Bourguignon was elected Framework Programme (via the large appeared in January 1999. The contents Chair of the EMS Committee on Special infrastructures programme of DGXII) for of the first two issues are given below; fur- Events. A Group on Relations with Zentralblatt-MATH was being finalised. ther information can be obtained by e-mail: European Institutions was appointed; this Consortia have been formed in several [email protected] will include Rolf Jeltsch (Chair), Luc countries to share the costs of subscribing Lemaire, Jean-Pierre Bourgignon, Mireille to Zentralblatt, and the possibility of indi- Volume 1, Number 1 Chaleyat-Maurel and M. Brunaud. viduals subscribing to Zentralblatt is under J. Jost, Editorial discussion. V. V. Batyrev, Non-Archimedean inte- Congresses Publishing matters grals and stringy Euler numbers of S. Xambó-Descamps reported on the log-terminal pairs preparations for the 2000 European The Committee agreed to a Memorandum of Understanding with The General M. Kurihara, On the ideal class Congress of Mathematics (3ecm) in groups of the maximal real subfields Barcelona. The first announcement of Assembly of the Union Matematica de America Latina y el Caribean (UMALCA) of number fields with all roots of unity 3ecm had been sent out and also appears A. Gamburd, D. Jakobson and P. in EMS Newsletter 31 and on EMIS, the for cooperation to improve the availability and accessibility of the services of Sarnak, Spectra of elements in the EMS web server. The second announce- group ring of SU(2) ment will be sent out in December 1999. Zentralblatt-MATH in Latin America and the Caribbean. L. Polterovich, Hamiltonian loops Some financial support will be available to from the ergodic point of view aid the travel of young mathematicians The first issue of JEMS, the Journal of the from Eastern and Central Europe to attend European Mathematical Society, was circulated and noted with pleasure; it is important Volume 1, Number 2 the Congress. A Colloquium on Lie Theory M. Gromov, Endomorphisms of sym- in Vigo, Spain, was added to the list of that members support subscriptions to JEMS. bolic algebraic varieties satellite meetings. [On the evening of 16 M. Burger and N. Monod, Bounded April several members of the Executive The Committee expressed its satisfaction at the March issue of the EMS cohomology of lattices in higher rank Committee visited the venue of the ECM Lie groups Congress, the Barcelona Conference Newsletter, which is in a rather different for- 6 EMS June 1999 FEATURE Making the Magical Maze: preparing the Royal Institution lectures Ian Stewart On the back of the current British £20 note My intimate acquaintanceship with The There were, for instance, lots of video – though, I gather, not for much longer – Bight arose because I gave the 1997 clips, and although the lecture was given there is an engraving of an intense-looking Christmas Lectures, with the title The ‘as live’ – more on that later – it is probably young man with his hair in some disarray, Magical Maze. Following Faraday’s lead, I best described as a TV programme made a signature that reads ‘Michael’ followed by with a studio audience. No overhead pro- an indecipherable surname, and the dates jectors, none of the usual academic lecture 1791-1867. It is, in fact, the face of the trappings. But, again, lots of demonstra- physicist Michael Faraday, founding father tions and experiments. of electrical technology. The note also How do you get chosen to give the bears a picture of him giving a lecture. He Christmas Lectures? The bare bones is that stands at a large desk with a curious semi- the Royal Institution makes the choice, circular indentation, and to his left rise tier and invites the prospective lecturer to take upon tier of seated Victorians – mostly on the job. There are early discussions with gentlemen, some ladies, a few children. the British Broadcasting Corporation Scientific apparatus of various kinds litters (BBC) which deals with the televisual side. the bench, and a curious machine with two But how do you become the sort of person handles sits in the foreground. who is going to get invited? Some kind of Underneath is a caption: Royal Institution track record in ‘public understanding of Christmas Lectures initiated in 1826: The mag- science’ is necessary. In any field of science neto-electric spark apparatus. there are always a few people who have For ten days either side of Christmas some sort of public profile and devote 1997 I got to know that desk like an old unusual effort to trying to make their sub- friend, and its indentation – known as ‘The published a book with the same title, but I ject comprehensible to non-specialists. In Bight’ – became a source of refuge, famil- managed to get my book in print before my case I had already published several iarity, and comfort. I too was surrounded the lectures took place. The lectures are hundred articles for magazines and news- by esoteric apparatus. The main differ- still given in the original lecture room, and papers, had taken part in about 150 radio ence, though, was that my audience con- The Bight is still there, but the seating has broadcasts, done about 30 items for televi- sisted mainly of children, and there were been refurbished and reduced in quantity sion, and given heaven knows how many six television cameras pointed at me. An to take account of modern safety regula- public lectures around the globe. These average of 1.3 million viewers were staring tions, and there have been lots of other activities secured me the 1995 Faraday at their TV screens at the other end. changes. The audience sits in a severely Medal (that man again!) awarded by The The Royal Institution is often confused raked (steep sloped) U-shape, with the lec- Royal Society for significant contributions with the Royal Society, although it has a turer at the open end of the U. The room to the public understanding of science – very different history. The confusion is holds about 450 people. For the Christmas one such medal being awarded each year understandable because in many ways the Lectures, the main audience in the lecture for the last dozen years. The Faraday two institutions overlap. Indeed, the foun- theatre itself consists of schoolchildren Medal is very much the Fast Track to the dation of the Royal Society – the UK’s pre- aged between about 11 and 16, but a lot of Christmas Lectures. mier scientific association – grew out of the adults attend as well, and we had at least Anyway, I’d got myself the right kind of Royal Institution and Gresham College (an one 8-year old. For televisual purposes the track record, and suddenly I was next in even more curious institution which exists adults are seated on the upper levels, out line. to this day as well). of the eye of the cameras. The Christmas Lectures are ‘an offer Michael Faraday began his career at the 1997 was precisely the second time in you can’t refuse’ – not in the sense of The Royal Institution as an assistant to Sir 168 years (now 169) when the topic was Godfather (well, not exactly...) but because Humphrey Davy, and eventually became mathematics – even if that’s not clear from they are such an unusual opportunity to the Institution’s director. Some time the title. (The aim was to find a non-threat- take your subject to a wide audience. They around Christmas 1826 he conceived the ening title: other publicity material made it are broadcast around midday for five con- idea of an annual series of ‘lectures for a abundantly clear that the lectures would be secutive days somewhere between juvenile auditory’, to be given at the Royal about mathematics.) The first time was Christmas and the New Year; they typical- Institution each Christmas, and the tradi- 1978 when Christopher Zeeman lectured ly get audiences of a million plus (slightly tion has been continued ever since. To on ‘Mathematics into Pictures’. There have above the average for the relevant channel date there have been 169 lectures in the also been a few lectures on applied mathe- at that time of day). The home audience is series (a few were missed during World matical topics such as waves and vibrations, much broader than the live audience: War II). The first lecturer was J. Wallis but mathematics has been somewhat many people make it a family affair with (title ‘Astronomy’), the second was Faraday neglected as a topic, probably because it everyone from the toddler to grandma himself (‘Chemistry’), and Faraday ended does not obviously lend itself to demon- watching. up giving the lectures 17 times in 34 years. strations. Both Zeeman and I proved that The Christmas Lectures also involve an The most famous such occasion was in with a little imagination this is not an enormous amount of work – by the lectur- 1854, when the lecturer was attended by obstacle. er, and by a support team of about twenty Prince Albert and one of the Royal When Zeeman did the lectures, there people. Some of the support team work for Princesses (‘The Chemistry of were six to the series, each one hour long. the Royal Institution, and one of the essen- Combustion’). The best known lecture, They were presented in normal lecture for- tial jobs that they do is to locate equipment though, is probably ‘The Chemical History mat – the main visual aid was an overhead for the demonstrations and, if necessary, of a Candle’ in 1860, which became the projector. However, they followed the build it. Ilya Eigenbrot and Bipin Parma topic of a book by the same name. The long-standing tradition of including a headed this part of the work. Most of the previous year Faraday had established large number of experiments and demon- rest work for the BBC, and a few are vol- what is now another long-running tradi- strations, involving volunteers from the unteers, in my case graduate students from tion of lectures leading to books, and this audience. By the time I gave them there Imperial College London, who acted as was its continuation; the 169 lectures so far were five lectures, and the influence of ‘runners’ during the actual filming. When, have generated about 50 books. television had become more obvious. for example, we needed half a dozen EMS June 1999 7 FEATURE teapots, one of the runners was sent out been given! What if I got ill? What if …? – Although there is a ‘script’, it is not pos- clutching several £20 notes to get them. But it did concentrate the mind, I must sible for the lecturer to use an autocue (a (Why did we need so many teapots? See say. device that projects the script on to a half- below.) While I was considering the invita- In the run-up to the filming, we did a silvered mirror in front of the camera tion to present the lectures, I asked a few of couple of ‘dry runs’ of the opening lecture lens). In a studio production, an autocue the previous lecturers. The most helpful in front of a live audience (who got in free would be normal, but for a ‘live’ lecture, advice I received was ‘write off the three because these were not the real lectures, the lecturer should be looking at the audi- months from November to December’. just a ‘preview’). The first attempt was pret- ence, not the camera. The lecturer also Fortunately I was in the first year of a spe- ty awful; the second a lot better. The film- should not be seen to consult notes, cial arrangement with the University of although notes can be visible on the desk. Warwick, which relieved me of all teaching Learning the script by heart is not really duties in return for running an outfit feasible, and would destroy any spontane- called the Mathematics Awareness Centre ity. So what happens is a compromise. The (MAC@W), so I could do just that without lecturer tries to learn the running order of having to rearrange my teaching. In the topics, the places where they should stand event, quite a bit of September and for the cameras, the route to use when October got written off too. (I suppose I going from one place to another, and the should also mention that the contract for general gist of what should be said. Then the lectures included an obligation to give they do their best to fit it all together on them all again in Japan six months later.) the day. Clever editing papers over any The detailed organisation, and the evo- cracks: for example the lecturer can lution of the lectures themselves, was a appear to get back to the correct position highly interactive enterprise and it’s during a cut-away to close-ups of attentive impossible to summarise it. The initial children in the audience. ‘Didn’t the chil- focus was on coming up with a working dren seem interested!’ everybody told me. draft of five scripts for the lectures, so that ing itself was done over a ten-day period, Well, they did, mostly – but a lot of the everybody knew what framework we were partly before Christmas and partly after. shots of the audience were carefully select- working with and could chip in with their For each lecture, the first day was devoted ed to look like that, and maybe half of own ideas for improvements, in the knowl- to a ‘stagger through’ the script, item by them cover up something that had to be edge that we all had the same general pic- item, finalising camera positions, making edited out. Indeed this is a necessary part ture. We selected the theme of the lectures: sure everybody (especially the lecturer) of the technique, as I finally figured out by the mathematics of nature. Two broad sub- knew the running order, the timing, the the time we got to lecture two: I realised I themes soon emerged: ‘up there’, the solar approximate script, and the main points was making a TV programme that was sup- system and the stars; ‘down here’, animals, we wanted to make. In the evening all the posed to look like a lecture – not actually plants, weather... We homed in on five top- resulting changes were transferred to a giving a lecture. So I kept the script handy ics: new version of the script. The second day at the back of The Bight, mostly hidden • Sunflowers and Snowflakes (a pot-pourri consisted of a full-scale dress rehearsal in from the cameras by set decor, and when- of mathematical patterns in nature) the morning, some rapid fine-tuning, a ever I forgot what was supposed to happen • The Pattern of Tiny Feet (mathematical rest period over lunch for me, and then the next I wandered round, consulted the patterns in animal locomotion) lecture itself. script, and returned to the correct place. • Outrageous Fortune (probability) Each TV programme lasts an hour All this faffing around was edited out of the • Chaos and Cauliflowers (chaos theory (actually, the second one was cut to 50 min- programme, but the audience had to put and fractal geometry) utes because for some reason it went faster up with it. • Fearful Symmetry (pattern formation) than we’d expected). It is filmed ‘as live’, Anyone with any experience of TV Now, I mentioned that the book based on meaning that the lecturer works through knows that in any TV production, be it the lectures was published before the lec- the material in order without any retakes, thirty seconds long, ridiculous things go tures were given. Clearly there’s not time aiming at just over an hour of lecturing. wrong. It all adds to the fun, and the live to do this in a few months. So, like the Then any necessary retakes that involve audience gets the delicious feeling that recipes of the TV cooks, this one was ‘made the audience are done at the end (and the they’re getting some secret knowledge of earlier’. The topics were then selected audience is not allowed out until this is what really happened. The lecturer just from the book. This back-to-front completed). Finally the audience gets let has to learn to put it out of their mind – to approach continued, because there was out, and then there are various technical have confidence that it will be edited out. one item that did have to be written during items, such as close-ups on bits of experi- (It might, of course, turn up on some com- those few months: a 32-page colour book- ments, that get filmed without the audi- pilation of ‘out-takes’ in which everyone let, to accompany the videotapes of the lec- ence being present. Because the design of can see what really happened. The BBC tures themselves. The booklet was already the building is Victorian, and the needs of gave me a set of tapes of everything that we being printed before we had fully settled television in cramped locations blocks off filmed, and I’ve made good use of them on the content of the lectures (and as a some access routes, it takes about half an since in public lectures about how the pro- result includes a few items that we never hour to get the audience into their seats. grammes were made, especially (for some actually put into the final programmes). So they end up sitting in the room for reason) at science fiction conventions. I’ll Then there was the pre-publicity – about two hours, for one hour of TV. give some examples in a moment. interviews, brief appearances on radio and As soon as filming is finished, the mas- The most dramatic mathematical topic TV, including the flagship childrens’ pro- ter-tape is edited (for length, to cut any of the first lecture was the Fibonacci series, gramme Blue Peter (yes, I got a badge – glitches, and to insert video clips and the which we introduced in the time-honoured UK readers will understand what I’m talk- like) in one of the three Outside Broadcast way as a problem on the population ing about here) and the Sky Book Show on vans that were parked outside the building dynamics of rabbits. Because of the satellite TV. And the BBC set up a website for the entire filming period. The fifth lec- cramped space in the lecture room, all for the lectures, and I did a big Christmas ture was filmed less than 16 hours before demonstrations are wheeled on and off puzzle page for a major national newspa- being broadcast. Incidentally, this hectic using trolleys. For Fibonacci, the trolley per, with copies of the book as prizes. We schedule has now been changed: the lec- bore a large top hat, out of which I first even filmed a follow-up TV programme for tures are filmed several weeks before produced (with magic wand) a live rabbit. the Open University before we had record- Christmas and edited in studio. New light- Bipin, hidden inside the trolley, handed it ed any of the actual lectures. With so much weight TV cameras were used from 1998 to me through the open bottom of the hat. of this kind of thing going on, an awful lot onwards, so my lectures were the last to be This was followed by pairs of stuffed toy was riding on lectures that had not yet done the old way. rabbits – they stay put better than live ones 8 EMS June 1999 FEATURE – spelling out the solution to Fibonacci’s along at once’.) Weeks later I got a puzzled the lecture theatre. All other openings problem. Eventually we had 24 toy rabbits letter from a bus driver who’d realised that seem drab in comparison. sitting on the desk. It would have been 40, something had been edited out, asking As well as the tiger, we had angel fish but despite scouring London for weeks we what I had said about them. with moving stripes (though it takes about were three rabbits short of target. I still By Lecture 4 we were really getting into six weeks to see that they have moved, so have two pairs of adults and one pair of the swing of things. The high point was a this feature had to be taken on trust) and a babies on a shelf in my office. cameo appearance by Suzanne Charlton, boa constrictor. Lecture 2 featured another rabbit, who who presents the TV weather forecast, to The ending of the final lecture was very gave a very professional demonstration of illustrate the ‘butterfly effect’ in the con- much a case of last-minute inspiration. We the ‘hop’ gait after a few gentle nudges; a text of weather prediction, using real data wanted to end with a bang – literally if pos- dog which could jump – and could also dis- from the European Medium Range sible – and we had a feeling we were a bit appear for a lengthy period in among the short of material. The evening after the feet of people in the audience – some giant stagger-through, we tore up the last bit of millipedes, and a stick insect. We also had script and rewrote the last ten minutes two walking robots. Towards the end of the from scratch. The topic became symmetry discussion we broadened the topic into colin time – time-reversal of the laws of lective movements of animals – flocks, nature, and time travel in relativity. The herds, shoals... and crowds of humans. We main demonstrations became a breaking demonstrated new state-of-the-art soft- teapot, reassembled by running the film ware, Legion, for simulating crowd flow. backwards; a ‘time tunnel’ made by linking And we showed the audience speeded-up a black hole to a white hole; and the lec- film of themselves forming a crowd as they turer disappearing into the future in a puff entered the building. of smoke. It was around lecture 3 that various You see where the teapots come in. The things began to go creatively wrong. To set idea was that a volunteer would be given an up the idea of probability, we had a large ‘incredibly valuable antique Royal plastic coin and a frying-pan, and a volun- Institution teapot’ to hold. They would teer from the audience had to toss the coin drop it on the floor, where it smashed. By using the pan. On her first attempt, the Weather Forecasting Centre in which the the miracle of reversed videotape, it would coin landed neatly on edge. Then came weather for Christmas day was predicted then be reassembled, instantly. You will ‘Marilyn and the goats’, otherwise known ten days ahead. The low point was when a appreciate that in this case – the only such as the Monty Hall problem. You know this hose came adrift in some apparatus being – our volunteer had to be rehearsed one. A game show contestant has to open used to demonstrate chaos in a dripping beforehand and play a role rather than just one of three doors. One door conceals the tap, spraying water everywhere. being their normal selves. The producer’s star prize, a sports car. The others hide (Fortunately this was at dress rehearsal.) son did a wonderful job. However, at booby-prizes – two goats. After the contes- Lecture 5... I’m particularly proud of rehearsal we found that the teapots that tant makes their choice, the host opens Lecture 5. It began with an offstage recital we’d bought didn’t smash very easily, so we another door to reveal a goat. Since he can of the final verse of William Blake’s ‘Tiger, sent out a runner to buy some flimsier always do this, it appears that no extra tiger...’ poem, and his own manuscript of ones. We got half a dozen, and tested one, information can be gleaned from his the poem, complete with tiger drawing, on which smashed convincingly at the first action. But then the contestant is given an the screen. Then... we brought on a real attempt. opportunity to change their mind and tiger. Nikka was a six-month old Bengal Come the actual lecture, though, the choose the only door not yet involved. tigress, whose mother had been killed by teapot bounced. (Wooden floor.) We tried Which strategy is best? I’m sure you know again, and again the teapot bounced, los- that (with suitable safeguards about the ing just its handle. After five tries, I had to procedure) the initial choice has a 1/3 join in, and with a cry of ‘If you’re going to probability of winning the car, and the spoil our valuable teapot, you might as well alternative has a 2/3 probability. That is, do it right!’ I hurled the teapot at the floor, the best strategy is to change your mind. and it exploded. Most of this was edited Despite the simple arguments that out, of course, but it took us five minutes to establish this fact, many people never man- induce spontaneous breakage of that age to grasp what’s involved. We tried to teapot. persuade them with an analogous demon- Then we got the same volunteer to stration using ten cards – one bearing a enter our wormhole time tunnel carrying a picture of a car and nine with goats. This plastic bag with the broken teapot in it, worked neatly. But when we came to stage only to emerge is the distant past when the the actual game show, with a set of minia- teapot was intact, and carrying an intact ture doors, an expensive toy car, and two teapot to prove it. (A new teapot was inside cardboard goats, it didn’t quite go as the tunnel, and that’s where the fragments planned. For when our volunteer, young were left.) Jeremy, had made his first choice, he poachers. (We did warn the audience, and The final sequence involved a fake time promptly opened the door to reveal the we took pains to get the tiger accustomed machine (we used some antique apparatus car! That time we broke the ‘retakes at the to the lecture room, the people and the TV originally made by Charles Wheatstone, end’ rule, and re-ran the whole thing, with lights.) Nikka, like Jeremy, was a pro – with lots of dials), some pyrotechnics, and more carefully worded instructions. she’d had long experience visiting schools me diving under The Bight and hiding Jeremy, like a true pro, managed to look and appearing in other TV programmes. myself from the overhead camera for the just as relaxed and uninitiated as he had I’m sure that in her short career she’d final title sequence. the first time round. done more television than I had. Her Then, suddenly, it was finished. We did The third programme overran and a mathematical role was to demonstrate pat- the retakes, got rid of the audience, and few items had to be edited out. In conse- tern formation in animal markings. Her had a party. I got my life back again… quence three toy buses, which started out stripy tail was perfect for the job, and she Until July, when we did the whole thing in a group, ended up spread along the displayed it with all the aplomb of a cat- again – with minor changes – in Tokyo. front of the desk – but only the live audi- walk fashion model. Very enjoyably, and accompanied by out- ence ever saw how they got there. (I was I doubt that I will ever give another lec- standing hospitality... But that is definitely explaining why ‘three buses always come ture where I get to bring a live tiger into another story. EMS June 1999 9 INTERVIEW Interview with Helmut Neunzert (Kaiserslautern) interviewer: Heinz W. Engl (Linz)

Q. You are the head of a new Institute for This is one of the specialities of the insti- fulfil for Fraunhofer is the ‘financial mix’. Technomathematics in Kaiserslautern. tute: alternative CFD methods, which still 72% of our total budget (including salaries, What are its aims? work if the domain is very complex. rents for the building, purchase of com- A. The aim of the Radiation shows a second competence of puters, etc.) must be earned, 42% has to be institute is to solve our institute: the combination of asymptot- ‘hard money’ – that is, money from indus- industrial prob- ic and numerical methods. For radiation try. 30% should be project money from lems using modern through glass, when in real 3-dimensional EU, the federal or state research min- mathematical situations standard methods (‘discrete istries, German research foundation, etc. methods. The ordinates’) become too expensive, we use a 28% is basic funding, which comes from main steps are 2-scale analysis which leads to approxima- Fraunhofer. In 1998 we overreached our- mathematical tions that are much better than the classi- selves: 100 = 75 (= 45+30) + 25. modelling and scientific computing and we cal Rosseland, but almost as fast. deliver software that simulates, optimises Another department is called ‘Flow in Q. Your institute has had a tremendous or controls processes and products which complex structures’ and deals more with growth rate so far. Can you elaborate on cannot be treated by commercial software. incompressible Navier Stokes flow in this? How large is it now? Currently we are an independent associa- porous media as textiles or solidifying A. We started in November 1995, with 26 tion (Verein); but we are in the process of metal flow in moulds. Again we try to scientists by the end of 1996, 30 in 1997, becoming a member of the Fraunhofer develop alternative methods such as ‘lat- 45 in 1998, and we currently have around Society, a prestigious Research Organis- tice Boltzmann methods’ and make them 50 fully employed scientists. We added ation in Germany. The final decision is useful for industrial applications. And 5/6/10/12 Ph.D. students and around 40 scheduled for March 2000. Fraunhofer has again we use rigorous transitions from the students who do a time job. The budget 48 institutes with around 9000 employees microscopic to the macroscopic to get increased from around 5 million DM in and an annual budget of 0.6 billion euros. information about macroscopic parame- 1996 to 7.3 million in 1997 and 8.6 million ters such as permeability and rarely used in 1998; we expect a budget of 10.8 million Q. Are there other mathematically-oriented equations such as Darcy with memory or DM for this year. You may compute from institutes in the Fraunhofer network, and Darcy with inertia. Moreover, we try to the percentages of the financial mix that how do you see your role within that net- develop parallel codes for the commercial we plan to earn around 8 million DM in work? codes on PC-clusters. 1999. The growth rate is around 25% per A. Of course, there is a lot of computation, The department ‘Adaptive systems’ uses year – since our basic funding was fixed, simulation and image processing going on tools from system and control theory, neu- this means a higher rate in our earnings, in many Fraunhofer institutes. But there is ronal networks, etc. There is a very wide for example, between 35% and 60% in our not yet a mathematics institute inside variety of problems, but one main applica- industrial money. Fraunhofer and we are looking forward to tion field is medical diagnosis: one has to being the first one. Fraunhofer institutes find hidden patterns in long-time records Q. What about recruiting? Was it easy to have a lot of independence, they solicit of some medical data. This is often an find qualified people? and solve the problems themselves. extremely difficult task and we need new A. Recruiting is not easy. We have a high However, there is also cooperation mathematical theories and concepts. The percentage of post-docs (over 70%) and between these institutes and we strive at design of analogue circuits belongs to the pay reasonably, but not overwhelmingly. becoming the mathematics institute in the same area, but also uses methods from Most of our scientists are mathematicians society, doing (properly paid) services for computer algebra. (over 50%), but we have also physicists, them. Fraunhofer is a fascinating world of Our department for ‘Image processing’ engineers and computer scientists. Last high tech and it is a dream for an applied deals mainly with the inspection of sur- year’s recruiting was very hard as the mar- mathematician to work in this world. faces: textile surfaces, metal surfaces, ket has been almost empty (due to the veneers, etc. There are many companies change of the century and the EURO), but Q. Which mathematical areas does your selling their image-processing compe- it is slowly getting better. We have to institute cover? What are some of your pro- tence; we try to cover the area in which attract people by the interesting work they jects? quality and precision of the processed are expected to do, and by the atmosphere A. There is a large variety of problems – image is more important than processing in the institute which is still influenced by and therefore of mathematical methods speed. Mathematically this means wavelet the idea that we are pioneers in a rather too. I can give only a very short sketch of filters, active contour methods, diffusion difficult, but fertile territory. And we still our activities: There is a department for filters and methods from stochastic geom- attract them – not only Germans: we are ‘Transport processes’, where we deal main- etry. striving to become an international insti- ly with compressible flows, with radiation Last but not least, our youngest depart- tute with presently 20% foreigners – from and with acoustics. Think of a side airbag, ment is for optimisation. They use mainly France, Italy, Russia, Bulgaria, India and which poses a more difficult problem than methods of combinatorial optimisation, for Indonesia. All come from excellent institu- a front airbag: one has to compute the gas example in designing an optimal control tions and with a PhD, and almost 20% of flow in the airbag, the extension of the for modern storage systems or in location the staff are women. envelope and the interaction of both. The of service centres, etc. computational domain for the gas flow is Q. What are the qualifications, both scien- very complicated and changes rapidly: one Q. What is your financing structure, and tific and personal, that you look for? What needs grid-free methods for Euler flow, how much does your institute actually have advice can you give students who want to and to do so we extend particle methods to earn from industry? work as mathematicians in an environment like ‘smoothed particle hydrodynamics’. A. The main entrance condition we have to like yours?

10 EMS June 1999 INTERVIEW A. Of course, we prefer applied mathe- est access to knowledge is still through A. I would just recommend that you read maticians with a solid basis in numerics for human brains (they are much more asso- the article. It takes some time to explain pde, in scientific computing, system and ciative than all the data bases you could the nature of the challenges for applied control theory, optimisation or image pro- imagine). ECMI provides excellent access mathematics in the design of materials, in cessing, etc. And we need people who have to relevant knowledge in Europe – how the design of products, the simulation and communication skills, a good ‘social behav- beautifully different are the mathematical optimisation of production processes, in iour’ – we need people with all the proper- cultures in Europe, what a rich multi- the discovery of patterns in data from ties that the SIAM study on mathematics in faceted landscape this ‘country’ has! We economy, image analysis, medicine. In all industry has mentioned. And, of course, also need close contact with SIAM, and of these fields new mathematical concepts they have to be able to handle a computer with applied groups in Japan, Australia, must be developed, new algorithms have to in a proper way. China, India, South-America, etc. I have to be found, new theories are necessary. But My advice to students? If I said: ‘study say that many of the students from third- how can I know what kind of problems a technomathematics in Kaiserslautern’, it world countries need a bit of additional technology that is not yet invented will would be good advice, but not everybody ‘western’ education: there is still far too pose in 20 years? Who thought about would like it. But it means: study applied much learning by heart there, too little cre- fatigue life analysis, financial mathematics, mathematics, which includes modelling ation of creativity in many universities. But wavelets in image processing, 20 years and scientific computing; learn to use a the brains are as good, the will is even ago? I am totally convinced that the num- computer and to write a C++ programme; stronger – and after two years’ education ber of problems in the world that need new learn the language of a technical field and we get excellent scientists. mathematics for their solution is strongly learn to communicate with non-mathe- increasing. There are really wonderful maticians; develop your creativity by Q. Your article ‘Mathematics as a key to key problems, striking challenges, important attacking non-mathematical problems with technologies’ will appear soon in the for knowledge and economy. It is still the mathematical methods on your own; do a Springer Journal Surveys on Mathematics best choice for a young intelligent human PhD if you are able to finish before you are for Industry. Can you briefly summarise the being to become a mathematician – at 30. views about the future of mathematics that least, if he/she keeps some of my advice in you expressed there? mind. Q. Do you have plans to extend your activities beyond Germany? EMS Summer Schools : Call for proposals A. Fraunhofer has a strong intention to become more international. In fact, the For some years the European Mathematical Society has run a suc- mathematics department of our university cessful series of Summer Schools. Readers of the Newsletter will is already very international – at least half recall reports of a 1996 Summer School in Hungary on Algebraic of our students after Vordiplom come from Geometry [issue 20] and a 1998 Summer School in France on other countries, many from third-world Wavelets in Analysis and Simulation [issue 29]. countries. We have excellent relations with The series is intended to include at least two summer schools India, Indonesia and some other countries in Asia, and very friendly relations with each year – preferably at least one in pure mathematics and at least similar institutes in Australia and the US. one in applied mathematics. With this activity, the Society aims to With Avner Friedman at IMA we tried to encourage young European mathematicians to meet and study establish a Fraunhofer research centre for current developments in mathematics and its applications. Topics mathematics in Minneapolis, but the con- (which may be single or composite) for summer schools, the sites, ditions that Fraunhofer offered in the US and the organisers of the schools are likely to vary from year to did not satisfy our American colleagues. year so as to cover a wide range of subjects. We are now trying to establish a close con- The Society’s Summer School Committee will consider sponsor- nection with IMA on a different basis. ing proposals for summer schools fully organised by other institu- Bangalore in India would also be a good tions. To meet EMS expectations, each school should be at pre- place to found a branch, and we are trying doctoral level, should last from 2 to 3 weeks, and have 100–200 to get into closer cooperation with the technical university of Saudi Arabia in participants – mainly graduate students or young mathematicians Dhahran. from several European countries. Costs of participation should be kept low, and (where possible) grants should be available to people from countries that cannot afford financial support. The EMS will Q. What role does international coopera- provide moral support to the selected Schools, plus advertising tion in research and education play? After within the European Mathematical community; it will also do its all, you were one of the founding fathers of best to help the organisers to raise funds. ECMI [see the interview with R. S. Mattheij The Society now invites proposals for at least two Summer in EMS Newsletter 31]. Schools for 2001. Proposals should contain at least: the topic (title A. International cooperation is for me one and short description), names of likely lecturers, the site, the tim- of the key points in research and educa- ing, anticipated costs, conditions for participants, the organising tion, for several reasons: it is a real pleasure to meet many people from other cul- committee membership, and the name and address of the organ- tures – you learn so much about human iser submitting the proposal. The deadline for proposals is 30 beings, especially about yourself; there is September 1999; the Committee hopes to decide on proposals so much brain in the world, eager to learn, within a month or so. to do research; since an institute like mine Please send proposals to Prof. David Brannan, Department of cannot make the money only from its own Pure Mathematics, The Open University, Walton Hall, Milton research, we need access to relevant Keynes MK7 6AA, UK. Fax: (+44)-1908-652140, e-mail: d.a.bran- research all over the world – and the easi- [email protected] EMS June 1999 11 ANNIVERSARIES 1999 Anniversaries by Jeremy Gray

more at home in the mountains of his was visiting him. Lie provided Klein with Felix Klein (b. 1849) native Norway than in German academic important new illustrations of Klein’s theo- society. Klein was something of a prodigy, ry from his own work, which were incorpo- and Sophus Lie (d. 1899) with a completed doctorate already behind rated in sections 7 and 9 of the Program. him; Lie had yet to finish his, which may Later, in the preface to his book Lectures on have caused him some embarrassment. But the Icosahedron (1884), Klein said that the what brought them together in the heady two had decided to divide group theory milieu of the large mathematical commu- into two: Lie taking the theory of continu- nity in Berlin was their shared passion for ous groups, Klein the discontinuous. This geometry, above all Plücker’s theory of much quoted remark conceals as much as line-geometry, a field that elicited little or it reveals. It implies that the direction of no interest in Berlin. their future work was clearer than it surely They wrote several papers either was, and it masks the extent to which the together or with Klein assisting with Lie’s Erlangen Program is a classification of all German, and Klein even presented Lie’s the then-known geometries (Euclidean work in Kummer’s seminar because of Lie’s and non-Euclidean) within projective lack of facility with the language. In the geometry. There they are distinguished by Spring of 1870 they went together to Paris, the nature of the spaces they describe and where they met several leading French the groups of allowable transformations mathematicians, including Chasles, Serret, they possess, but the emphasis in 1872 was Darboux and Jordan. Klein may well have on organising geometry, not promulgating been influenced by Jordan, but for Lie the group theory. most vital contact was with Darboux and Lie returned to Norway at the end of through him Monge’s work on differential 1872, and his mathematical interests geometry and partial differential equa- began to diverge from Klein’s, but over the tions. Then they were separated by the next ten years they remained in steady Franco-Prussian War. Klein returned contact and still managed to see each other Felix Klein home to fight, and was invalided out with on Lie’s occasional trips to the continent. typhoid. Lie, as citizen of a neutral country On the other hand, Lie began to feel math- 1999 marks the anniversaries of two inter- was allowed to stay, but was then arrested ematically isolated. The only foreign jour- twined lives, those of Felix Klein and his on suspicion of being a German spy; letters nal in which Lie published anything sub- friend Sophus Lie. They first met in from Darboux helped ensure his release stantial during these years was the October 1869 at a meeting of the after a month. Mathematische Annalen, edited by Felix Mathematischer Verein in Berlin and hit it off The most famous fruit of their friend- Klein. His expository style, and his geo- almost at once. They made a contrasting ship is Klein’s Erlangen Program, the pam- metric way of thinking, did not fit with the pair. Klein was a thin, highly verbal young phlet he distributed on the occasion of his dominant Berlin mixture of algebra and man with a precocious confidence in his appointment as a Professor at Erlangen in analysis. Weierstrass even insisted that abilities. Lie was a towering physical pres- 1872. Klein wrote much of it during everything Lie did would have to be ence who spoke uncertain German and was September and October 1872, while Lie reworked completely [1]. In 1886 Lie

Title page and diagram from Felix Klein’s Lectures on the Icosahedron 12 EMS June 1999 INTERVIEW to speak, as the logical consequence of Grundring which since 1994 has been much Lie’s long and continuous works in the used in algebraic coding theory under the area of geometry, in particular, his theory name of Galois-ring. In 1925 he proved the of continuous transformation groups”. Krull-Schmidt decomposition theorem for One notes that this was the very topic upon abelian groups of operators. In 1928 he which Lie had attacked Klein. went to Erlangen, where he showed how to In the spring of 1898 Lie returned to extend Galois theory to infinite extensions Oslo. According to Klein’s wife, Anna, a by introducing topological ideas. Then the ‘reconciliation’ of sorts did, in fact, take influence of Emmy Noether took hold. place: “One summer evening as we came A significant achievement in ring theory home from an excursion, there, in front of was his introduction of what today is called our door, sat a pale sick man. ‘Lie!’, we the Krull dimension of a commutative cried, in joyful surprise. The two friends Noetherian ring, and the proof of the shook hand, looked into one another’s principal ideal theorem in this setting. eyes, all that had passed since their last This result was quickly recognised as a meeting was forgotten. Lie stayed with us decisive advance in Noether’s programme one day, the dear old friend, and yet of emancipating abstract ring theory form changed. I cannot think of him and his the theory of polynomial rings. The Krull tragic fate without emotion. Soon after, he dimension of a Noetherian ring is the died, but not before the great mathemati- maximal length of a chain of distinct prime cian had been received in Norway like a ideals (and in simple cases it corresponds king” [4]. to the chain of geometric inclusions: point, Acknowledgement: I would like to thank curve, surface . . .). The theorem asserts David Rowe for providing me with a vast that if a local ring with unique maximal store of information and advice upon ideal m has (Krull) dimension n then n is which this article is based. the smallest number such that there are n distinct elements of m which are not con- Bibliography 1. K.-R. Biermann, Die Mathematik und ihre Dozenten an tained in any other prime ideal of the ring. Geometrically, if m is the maximal ideal of Title page of Lie’s Collected Works der Berliner Universität 1810–1920, Akademie Verlag, Berlin, 1973, pp. 130, 133. functions that vanish at a point on a vari- 2. C. F. Klein, Gesammelte Mathematische Abhandlungen, ety, this is the claim that at least n functions became a Professor in Leipzig, but the 1, Springer-Verlag, Berlin, 1921, pp. 384–401. move did nothing to solve his problems. 3. S. Lie, Theorie der Transformationsgruppen, Vol. 3, are needed to pick out a point. Now in the mainstream he became acutely 1893, p. 17. In 1932 Krull introduced general addi- aware that other mathematicians had simi- 4. D. E. Rowe, The Early Geometrical Works of tive valuations, now known as Krull valua- Sophus Lie and Felix Klein, The History of Modern tions. In 1935 he published his book lar ideas to his. So, when Klein visited Lie Mathematics, 1 (ed. D. E. Rowe and J. McCleary), in February 1891, he raised the idea that Academic Press, Boston, 1989, pp. 209–274. Idealtheorie, which was to prove an accessi- Lie republish his early work much of which 5. W. H. Young, Christian Felix Klein 1849–1925, ble source for his ideas after the war, and had appeared in Norwegian journals. This Proceedings of the London Royal Society (A) 121 in 1938 he initiated the theory of local (1928), 1–19. would establish Lie’s claims more securely, rings that was then taken up by Chevalley, present them in their proper geometric Wolfgang Krull (b. 1899) Zariski and Cohen. In 1939 he moved to garb (and doubtless shed a favourable light Bonn, and during the war he worked in the indirectly on Klein). Klein would take the naval meteorological service. He then opportunity to republish the Erlangen resumed his career as a mathematician at Program. Bonn, and 32 of his 35 doctoral students This was a tricky matter. Klein had also came out of this second phase of his career. suggested, not for the first time, that Lie Krull laid great store by the mathemati- respond to Helmholtz’s ideas on the foun- cal imagination. In his inaugural address dations of geometry, which cried out for a at Erlangen he spoke of the mathemati- group-theoretic analysis, but Lie had cian’s task as not only finding theorems already commented caustically on Klein’s and giving them valid proofs, but also account of the topic, not least because arranging the theory until they become Klein’s version neglected his (Lie’s) contri- self-evident. His own work is marked by butions from the 1880s. Relations between the profundity of his ideas, the rigour of the two men deteriorated and then in 1893 his proofs, and also by a strong aesthetic Lie attacked Klein in public. sense. In this way he did indeed continue In the preface to Volume 3 of his Theorie the tradition of his mentors in Göttingen, der Transformationsgruppen, Lie [3] wrote: ‘I Felix Klein and Emmy Noether. am not a student of Klein’s nor is the Bibliography reverse the case, even if it comes closer to H. Schöneborn, In Memoriam Wolfgang Krull, the truth ... I value Klein’s talent highly Jahresberichte der DMV 82 (1980), 51–62 and will never forget that part he had in accompanying my scientific efforts from Jeremy Gray [[email protected]] is a senior the beginning. I believe, however, that he lecturer at the Open University,UK. does not always distinguish sufficiently between induction and proof, between the introduction of a concept and its utiliza- tion.’ Whatever personal pain Klein felt, he An error crept into my obituary of dealt with the matter professionally. In André Weil in EMS Newsletter 31. Krull is remembered as one of the follow- Although he did write at length about 1897 he wrote a report for the Kasan ers of Emmy Noether, but he also derived Scientific Society proposing that Lie be the work of Fermat he never produced a strong desire to ‘see’ mathematics from an edition of it. I am grateful to Prof. awarded the first Lobachevskii Prize [2]. Felix Klein, whose seminar he attended in He drew particular attention to Lie’s treat- Dr. Klaus Barner for bringing my 1920–21. He first worked at Freiburg, attention to this mistake. Jeremy Gray ment of the Riemann-Helmholtz problem, where his 1922 Habilitation Thesis intro- stressing that “this treatment appears, so duced (among other things) a finite EMS June 1999 13 Letters

The article by John Fauvel on the sale of 8. No “private buyer” has ever been iden- sought, nor who it was received from, nor the Turner Collection in EMS Newsletter tified and it seems that the person Mr what it consisted of. The suspicion must 31 and its reponse by Allen Foster pro- Foster refers to as “the private buyer” is a be raised that there was not any. duced a lively postbag. second-hand book dealer in London. 17. “Retaining” material as photocopies 9. It is hard to believe that the students (very poor, few and hasty photocopies by From John Fauvel ([email protected]) “were unanimously behind the sale”, and what has been seen) is daft: as well the Fulbright Scholar and Visiting Professor of indeed subsequent inquiries have shown National Gallery sell its paintings & keep Mathematics, Colorado College, USA. this statement to be false. What students the post-card booth. Perhaps I may comment briefly on a few were no doubt unanimously behind was 18. The reference to proceeds of the of the more misleading claims in Allan raising more money for the Library (like Turner sale being used to fund Keele’s Foster’s response to my article about the every sensible person), and it may well be MBA programme comes directly from Mr way the University of Keele has exercised that some were deceived into thinking Foster’s own information office, so it is its custodianship of the Turner Collection that secretly selling the Turner hard to see why he is now claiming it is of mathematical texts? Collections was the only or best way to “quite wrong”. 1. There is no “campaign of vilification” achieve this. 19. If the decision to sell the Turner but a justifiable world-wide protest about 10. In the light of evidence that has Collections was really “the collective wis- something which ought not to have hap- emerged subsequently, Mr Foster’s claim dom of the University community” then pened and has variously been described that “the process was conducted with pro- God help Keele. as “disgusting” (a mathematics professor bity throughout” is quite unbelievable. from Germany), “astonishing and dis- 11. The claim that the sale followed “a From Robert A. Jackson (r.a.jackson@ gusting” (a librarian from France), very careful consideration of the issues chem.keele.ac.uk), Senior Lecturer in “unbelievable” (a professor from the US), involved” overlooks the fact that the Chemistry, Keele University, UK “hasty, secretive and ill-advised” (fifty UK issues involved were presented and dis- I was pleased to have the opportunity to academics), . . . torted, with a range of false or misleading read John Fauvel’s article, ‘Caring for the 2. The legality of Keele University’s statements, by Mr Foster, while wider mathematical past: a recent British expe- actions is not at issue, but their moral and issues of ethics, public policy and the rience’. It describes the unfortunate ethical justification and the probity of repercussions of the sale were barely con- events that occurred at Keele over the their actions. sidered. sale of the Turner collection very well, 3. It is hard to see how the Keele 12. The other book collections men- and I agree wholeheartedly with his con- University managers have persuaded tioned by Mr Foster, in Cambridge, clusions. themselves that they “acted . . . with London, Edinburgh, and Manchester, However, as a member of Keele integrity”: by other people’s standards are not for the most part “much more University’s Senate, which voted against there was neither moral integrity in the accessible for scholars” in the West the sale of the collection, I must point out secretive way the decision was taken nor Midlands to Merseyside belt, and they are several inaccuracies in Allan Foster’s pragmatic integrity in destroying an aca- all far harder to access and make use of reply. Most importantly, there was no demic resource for future generations. within the libraries concerned. “extensive debate” over the sale. Indeed, 4. Keele University’s financial need is Destroying the Turner Collection some expert users of the collection at agreed and lamented on all sides. That because other libraries exist is like closing Keele were not consulted, and scant has no bearing on the fact that the solu- down Keele because of the existence of regard was paid to the Senate vote, how- tion the managers chose was the wrong the University of Luton. ever good the debate may have been. It is one. It deliberately confuses the issues to 13. The mathematical community’s inter- also clear that the possibility of selling the argue, in effect, ‘we needed money, there- est in the Turner Collection was (a) much collection to a public body like the fore our secret selling of the Turner greater than Mr Foster admits and (b) London Mathematical Society was not Collections to a second-hand book dealer consisted of more than physically visiting properly looked into. It is also irrelevant was justified.’ the Collection. Well-documented use by to make capital of student opinion on this 5. The Turner Collections were “relevant the Open University, the British Society issue, since the collection was primarily to teaching and research programmes”, for the History of Mathematics, and the for research, not teaching. as attested by several members of Keele British Association for the Advancement In conclusion, I agree with John University’s faculty – who were not even of Science, along with numerous private Fauvel’s conclusion – university adminis- informed about, let alone consulted in, visits, constitute a considerable body of trators are no longer our natural allies. Mr Foster’s “open”, “extensive” debates. external interest which would have Colleagues in other universities should 6. Whatever Mr Foster may now claim, increased even more in the future. take note of our experience at Keele, in the decision was undeniably “taken in 14. If Mr Foster seriously claims to have case something similar is proposed in secret”, with a heavy confidentiality clam- had an “earnest objective of doing noth- their institutions. pdown, and furthermore this enabled the ing that would lead to the break up of the Council “debate” to be predicated on Collection” then he would hardly have From David Singmaster ([email protected]. misleading information supplied by Mr gone about disposing of it secretly to a uk), Professor of Mathematics and Meta- Foster and his colleagues. second-hand book dealer. grobologist, South Bank University, London, 7. No satisfactory account has ever been 15. The Graves Collection (or any other) UK offered of the nature of the “further does not “replicate” items in the Turner Allan Foster’s response is flawed and even investigation and consultation” allegedly Collection. Most early books are unique misleading in many ways. He starts by carried out by the Vice-Chancellor and for a variety of reasons involving print- denigrating the newspaper articles as two lay folk which led to the Turner ing, ownership, annotations, and history. “tabloid-style”. I am sure that The Times, Collections being rushed off the premises 16. We have never been told what “pro- The Guardian, The Daily Telegraph, The within a fortnight. fessional advice” about the sale was Times Higher Education Supplement and

14 EMS June 1999 Nature would object to being compared There were also about 200 ‘with There is no doubt that there are better with tabloids. Turner’ books which Keele had acquired collections on history of science and It is probable that Keele has behaved to supplement the Turner Collection. mathematics in London, Oxford, legally in that there was no written con- These vanished with the Turner Cambridge, Edinburgh and possibly tract between Turner and Keele. Collection, though their disposition had Manchester (whose library I haven’t However, David Ingram remembers a never been mentioned in the discussions used). However, this completely loses meeting between Turner and the of the Turner Collection. sight of Turner’s vision. He wanted his Librarian of the time, when Turner asked Foster also says the options were collection to go to somewhere where it what would happen if the University had weighed up carefully. However, Council’s would be useful, i.e. a new university to sell the Collection. The Librarian approval of the sale in principle took some way removed from the standard assured him that that would never hap- place on 26 June and within ten days the centres. It is sad that Keele is so blind that pen and Turner said he would like the books were gone. This does not seem like it did not try to place the Collection Collection to remain together. So I would much time to determine options, much where it would continue to be of some say that there was a verbal understand- less investigate or consider them. use. ing, though verbal agreements are diffi- Foster says the books went to a private Foster asserts that professional advice cult to verify or enforce, especially as buyer. In fact the books went to a small was that no other public institution was Turner had no close relatives to object to bookdealer in Shropshire and have since likely to buy the Collection. However, no the sale. passed on to a major London dealer, and other public institution seems to have The beginning of Foster’s second a third dealer was involved. At least been consulted – we have spoken to all paragraph is nonsensical, though this Foster is no longer putting forth the bla- the most likely candidates, no one else may be due to an typographical or edit- tant lie that the University issued in has come forward and Keele has stead- ing error. But then he reveals one of the December and January that the books fastly failed to name any such institution. most damning facts about Keele: “for had gone to a major private collector and So as far as we can tell, Keele’s profes- many years the University has been would remain in the UK and be available sional advice seems to consist only of unable to allocate sufficient funds for for research – though Keele couldn’t say advice from the dealer who was offering library resources.” Indeed their Council who the buyer was. However, it seems to buy the books, hardly the most disin- Minutes of 26 June state: “Keele is 47th clear that Keele’s Council put this story terested source. (bottom of the old universities) for library about in order to defuse protest about the Sources at Keele tell me that the ‘fac- funding, spending about 75% per student sale. Indeed the Keele Council minutes similes’ retained are mostly reprints that FTE compared with our comparator uni- state: “The private buyer has given an the University already had and that the versities; the underfunding cannot be assurance that the collection would not new photocopies are few and not very explained by over-staffing since Keele is leave the UK nor be broken up.” This was helpful. Indeed a letter from the library 77th in terms of library staff/FTE . . . stated despite the fact that the buyer had in November states: “we retained facsim- There needs to be additional expendi- clearly already been selected and Keele iles of some of the more important items, ture in the library of about £200K per made no attempt to formalise this verbal as well as photocopies of a small number year, whereas the sale would realise only assurance. Keele’s statements during of others.” This hardly sounds like a £70K per year and so would not solve the December and January were made major effort to make material available – problem.” It is difficult to see how a though the London dealer was already in any case the Library only had about ten University can so drastically undervalue applying for export licenses for some of days to do this. its library as to get to such a state of the books. Professor John Rogers (g.a.j.rogers@ affairs and how a University Librarian did It may well be that the external usage phil.keele.ac.uk) has just circulated a docu- not resign in protest over this. Indeed, it of the Turner Collection has been small. ment comparing Keele’s behaviour with is reported that the University is also sell- However, I have visited it three times in the published advice of the Library ing off land which has been given to it. the past decade, totalling about six full Association’s Rare Book Group’s Policy Clearly the financial state of Keele is par- days of usage, and I had correspondence Statement on the Sale of Rare Books and lous if it is having to sell off its endow- about having slides made from some of Manuscripts. Keele has violated almost ments and one can only wonder at the the books. I was thinking about taking a every relevant part of this advice. competence of its administrators. friend from New York to see it in early In view of the above, I feel that Keele When the proposal to sell was debated December but he didn’t have time. The has behaved dishonourably, blindly, mis- last May and June, the documents were last time I visited, I found that the leadingly and incompetently. Foster’s not circulated to Faculty Boards and were Collection had been removed from a spe- claim that this was the collective wisdom labelled confidential. Further, staff were cial room in the basement to being part of the University community seems at instructed not to convey information out- of the Special Collections and I was told odds with the Senate rejecting the sale by side the University – e.g. the Council this was because the then Vice-Chancellor 22 to 19. Rather it seems to be the deci- Minutes of 26 June say: “It was agreed wanted the room. The Special Collections sion of the University Council, whose that the issue was sensitive, and confiden- Librarian asked me to sign the visitors’ administration of Keele’s finances is obvi- tiality within the University should be book because he was worried that the ously rather poor. In any case, it reminds maintained at present.” Several staff at Vice-Chancellor would get rid of the me of Dr. Johnson’s famous epigram Keele have informed me that they heard Collection, again for reasons of room. “Patriotism is the last refuge of a nothing about the sale until the books Since the Collection only fills one room, scoundrel.” All in all, I feel that ‘philis- were gone. To me this seems like a prima these reasons seemed pretty petty at the tine’ is an appropriate description, facie case of secrecy and quite at odds with time. though ‘stupid vandals’ seems more Foster’s claim that this was the collective Since December, I have discovered appropriate. It seems that Keele’s admin- wisdom of the University. Foster says that Keele has several researchers active- istration is still unaware of the damage reports of the debates are on Keele’s web ly engaged in history of science and phi- they have done to the University. site, but when we tried to access these in losophy who had been making regular December, we found one needed a pass- use of the Collection in their research word. and teaching.

EMS June 1999 15 SOCIETIES Societies Section

younger people in order to encourage ning of every second year. It aims to give Finnish them to enter mathematical studies at a an overview of current mathematical university. For that purpose SMY now pub- research in Finland. SMY also organises Mathematical lishes a bulletin Silmu and promotes par- different Nordic conferences, together ticipation in mathematical competitions with other Scandinavian mathematical Society such as the International Mathematical societies. Olympiad and the Nordic Mathematical Together with the Finnish Physical Aatos Lahtinen Contest. Society (SFS) SMY publishes a journal For the promotion of mathematical Arkhimedes, which aims to publish mathe- The Finnish Mathematical Society is one of research there are mathematical presenta- matics and physics articles of general inter- the oldest mathematical societies. It was tions at SMY meetings. At first all the est. The articles are usually written in founded in 1868, three years after the speakers were Finnish. The first foreign Finnish with an English summary. London Mathematical Society and four speaker was M. Riesz in 1926. After that Arkhimedes has five issues per year and is years before the Société Mathématique de the number of foreign speakers gradually sent to every member of SMY and SFS free France. increased. Finally it was taken to one of the of charge. SMY, together with other The official name of the Society is main activities of SMY to invite eminent Scandinavian mathematical societies, is Suomen Matemaattinen Yhdistys (SMY). From mathematicians to visit Finland and give responsible for the publication of the jour- the beginning the Society’s purpose has talks at SMY meetings. There were about nals Mathematica Scandinavica and Nordisk been to encourage and maintain interest in Matematisk Tidskrift. For information of its domestic members SMY has a newsletter called Eukleides. The Society has been closely linked to the European Mathematical Society since its foundation. In fact, SMY was already a member of its predecessor, the European Mathematical Council and a delegate of SMY participated also in the meeting where it was decided to create EMS legally as a Finnish scientific society with its seat in Helsinki. SMY has been active in EMS in the firm belief that via EMS mathematicians can influence the welfare of mathematics in Europe and that this benefits also all the European countries. The Society currently has about 350 One of the major undertakings of the Finnish Mathematical Society was the organising of the 1978 members. Its supreme authority is the International Congress of Mathematicians in Helsinki. In this picture are the main organisers: from General Meeting, held once a year. The the left, Olli Lokki, Olli Lehto, Rolf Nevanlinna and Ilppo Simo Louhivaara, all past presidents or general charge of all matters lies in the secretaries of the Society. Board, consisting of the President, Vice- President, Secretary, Treasurer and one mathematical thinking and to promote additional member. All of these are elected mathematical research in Finland. Later for one year at the General Meeting and on it was specified that SMY should pre- may be re-elected. Currently the President pare proposals, organise seminars, is Professor Antti Kupiainen, the Vice- arrange meetings and award grants, and it President is Professor Sören Illman, the represents its membership for that pur- Secretary is researcher Mikko Pere and the pose. Treasurer is Professor Aatos Lahtinen. In the 19th century Finland had only Individuals, as well as corporate bodies, one university and only one chair of math- can apply for membership by sending an ematics there. Therefore in the first years application to the Board of the Society, the activities of SMY for raising interest in which has the power to accept members. mathematical thinking were mainly direct- The stamp of the Congress Members pay an annual fee, which is cur- ed towards university students. At that time rently 160 FIM. The Society has reciproci- it was even in the statutes that students 30 such visits last year. The international ty agreements with some societies. were entitled to ask and receive guidance ties thus formed have had a very positive Reciprocity members pay one half of the on points on any mathematical lecture that effect on the development of mathematical annual fee. had remained obscure to them. This article research in Finland. On the other hand, The address of the Society is: was later removed, not because students there are also other channels nowadays for Department of Mathematics, P.O. Box 4, had started to understand everything, but inviting visiting mathematicians; this FIN-00014 University of Helsinki, because in the 20th century there was a lessens the responsibility of SMY in this Finland. considerable growth in the universities and context. in the number of university students. This Another regular scientific activity of Aatos Lahtinen is in the Department of made the old article impractical. SMY has SMY is a conference called Matemaatik- Mathematics, University of Helsinki, Finland. instead enlarged the emphasis to include kopäivät, which is organised at the begin- 16 EMS June 1999 SOCIETIES that an all-Polish Mathematical Society is in the 71. making in Warsaw and he proposed the motion 10) Otton Nikodym prof. gimn. residing in Polish to initiate a “Mathematical Soc. in Cracow” Kraków Kochanowskiego 23. which might later become associated with the 11) Dr Leon Chwistek prof. gimn. residing in Mathematical Warsaw society. The motion passed unanimous- Kraków Szujskiego 7. Society ly and Dr S. Zaremba was elected to preside over 12) Dr Antoni Wilk prof. gimn. residing in the Constituting Session. Kraków XV. Józef itów 208. The chairman expressed his thanks for the 13) Dr Ludwik Horodyñski prof. gimn. resid- Józef Piórek election, asked Dr A. Hoborski to take minutes of ing in Kraków £obzowska 12. (remark in the meeting and allowed Dr Fr. Leja, the the margin: “passed away in 1919”) From the minutes of the Mathematical Society in reporter, to read out the drafts of the statutes and 14) Dr Alfred Rosenblatt docent uniw. residing Cracow regulations of the Society. in Kraków Basztowa 8. In 1999 the Polish Mathematical Society A longer discussion followed, concerning 15) Dr Antoni Hoborski docent uniw. residing celebrates its 80th anniversary, and a spe- mainly the definition of the aim of the Society, in Kraków Smoleñsk 26. cial jubilee Meeting of Polish mathemati- admission of new members, Department mem- 16) Ludwik Kaszycki in zynier residing in cians will be held in Cracow (Kraków) in bers’ terms of office, reelection of the president of Kraków Garbarska 4. September. This article contains a selec- the Society. The aim of the Soc. has been defined According to clause 10 of the Statutes, the tion of documents from the earliest ses- as follows: comprehensive stimulation of the assembly proceeded to the election of the presi- sions of the Mathematical Society in development of pure and applied mathematics. dent and Department members of the S-ty. 15 Cracow, which later developed into the The motion to add that popularization of math- members took part in voting. The following were Polish Mathematical Society. It is a modi- ematics is also an aim of the Soc. was rejected. elected: fied version of an article that appeared in Some amendments, proposed mainly by prof. Dr St. Zaremba the president (15 votes) the journal Mathematics-Society-Teaching, Zaremba, were agreed upon. Then the statutes Dr A. Hoborski the vice-president (14 votes) published by the Polish Centre for went through in the reading given by the Dr F. Leja the secretary (15 votes) Mathematical Culture. reporter, and next – the regulations fixing the Dr L. Horodyñski the treasurer (13 votes) Regretfully, in English, the charm of the membership fees and dates of ordinary sessions. The first ordinary meeting was agreed upon original documents, the now-forgotten old The membership fees were fixed at 10K and to be held next Wednesday, i.e. April 9. Dr A. Polish style and expressions, and the the annual fee at 12K; also, it was agreed to Hoborski announced that he would give a talk strange grammar and spelling have all dis- make it possible for members to replace all annu- on the theory of functions of real variable. appeared. Names, however, do not change al payments by a single payment of 250K which Upon this the Constituting Session was under translation and I hope that at least transforms an ordinary membership into a life closed. some of them (such as the ‘citizen’ Stefan membership. Banach) will add spice to the whole story. Ordinary sessions of the Society, with talks, Months passed. Mathematicians from Some funny mistakes have remained, too. will be held on the first and, if necessary, also on Warsaw, reluctant at first, finally started to It may also be worth reminding the for- the third Wednesday of the month except for the feel the need to put the scientific move- eign reader that the events related here three months of summer holidays, at 5 p.m. in ment into some organisational form. This took place almost on the morrow of the rooms of the Mathematics Seminar, ul. Œw. feeling is expressed in the next text. Poland’s regain of independence after over Anny 12. 100 years of absence from the maps of At the Constituting Session the following Minutes of the 9th ordinary session Europe and before the end of the wars that members acceded to the Society on the principles held on September 19, 1919. settled the country’s borders. as defined by the statutes and regulations: Dr A. Hoborski presiding. After a vote, the fol- 1) Dr Stan. Zaremba prof. uniw. residing in lowing were admitted as new members of the S- The Constituting Session Kraków XVIII. •ytnia 6. ty: Minutes of the Constituting Session, held on 2) Dr Franciszek Leja asyst. uniw. residing in 32) S. Dickstein prof. uniw. in Warszawa April 2, 1919 at 5 p.m. in the rooms of the Kraków ul. sw. Krzyza 16. ul. Marszalkowska 117. Philosophy Seminar, 12 St. Anne Street. 3) Dr Jan Sleszyñski prof. uniw. residing in 33) Dr Waclaw Sierpinski prof. uniw. in Present: Ob. [citizen] Stefan Banach, Julian Kraków Wygoda 7. Warszawa ul. Marszalkowska 117. Chmiel prof. gimn. [grammar-school professor], 4) Dr Kazimierz •orawski prof. uniw. residing 34) Dr Z. Janiszewski prof. uniw. in Leon Chwistek prof. gimn., Miros³aw Gibas in Kraków Garbarska 7. (crossed out and Warszawa ul. Marszalkowska 117. prof. gimn., Dr A. Hoborski docent uniw. [uni- corrected to Warszawa, Koszykowa 75.) 35) Dr Stefan Mazurkiewicz prof. uniw. in versity dozent], Dr L. Horodyñski prof. gimn., 5) Xawery Stankiewicz residing in Kraków Warszawa ul. Marszalkowska 117. Ludwik Kaszycki inŸynier [engineer], Dr Fr. D³uga 50. 36) Stanislaw Zakrocki prof. gimn. in Leja asystent uniw. [university assistant], Otton 6) Julian Chmiel prof. gimn. residing in Kraków ul.Smolensk 21. Nikodym prof. gimn., Dr A. Rosenblatt docent Kraków Tomasza 33. The president passed on the information that uniw., Antoni Rozmus prof. gimn., Dr J. 7) Miros³aw Gibas prof. gimn. residing in the Extraordinary General Assembly will be held Sleszyñski prof. uniw. [university professor], Kraków Krupnicza 28. on September 29. Mathematicians from differ- Xawery Stankiewicz, Dr A. Wilk prof. gimn., 8) Antoni Rozmus prof. gimn. residing in ent parts of Poland have been invited to partic- Dr St. Zaremba prof. uniw., Dr K. •orawski Kraków Gimnazyum ipate in it. The aim of the meeting is to organise prof. uniw. 9) Stefan Banach residing in Kraków Grodzka a reporting bureau for collecting and spreading Dr K. •orawski opened the session by saying

Four stamps featuring Polish mathematicians, issued for the International Congress of Mathematicians in Warsaw. From left to right: Stanis³aw Zaremba, Wac³aw Sierpinski, Zygmunt Janiszewski, Stefan Banach. EMS June 1999 17 SOCIETIES abroad information about the scientific move- opinion that the bureau should be organised and the Society’s sessions, be circulated among circles ment in Poland, and consider a possible reor- the aim of the bureau is to publish accounts of of mathematicians in other cities, and it is only ganisation of the Society as well as a change of works of Polish mathematicians in one of the after hearing their remarks and suggestions that the Statutes, as the Society was founded mainly Polish mathematical journals, e.g., in the new statutes could be passed at a special for assembling mathematicians working in “Wiadomoœci Matematyczne” [Mathematical meeting of the Society. Upon this Mr Leja read Cracow whereas now the idea to enlarge the News] upon which Professor Dickstein expressed his own proposal of principles on which to base sphere of activities of the Society to the entire consent, and, moreover, to inform some foreign the new statutes. These were as follows: the seat country has come up. Italian, French and English journals about the of the Society is fixed in Cracow; ordinary mem- whole mathematical movement in Poland . . . bers can be local or non-local; the latter are And now – minutes of the Extraordinary Further, the President opened up the discus- allowed to form separate branches, e.g., “the General Assembly announced by doctor sion on the question of the possible reorganisa- Warsaw branch of PTM”, about which the Hoborski. Here we find, among others, the tion of the Society and the change of Statutes. Board of the Society in Cracow is to be informed. ‘pre-history’ of the organised scientific Here the opinions diverged a little. Professor The Board of each branch has the right to admit movement of Polish mathematicians. Dickstein proposed to change the Statutes so as new members, but part of its income is to be to allow branches of the Society in different uni- assigned for general purposes of the Society, Minutes of the Extraordinary General versity towns in Poland, and to call the central such as, e.g., the accounts of publishers. Assembly society “Polskie Towarzystwo Matematyczne” The members of the Board of the Society are held on September 29, 1919, in the [The Polish Mathematical Society]. This calls to be chosen from amongst the Cracow members, Mathematics Seminar, at 5 p.m., with the fol- for the decision whether the central society except for the president or the vice-president, one lowing agenda: should have a fixed seat or rather a moveable of which can be chosen from the midst of non- 1) Organization of a reporting bureau for one, and thus to reside some time in Cracow, local members. Non-local members, absent from collecting and spreading abroad informa- and some time in Warsaw and Lvov, etc. Mr a General Assembly, may participate in the vot- tion about the scientific movement in Leja pointed out the inconveniences of a move- ing for the Board members of the Society through Poland. able seat, and added that even if the decision to sending their vote by closed mail. 2) Reading out binding Statutes and regula- change the Statutes is carried it may turn out to A longer discussion followed which led to the tions. be a void one because Circles of mathematicians conclusion that these principles can be used as 3) Possible motions concerning changes in from outside Cracow may well disagree with the guidance in drawing up the new statutes. Statutes and regulations. reading of the changed Statutes which is all the 4) Other motions and interpellations. more probable as the only mathematician from We are now close to the end of the first Professor S. Zaremba, the President, greeted outside Cracow present at the meeting is period of the Society’s existence. Here are new members of the Society, among them Professor Dickstein. Professor Zaremba the Professor S. Dickstein, who arrived from expressed the opinion that the present period Minutes of the Extraordinary General Warsaw, and said that the Extraordinary seems transitional and perhaps time has not yet Assembly General Assembly was convened for two reasons. come to establish an all-Polish mathematical held on December 22, 1920. The first is concerned with the need to organise, society. It would be rather advisable that local Present: Professor Sleszyñski, Dr Hoborski, Dr within the S-ty, a reporting bureau aimed at for- mathematical societies should first be founded in Rosenblatt, Dr Wilkosz, Dr Irena Wilkoszowa, warding information about scientific mathemat- different towns which might later start to think Dr Banach, Mr Nikodym, Mr Ziobrowski, Mr ical movement in Poland to foreign journals. of common Statutes. In further discussion, in Fijol, Dr Leja. The second reason is that the Department wished which almost all members present participated, Presiding Dr Hoborski. On the agenda: to submit for consideration of the assembly the it was decided to leave the Statutes unchanged reading of the statutes and the suggestions of possible reorganisation of the Society and the for the time being, and to postpone the decision amendments sent in by other members of the change of Statutes because the Society was of founding an all-Polish mathematical society. Society. founded mainly to gather mathematicians from After a long discussion the statutes passed Cracow, whereas lately an opinion was But the question of the society reorgan- and it was enjoined to print the new statutes and expressed by Polish mathematicians from outside isation came to a head very quickly. Here regulations. The President moved that, in the Cracow that the activities of the Society should be are excerpts from the minutes of the face of the change of statutes, a new Board of the extended to the whole of Poland. Extraordinary General Assembly held on Society should be chosen. On the motion from The President said that a letter had just April 21, 1920. Mr Nikodym it was decided that the Board be arrived from Dr A. £omnicki, Lvov saying that kept unchanged until the end of term of office, two years ago a mathematical society had also Opening the discussion, Professor Zaremba said i.e., May 1921. Upon this the General Assembly come into being in Lvov but, during wartime, its that the change of the Society name to “The was closed. activity dwindled and therefore the members Polish Mathematical Society”, agreed upon by The first Reporting General Assembly plan to join the Mathematical Society in Cracow the mathematicians from outside Cracow, is according to new Statutes was held on June 4, in case of an extension of the activities of the lat- advisable with regard to, first, future contacts 1921 in Cracow in the presence of 10 local ter. with foreign mathematical societies, and, second, members. Other 16 members sent in their votes The President proposed to discuss the ques- better chance of obtaining government grants for the elections of the new Board. Dr •orawski tion of the reporting bureau organisation and for the Society if the change is made. Dr A. from the Warsaw School of Technology was allowed Professor S. Dickstein to address the Hoborski moved that a commission be elected elected the new President of the PTM. Prof. S. meeting. which would take care of preparing a proposal Zaremba from Cracow became the first vice- Professor Dickstein recalled that as early as of new Statutes. The meeting passed Professor president, and Dr Z. Krygowski, professor at the in 1880 a Circle of Polish Mathematicians was Zaremba’s motion to change the name of University of Poznañ – the second. However, as founded in Petersburg and had published four “Mathematical Society” to “The Polish the presidential honour was not accepted by volumes of transactions containing mathemati- Mathematical Society” as well as of Dr Professor •orawski, absent from the meeting, by- cal works of Polish mathematicians. Later the Hoborski’s motion, and Drs A. Rosenblatt, A. elections had to be called for the next General task was overtaken by “Prace Matematyczno- Wilk, and Fr. Leja were elected to the commis- Assembly where votes were given to Dr Wiktor fizyczne” [Mathematical and Physical Works] sion. Stankiewicz, professor at the University of established in Warsaw in 1888. Further in the Mr F. Leja proposed that the commission be Vilna. discussion rose to speak: Professor Zaremba, given directions and general principles of elabo- Professor Dickstein, Mr Wilkosz, Mr rating the new statutes at the present General Józef Piórek is at the Mathematics Institute at Rosenblatt, Mr Chwistek, Mr Leja and Mr Assembly, and that a draft version of new the Jagiellonian University in Cracow, Poland. Ziobrowski who unanimously expressed the statutes, after having been discussed at one of

18 EMS June 1999 PROBLEM CORNER Problem Corner : The Norwegian Niels Henrik Abel Contest Paul Jainta

This is the first time that I’ve sifted the deduction of one point. Thus, if was founded in 1918, and it soon decid- through web sites before writing a answers are marked randomly, the ed to establish an annual national math- Problem Corner. Our Corner has includ- expected score of 20 points is the same as ematics competition. The first such event ed many examples of competitions and if all questions are unanswered. The best was in 1921 and then took place annual- other mathematical events around the 10% of the contestants proceed to the ly until the early 1970s. Crown Prince World, but there has never been any- second round in which only ten problems Olav, and his successor Crown Prince thing about contests for the talented are posed but which are much harder Harald, endowed the ‘Crown Prince’s youngsters of Scandinavia. than those of the initial round; the max- Prize’. However, participation was poor: The first such event arose in Norway. imum score is 50, and marking follows usually ten or less contestants had the Niels Bejlegaard, a ‘problemist’ from the same pattern. The top 20 or so scor- courage to match their mathematical Stavanger, awakened my curiosity by ers are invited to perform in the final, skills against others. So, in the mid-70s writing: ‘I have the unmistakable feeling held annually at the University of Oslo; the Abel contest’s forerunner passed that the Nordic countries lack the disci- the finalists battle with four problems in pline and well-ordering that is character- four hours. The papers are then marked away peacefully and unnoticed. But it was istic of Central European countries. on the same day so that the results are not long before the contest was resusci- Being a member of diverse Nordic math- ready for the prize-giving ceremony the tated. In 1979/80, on the 150th anniver- ematical societies I try hard to alter this, same evening. The Abel contest is the sary of Abel’s death, a new contest for but I do not seem to be very successful’. first hurdle for talented Norwegian stu- high-school students was born, and 28 It took me less time and effort than dents who wish to qualify for member- courageous pupils participated in the expected to find an expert on the pre- ship in the Norwegian team for the fol- reshaped competition. In 1981, the Abel eminent Norwegian competition, the lowing year’s International Mathematics contest became a joint action between Niels Hendrik Abel contest. Einar Rødland Olympiad. The six best finalists are invit- the Norwegian Mathematical Society and has organised this contest for many ed to participate in the IMO. In prepara- Aftenposten, the leading Oslo daily news- years, and his account reports on this tion for this yearly highlight in interna- paper. The problems appeared in the showpiece of Norwegian contests. This tional mathematics events, the finalists paper and at first the number of com- young Norwegian fellow-organizer of the take part in the Nordic Mathematical petitors shot up to 65. But for the next Abel contest has also created a web site Contest, together with teams from three years participation fell dramatical- for the contest. Denmark, Finland, Iceland and Sweden. ly. This caused another reconsideration The Niels Henrik Abel mathematics The Norwegian Mathematical of the format of the contest. contest started in 1980 as a contest in Olympiad is arranged by the national Four years later the contest was mathematical problem solving for high- Mathematical Society in cooperation remoulded for the third time and, school pupils. However, junior pupils with Telenor AS, the Norwegian tele- achieved a breakthrough. A 100-minute have also occasionally participated, and phone company, with support from the test at all national schools now precedes indeed qualified for the final and for the Norwegian Ministry of Education. The the annual contest, and the top 20 scor- International Mathematics Olympiad responsibility for posing and distributing (IMO). The aims of the Abel contest problems, for collecting and processing ers nationally enter the final. Since then, include the nurturing of students’ inter- the results, for arranging the final exam- the number of participants has continu- est in mathematics, both for the most tal- ination and drawing up diplomas, and ally increased, culminating in about 4000 ented who find little challenge at school finally for preparing the IMO-team, lies contestants in 1994. Incidentally, the and for those who are less interested in solely in the hands of the Abel commit- Nordic Mathematics Contest has started experiencing different types of mathe- tee. The organising committee is self- to cooperate with other Scandinavian matical problem. It also allows promot- appointed and self-governed, although it countries. In Autumn 1994 the contest ers of young talent to reach the most able is formally under the aegis of the underwent a cosmetic repair with an students, but so far they have had little Norwegian Mathematical Society, and at extra round inserted at school level. Its success in doing so. Norway simply lacks the start consisted of 4 to 8 university aim was to achieve a more reliable selec- the resources to provide an adequate mathematicians and high-school teach- tion and to give the best 10% of all programme of encouragement. Until ers. Nowadays, students (mostly former entrants an extra challenge. This mathe- recently, there has been no correspond- contestants such as Einar Rødland) pre- matical encore was warmly accepted ing contest for younger pupils, but an dominate. The organization of the con- among the competitors, and is now an examination for youngsters has now test is done chiefly by undergraduates. indispensable component of the contest. been initiated so as to identify young stu- Ph.D. students with scholarships and Nils The contest now serves as a vehicle for dents with the greatest talent; this ven- Voje Johansen, the official responsible modestly mathematically gifted young ture is currently at an experimental for school affairs, have taken over the people to get a glimpse of a different, stage. daily administrative duties. Another vital, more enjoyable and inspiring class of The Abel contest was named after the though less visible, role is played by the mathematics problems. Einar Rødland mathematician who proved that there is teachers of the participating schools. no general formula for solving polyno- They run the first two rounds and mark sees several students who do well in the mial equations of degree 5. Today, the the papers and their commitment is piv- contest, particularly those who qualify for contest consists of two rounds and a final otal to the success of the contest. During the IMO, with many of them taking up exam. In round 1 all contestants are the final they are needed as judges, mon- the study of mathematics and gaining an given twenty multiple-choice problems itors and officials, and later on as facilita- outstanding degree. An overview of earli- each with five options, to be answered tors to help the students prepare for the er winners in the contest and its forerun- within 100 minutes; a correct answer is IMO. Here, teachers are supported by ners reveals a striking list of people who credited with five points, each unan- both university mathematicians and stu- took up careers as mathematicians or top swered question is awarded one point, dents of mathematics. scientists, or became significant members and an incorrect answer is ‘punished’ by The Norwegian Mathematical Society of Norwegian society. EMS June 1999 19 PROBLEM CORNER The following problems exhibit the lucidity and crispness of Scandinavian questions. I hope that I have collected another set of exact- ing questions.

104 (Abel contest, final round, 1992) Choose a point P on the bisector of an angle with vertex A. A line through P meets the arms of the angle in points B and C. Show that 11+ AB AC is constant as the line rotates about P. 105 (Abel contest, final round, 1992) Find all non-negative integers x, y, z which satisfy the equation 3(x + y + z) = xyz . 106 (Abel contest, final round, 1992) Let (x, y, z) be the coordinates of a point on the surface of a sphere with centre 0 and radius 1. Find the greatest and least values of the expression xy + xz + yz . 107 (The Baltic Way, 1992) The towns in a country are connected by one-direction roads. For any two towns, one can be reached from the other. Prove that there is a town from which all the other towns can be reached. 108 (Swedish Mathematical Olympiad, final round, 1974) Find all polynomials p(x) for which p(x2) = (p(x))2 for all x. Use the result to determine which polynomials fulfil the following condition: p(x2 – 2x) = (p(x – 2))2.

109 (Proposed problem for The Baltic Way, 1995, from Estonia) Find all positive real numbers c such that the sequence a0, a1, a2, ... , where

ai−1 a0 = 1, ai = c , i = 1, 2, ...

is bounded (i.e. there exists a real number M such that |ai| ≤ M, for all i = 0, 1, 2, ...). Solutions to some earlier problems

90 With respect to an orthonormal basis we consider the curves determined by the equations x² + y² = r² (r ≥ 0, rn ∈ R ) and (xy)² = 1 Let F(r) denote the convex polygon having the intersection points of these curves as vertices (assuming that they exist). (a) Find an expression f(r) which describes the area of the polygon F(r). (b) For which values of r is F(r) a regular polygon ?

Solution by Dr J. N. Lillington (Dorchester); also solved by Niels Bejlegaard (Stavanger) and Oren Kolman (London).

We have x² + y² = r², (xy)² = 1, so x² + (1/x²) = r² and x + (1/x) = ±√(r² + 2). Thus, x² ± x √(r² + 2) + 1 = 0 and x = ± √(r² + 2) ± √(r² – 2) = y, by symmetry. Now, f(r) = 4.{[√(r² + 2) + √(r² – 2)]² – ½.[2.√(r² – 2)]²} = 8.[√(r4 – 4) + 2], for r ≥√2. For a regular polygon, this means that [2.√(r² + 2)]² + [2.√(r² – 2)]² = {2.[ √(r² + 2) – √(r² – 2)]}², or √(r4 – 4) = 2, which yields r4 = 8, or r = √(2√2).

5 4 3 2 92 Find all polynomials p(x) = x + a4x + a3x + a2x + a1x + a0, where the coefficients ai are real constants which satisfy the following condition: if a is a real or complex root of p(x), then 1/a and 1 – a are also roots of p(x).

Solution by Niels Bejlegaard (Stavanger); also solved by Oren Kolman (London), Dr. J. F. Lillington (Dorchester) and Dr Z. Reut (London).

If a is a real root of p(x) = 0, then p(x) must be of the form p(x) = (x – a) . [x – (1/a)] . (x – 1 + a) . q(x), where q(x) = x² + rx + s, for r, s∈R, giving a double infinity of polynomials. 20 EMS June 1999 PROBLEM CORNER

If a is a complex number a = c + id, then two of the roots must be equal or conjugate to each other, by the Fundamental Theorem of Algebra. The roots a, 1/a, 1 – a, 1 – (1/a), 1/(1 – a) and a/(a – 1) are not all distinct. In particular, a = 1/a gives a² = 1 or a² =± 1. Now if a ≠ +1, then a = –1, and we get the set of solutions {–1, ½, 2}. If a = 1 – a, then a = ½, and we obtain the same solutions. If a = a/(1 – a), then a² – a + 1 = 0, whose roots are ½ + ½i√3 and ½ – ½i√3. In this case, the three solutions a = 1/(1 – a) = 1 – (1/a) and 1/a = 1 – a = a/(a – 1) are identical. If 1/a = 1 – a, then a² – a + 1 = 0; this gives no new solutions. Finally, a = a/(a –1) is equivalent to a² – 2a = 0, with solutions {–1, ½, 2}. Thus, we have p(x) = (x + 1)α.(x – ½)β.(x – 2)γ, with α+ β+ γ = 5 and α, β, γ ≥ 1. In the case of complex roots, we obtain the polynomial p(x) = (x + 1).(x – ½).(x – 2).(x² – x + 1) = x5 – (5/2)x4 + 2x3 – (5/2)x + 1.

93 If a and b are non-negative real numbers such that a² + b² = 4, show that ab/(a + b + 2) ≤√2 – 1.

Solution by Dr Ranjeet Kaur Sehmi (Chandigarh, India); also solved by Niels Bejlegaard (Stavanger), Oren Kolman (London), Maurice Brémond (Avignon), Dr J. N. Lillington (Dorchester), Dr Z. Reut (London) and Claude Lamoureux (Paris).

Since a² + b² = 4, where a and b are non-negative real numbers, we can write a = 2 cos θ and b = 2 sin θ, where 0 ≤ θ ≤ π/2. Now, ab/(a + b + 2) = 4 sin θ cos θ / (2 sin θ+ 2 cos θ+ 2) = [(2 sin θ cos θ + sin θ + cos θ + 1)/(sin θ + cos θ + 1)] – 1 = [(sin θ + cos θ)(sin θ + cos θ + 1)/(sin θ + cos θ + 1)] – 1 = sin θ + cos θ – 1 = √2 sin [θ + (π/4)] – 1 ≤√2 – 1, since sin [θ + (π/4)] ≤ 1.

94 Prove, that in any convex polygon of 2n sides, there exists at least one diagonal which is not parallel to a side.

Solution by Oren Kolman (London); also solved by Niels Bejlegaard (Stavanger).

Since the polygon is convex, it has ½.2n.(2n – 3) = 2n² – 3n diagonals. Each side is parallel to at most n – 2 diagonals, because the polygon has 2n vertices. Hence the total number of diagonals parallel to some side is at most 2n.(n – 2) = 2n² – 4n. So there are at least (2n² – 3n) – (2n² – 4n) = n diagonals which are not parallel to any side.

95 Let a be a real number. For what values of a do the following simultaneous equations have real solutions? x² + y² + z² = 5, xy + yz + xz = 2, xyz = a.

Solution by Dr Z. Reut (London); also solved by Maurice Brémond (Avignon), Niels Bejlegaard (Stavanger) and J. F. Lillington (Dorchester).

The given equations are (1) x² + y² + z² = 5; (2) xy + yz + xz = 2; (3) xyz = a. Let us assume that a > 0 and that x, y, z > 0 – that is, we restrict the solutions geometrically to the first octant. Noting that (x + y + z)² = x² + y² + z² + 2(xy + yz + xz), we deduce from (1) and (2) that (x + y + z)² = 9, and x + y + z = 3. (4) The elimination of z by equation (4) gives, from either (1) or (2), x² + y² + xy – 3x – 3y + 2 = 0, (5) and with equation (3), we obtain 3xy – x²y – xy² – a = 0. (6) Multiplying (5) by x and adding to (6), we eliminate y to give the cubic equation x³ – 3x² + 2x – a = 0. (7) Multiplying (5) by y and adding to (6) gives the same equation (7) for y.

EMS June 1999 21 PROBLEM CORNER Eliminating x and y from (1) or (2), equations (3) and (4) give the same equation (7) for z. Because of the geometrical symmetry, (7) must have three real roots and the discriminant D must be positive. Since D = √(4 – 27a²), it follows that a² < 4/27 and |a| < 2/√27.

96 Consider sequences of the form x1, x2, ... , xn in which each xi is either a, b or c. Determine the number of different sequences (i) which have length n, (ii) which begin and end with the letter a, and (iii) in which adjacent terms are always different letters.

Solution by Oren Kolman, London; no other correct solutions were received. Let F(n) be the number of sequences which satisfy conditions (i), (ii) and (iii). Let T be the (binary) tree whose nodes are labelled in the following way: the initial node is labelled a, and if x ∈{a, b, c} labels a node, then the labels of the two immediate successors of that node are the two elements in {a, b, c}\ {x}. Note that F(n) is the number of branches of length n with terminal nodes labelled a, which we shall call the good branches. Since for each non-zero natural number k, there are 2k–1 nodes at level k in T, and each good branch of length k + 1 passes through a bad node at level k labelled b or c, it follows that (1) F(k + 1) = 2k–1 – F(k), and hence F(k + 2) = 2k – [2k–1 – F(k)], so that (2) F(k + 2) – F(k) = 2k – 2k–1. The recursive relation (2) for even arguments yields a telescoping sum: [F(2(k + 1)) – F(2k)] + [F(2k) – F(2k – 2)] + ... + [F(4) – F(2)] = (22k – 22k–1) + (22k–2 – 22k–3) + ... + (22 – 2) = (1/3).{1 – (–2)2k+1} – 1. Since F(2) = 0, it follows that (3) F(2k + 2) = (1/3).{22k+1 + 1} – 1. Using (1), and applying (3) to the argument 2k, we deduce that (4) F(2k + 1) = (1/3).{22k – 1} + 1. Putting (3) and (4) together, we find that F(n) = (1/3). {2n–1 + (–1)n} + (–1)n+1 = (1/3). {2n–1 – 2(–1)n}.

longer the major sponsor for the to promote, even to run their own com- Postscript Australian Mathematics Contest petition locally.’ As a reaction to the last Problems (AMC), neither in Australia, nor in That completes the Problems Corner I received a letter from Tahiti. In Tahiti we stopped our spon- Corner for this issue. I need suit- Prof. Pierre-Olivier Legrand, the sorship with Qantas and the number able contests and solutions, and leading organiser of mathematics of entrants decreased. The AMC is still welcome comments, criticisms competitions in French Polynesia. an institution, and still carried by and suggestions for the future In his reply he sounded a bit disil- their users, the pupils. We now have direction of this feature. lusioned, comparing his situation ‘second generation entrants’, sons and Finally, please propose prob- with that offered by Europe to its daughters whose parents entered the lems for our readers to solve. mathematically talented young- AMC 16 or 17 years ago. The Proposals should include a solu- sters: Australian Mathematics Trust is, in tion, references, and other ‘I discovered that in small countries, it my estimation, by far the best existing insights which are likely to help is difficult to build a local structure to structure to foster students. I tried to the editor. They can range from run a competition because I had reck- cooperate with the French equivalent elementary to advanced, from oned without the intricate human fac- ‘Le Kangourou des Mathématiques’, easy to difficult. Original prob- tor. A one-man structure is a weak but the logistics never got close to what lems are particularly sought, as construction; each adversity or pres- the Australian Trust is able to provide. are questions from problem books sure of time is a nuisance to the organ- In Europe, I think, a cooperation with and contests that are not easily iser and cripples the competition. I Eastern countries could be more bene- accessible. Other interesting prob- would like to add another lesson to my ficial. They have accumulated a lot of lems are also acceptable, provided former paper, ‘try not to be alone’. I experience in this field and they had a they are not well known and refer- under-estimated this simple fact. long tradition of doing good maths, ences are given as to their prove- Regarding the sponsors, Wespac is no but most of the time they had no means nance.

22 EMS June 1999 CONFERENCES Forthcoming conferences compiled by Kathleen A S Quinn

Please e-mail announcements of European con- Mathematical Institute of HAS, Budapest, Zahariuta (Feza Gursey Institute) ferences, workshops and mathematical meetings P.O. Box 127, H–1364 Hungary Site: Feza Gursey Institute, Istanbul, of interest to EMS members, to e-mail: [email protected] Turkey [email protected]. Announcements URL: http://www.math-inst.hu/~erdos99 Deadline: 15 June 1999 should be written in a style similar to those [For details, see EMS Newsletter 31] Information: below, and sent as text files (but not as TeX 5: CEMRACS: Centre d’été de mathéma- URL: http://www.gursey.gov.tr/complex.html input files). Space permitting, each announce- tique et de recherches avancées en cal- 6: IMLA’99 Intuitionistic Modal Logics ment will appear in detail in the next issue of the cul scientifique, Orsay / Luminy, France and Applications, Trento, Italy Newsletter to go to press, and thereafter will be Information: e-mail: [email protected] Aim: to seed a more concerted organisa- briefly noted in each new issue until the meeting URL: http://www.asci.fr/cemracs/ tion of research in intuistic modal logic takes place, with a reference to the issue in which [For details, see EMS Newsletter 31] (IML), bringing together the method-ori- the detailed announcement appeared. The pre- 5–9: Quadratic Forms and their ented and the problem-oriented sent issue includes conferences up to August approaches, and the proof-theoretic and 2000. Applications, Dublin, Ireland Information: contact Prof. D. Lewis, model-theoretic approaches Topics: applications of intuitionistic Organisers: Department of Mathematics, University July 1999 College, Dublin; tel: (+353)-1-706-8373 necessity or possibility, strong monads, evaluation modalities; use of IML and 2–5: VIIIth Oporto Meeting on e-mail: [email protected] URL: http://mathsa.ucd.ie/TMR/quadconf. modal type theory (MTT) to formalize Geometry, Topology and Physics, mechanisms of abstraction and refine- Portugal html [For details, see EMS Newsletter 31] ment; applications of IML and MTT to [Series formerly known as ‘Oporto formal verification, abstract interpreta- Meetings on Knot Theory and Physics’] 5–9: Fourth International Conference tion, program analysis and optimisation; Aim: to bring together mathematicians on Industrial and Applied Mathematics applications of modal types to integration and physicists interested in the interrela- (ICIAM 99), Edinburgh, Scotland of inductive and co-inductive types, high- tions between geometry, topology and Information: URL: http://www.ma.hw.ac.uk er-order abstract syntax, strong function- physics /iciam99/ al programming; extraction of constraints Speakers: Ron Donagi (Pennsylvania), or programs, non-standard information spectral curves, integrable systems, and mod- 5–21 August: Summer Research Semester on Complex Potential Theory and its extraction techniques; Curry-Howard cor- uli; Jürg Fröhlich (Institut für respondence between computational Theoretische Physik), Supersymmetry and Applications, Istanbul, Turkey Programme: this is a research-teaching lambda calculi and computational logics; non-commutative geometry; Ezra Getzler extensions of this correspondence by (Northwestern): The Virasoro conjecture for semester (5 July–6 August and 16–21 August 1999) on complex potential theo- other modalities or quantifiers; models of Gromov-Witten invariants: a status report; IML such as algebraic, categorical, Igor Krichever (Columbia), Moduli spaces ry (CPT) and its applications. There will be a workshop in Edirne from 9–16 Kripke, topological, realisability interpre- of Riemann surfaces and 2D integrable systems tations; notions of proof for IML and Programme: short courses of about three August 1999, emphasising the connection between functional analysis and complex intermediate constructive logics; proof lectures each, given by the main speakers, search in and implementations of IML and a limited number of seminars analysis Aim: to impart the main ideas of complex Invited speaker: Frank Pfenning Organisers: P. Gothen, J. Mourao, R. (Pittsburgh) Picken, J. N. Tavares potential theory to advanced graduate students and other interested mathemati- Programme committee: Matt Fairtlough Sponsors: Fundacao para a Ciencia e (Sheffield), Zhaohui Luo (Durham), Tecnologia, Centro de Matematica da cians; to advance scientific discussions of results and problems in CPT Michael Mendler (Sheffield), Pierangelo Universidade do Porto, Centro de Miglioli (Milan), Eugenio Moggi Matematica Aplicada, Instituto Superior Scope: CPT is a relevant potential theory for multidimensional complex analysis; it (Genova), Andy Pitts (Cambridge), Terry Tecnico, Centro Interdisciplinar de Stroup (Passau) Astrofisica, Instituto Superior Tecnico, deals with plurisubharmonic functions and maximal plurisubharmonic func- Organisers: Matt Fairtlough (Sheffield), Caixa Geral de Depositos Mauro Ferrari (Milan), Michael Mendler Site: Faculdade de Ciencias da tions, and is strongly connected with the study of the complex Monge-Ampere (Sheffield) Universidade do Porto Information: contact Matt Fairtlough, Information: contact Peter Gothen, equation. It has applications in approximation and interpolation theory, partial The University of Sheffield, Department Departamento de Matematica Pura, of Computer Science, Regent Court, 211 Faculdade de Ciencias, 4099-002 Porto, differential equations, complex dynamical systems, differential geometry and Portobello Street, Sheffield S1 4DP, UK; Portugal; tel: (+351)-2-3401441 tel: (+44)-11422-21826 or (+44)-11427- e-mail: [email protected] number theory Lecturers: S. Ko³odzej (Cracow), The main 80972 URL: http://fisica.ist.utl.pt/~jmourao/om/ e-mail: [email protected] omviii/om99b.html aspects of CPT and Monge Ampère equations; D. Vogt (Germany), CPT Phragmen- URL: http://www.dcs.shef.ac.uk/~matt/ 3–9: Computer Vision and Speech Lindelöf Principles and applications to partial mendler/floc-ws.html Recognition: Statistical Foundations differential equations; J. Siciak (Cracow), 6–16: Advanced course on mathematical and Applications, Anogia, Crete, Greece Pluripotentials and their applications in inter- aspects of image processing, Centre de Information: contact B. Gidas, Division polation and approximation theory; E. Recerca Matemàtica and Centre de Visió of Applied Mathematics, Brown Poletsky (USA), Plurisubharmonic currents per Computador University, Providence, Rhode Island and pluripotentials; A. Aytuna (Turkey), Speakers: V. Caselles (Illes Balears) and 02912, USA Introduction to classical potential theory; V. J.M. Morel (Cachan), Mathematical amodels e-mail: [email protected] Zahariuta (Russia), Plurisubharmonic func- in image processing; J. Serra (Paris), [For details, see EMS Newsletter 31] tions and analytic functions of several complex Mathematical morphology; S. Mallat 4–11: Paul Erdös and his Mathematics, variables (Palaiseau) and Y. Meyer (Cachan), Signal Budapest, Hungary Organisers: A. Aytuna (METU), T. processing with wavelets Information: contact A. Sali, Terzioglu (Sabanci University), V. EMS June 1999 23 CONFERENCES Information: URL: http://crm.es/info/ 12–17: Workshop on Model Theory and Matching, Coventry, UK acmaip/acmaip.html Permutation Groups, Trento, Italy Information: 8–17: School on Singularities in Information: URL: http://www.dcs.warwick.ac.uk/cpm/ Algebraic Geometry and String Theory, URL: http://www.science.unitn.it/~puglisi/ 24–30: Groups of Tree Automorphisms Lisboa, Portugal workshop.html and Lattices, Anogia, Crete, Greece [activity of Centro Internacional de [For details, see EMS Newsletter 31] Information: contact S. Mozes, Matematica] 12–18: Third International Conference Department of Mathematics, Hebrew Topic: the interface between singularity on Symmetry in Nonlinear University of Jerusalem, Givat Ram, theory (in complex algebraic geometry) Mathematical Physics, Kiev, Ukraine 91904 Jerusalem, Israel and superstring theory Information: contact A. Nikitin, Institute e-mail: [email protected] Programme: six courses by leading of Mathematics, National Academy of [For details, see EMS Newsletter 31] experts on both mathematical and physi- Sciences of Ukraine, 3 Tereshchenkivska 26–6 August: Structure Formation in the cal aspects of singularity theory Street, Kyiv 4, Ukraina; tel: (+38)-044- Universe, Isaac Newton Institute, Lecturers: P. Aspinwall (Duke 224-63-22 or (+38)-044-250-08-96; fax: Cambridge, UK University), V. Batyrev (Tübingen), P. (+38)-044-225-20-10 Information: Candelas (Texas), Le Dung-Trang e-mail: [email protected] / app- e-mail: [email protected] (Provence), M. S. Narasimhan [email protected] URL: http://www.newton.cam.ac.uk/programs (International Center for Theoretical URL: http://www.imath.kiev.ua/~appmath/ /sfu.html Physics), M. Reid (Warwick) first_in.html [For details, see EMS Newsletter 31] Organisers: Carlos Florentino, [For details, see EMS Newsletter 31] Organisers: Margarida Mendes Lopes, Jose Mourao, 13–17: School on Category Theory and August 1999 Orlando Neto, Joao Pimentel Nunes Applications, Coimbra, Portugal 1–6: 1999 ASL European Summer Sponsors: Fundacao para a Ciencia e Information: Tecnologia, Centro de Algebra da Meeting (Logic Colloquium ‘99), e-mail: [email protected] Utrecht, The Netherlands Universidade do Lisboa, Centro de URL: http://www.mat.uc.pt/~scta/ Analise Matematica, Geometria e Information: Association for Symbolic Sistemas Dinamicos, Centro de 13–22: International Conference on Logic, 1409 West Green Street, Urbana, Matematica e Aplicacoes Fundamentais, Biomathematics–Bioinformatics and IL 61801, USA; tel: (+1)-217-244-7902; Centro Interdisciplinar de Astrofisica Applications of Functional Differential fax: (+1)-217-333-9576 Site: Complexo Interdisciplinar of Equations, Antalya, Turkey e-mail: [email protected] Universidade de Lisboa Information: URL: http://www.math.uiuc.edu/~asl/ Deadline: for registration, passed e-mail: [email protected], [For details, see EMS Newsletter 31] Information: contact José Mourao, [email protected] or 1–7: EQUADIFF 99, Berlin, Germany Departamento de Fisica, Av. Rovisco Pais, [email protected] Information: contact Mrs. R. Loehr, 1049-001, Lisboa Codex, Portugal, tel: 16–18: ESA’99: Seventh Annual Freie Universität Berlin, Mathematisches (+351)-1-8419118 European Symposium on Algorithms, Institut I, Arnimallee 2–6, D–14195 e-mail: [email protected] Prague, Czech Republic Berlin, Germany URL: http://www.fisica.ist.utl.pt/~jmourao/ Information: e-mail: [email protected] cim/main.html URL: http://www.ms.mff.cuni.cz/esa99/ URL: http://www.math.fu-berlin.de/~equadiff/ 8–24: XXIXth Probability Summer [For details, see EMS Newsletter 31] [For details, see EMS Newsletter 31] School, Saint-Flour, Cantal, France 18–28: Foundations of Computational 2–6: Fifth International Conference on Information: contact P. Bernard, Mathematics (FoCM), Oxford, UK Finite Fields and Applications, Université Blaise Pascal, Mathématiques Information: Augsburg, Germany Appliquées, F63177 Aubière Cedex, URL: http://www.dampt.cam.ac.uk/user/na/ Information: France; tel: 04-73-40-70-52 or 04-73-40- FoCM/ URL: http://www.Math.Uni-Augsburg.DE 70-50; fax: 04-73-40-70-64 19–24: Representations of Algebras /fq5/ e-mail: [email protected] [For details, see EMS Newsletter 31] [For details, see EMS Newsletter 31] (CRASP), Sao Paulo Information: e-mail: [email protected] 5–6: International Conference on the 9–17: Symposium on Computation in URL: http://www.ime.usp.br Collatz Problem and Related Topics, Group Theory and Geometry, Coventry, Germany UK 19–24: CT99 International Category Theory Meeting, Coimbra, Portugal Topic: the 3x + 1 problem (also known as Information: contact Peta McAllister, the Syracuse algorithm, and Collatz’s, Mathematics Institute, University of Note: satellite event: School on Category Theory and Applications, 13–17 July 1999, Kakutani’s, or Ulam’s problem), and Warwick, Coventry CV4 7AL, England; related mathematics tel: (+44)-1203-524403 at the same site Information: Programme committee: Günther e-mail: [email protected] Wirsching, Marc Chamberland URL: http://www.maths.warwick.ac.uk/~dbae/ e-mail: [email protected] URL: http://www.mat.uc.pt/~ct99/ Organisers: Günther Wirsching, Marc symposium99html Chamberland [For details, see EMS Newsletter 31] 19–29: LMS Durham Symposium on Site: Katholische Universität Eichstaett, 12–13 Hydrodynamic instabilities, Quantum Groups, Durham, UK Germany waves and geophysical fluid dynamics, Information: Prof. A. N. Pressley, Deadlines: for early registration and con- Bristol, UK Department of Mathematics, King’s tributed talks, passed [meeting to mark the retirement of Prof. College, Strand, London WC2R 2LS, UK Information: contact Marc Chamberland, Philip Drazin] e-mail: [email protected] Department of Mathematics, Grinnell Information: [For details, see EMS Newsletter 31] College, Grinnell, Iowa 50112, U. S. A., e-mail: [email protected] 19–1 August: Banach Center tel: (+1)-515-269-4207 / (+1)-515-269- URL: http://www.maths.bris.ac.uk/~amnag/ Symposium on Ordered Sets, Warsaw, 4984 conference.htm Poland e-mail: [email protected] Information: URL: http://www.math.grinnell.edu/~cham 12–16: 17th British Combinatorial berl/conf.html Conference, Canterbury, UK e-mail://[email protected] Information: 22–24: CPM ’99, 10th Annual 9–14: György Alexits Memorial URL: http://speke.ukc.ac.uk/cbs/ms/bcc17/ Symposium on Combinatorial Pattern Conference, Budapest, Hungary [For details, see EMS Newsletter 31] Information: contact S. Fridli, 24 EMS June 1999 CONFERENCES Department of Numerical Analysis, Scattering Theory, Warsaw, Poland Karlskrona, Sweden Eötvös L. University, Muzeum krt. 6–8, Information: contact Prof. Thomas Aim: to honour the memory of Jean Budapest, H–1088 Hungary; Friedrich, Institut für Mathematik, Leray with lectures on fields related to tel: (+36)-1-2669-833, ext. 3113 Humboldt-Universität zu Berlin, Leray’s work e-mail: [email protected] Ziegelstrasse 13a, Unter den Linden 6, Organisers: Maurice de Gosson [For details, see EMS Newsletter 31] D–10099 Berlin, Germany; tel: (+49)-30- (Karlskrona), Jean Vaillant (Paris) 10–15: International Conference on 2093-1825; fax: (+49)-30-2093-1824 Information: contact Charlyne de Mathematical Logic, Novosibirsk, e-mail: [email protected] Gosson, University of Karlskrona- Russia URL: http://www-irm.mathematik.hu-berlin. Ronneby, Mathematics Department, Information: tel: (+7)-383-2-356237; de/~pahlisch/Banach-99html camus Annebo, 371 79 Karlskrona, fax: (+7)-383-2-357808 [For details, see EMS Newsletter 31] Sweden; tel: (+46)-455-89-270; e-mail: [email protected] 25–28: ORDAL ‘99, Third International fax: (+46)-455-89-377 [For details, see EMS Newsletter 31] Conference on Orders, Algorithms and e-mail: Charlyne. de [email protected] 16–20: International Conference on Applications, Montpellier, France Organisers:September 1999 Analysis and Mathematical Physics, Information: e-mail://[email protected] Lund, Sweden 27–29: GAMM–Workshop on 1–3: SOR ’99, Symposium on [in honour of Lars Gaarding on his 80th Computational Plasticity, Kiel, Operations Research, Magdeburg, birthday] Germany Germany Theme: differential equations and their Topics: mathematical analysis of (visco-) Information: relation to mathematical physics, includ- plasticity, well-posedness of (perfectly) URL: http://www.uni-magdeburg.de/SOR99/ ing spectral theory and scattering theory, plastic problems, numerical analysis of 1–10 International Conference on both direct and inverse problems, stabili- variational inequalities, computational Geometry, Integrability, and ty of matter and related subjects. (visco-)plasticity, numerical analysis of Quantization, St. Constantine, Bulgaria Plenary speakers: include M. Atiyah, M. localisation, a priori error analysis, a poste- Aim: to bring together experts in differ- S. Birman, J. Brüning, P. Deift, G. Grubb, riori error analysis, adaptive algorithms ential geometry, complex analysis, math- A. Jensen, P. D. Lax, B. M. Levitan, V. for spatial and time-step discretization, ematical physics, and related fields, to Maz’ya, J. Ph. Solovej, J. Sjöstrand, A. S. coarsening and special adaptive strategies assess recent developments in these areas, Wightman Programme committee: Martin Brokate and to stimulate research Programme: 15 plenary lectures, 30- and Carsten Carstensen (Kiel), B. D. Scope: the geometry of real and complex minute invited talks and contributed talks Reddy (Cape Town) manifolds, including Seiberg-Witten and Sponsor: Crafoord Fund Organisers: the Mathematical Seminar of minimal surface theory, integrability of Deadline: for submission of abstracts, 30 the Christian-Albrechts-Universität zu complex structures and classical dynami- June 1999 Kiel in cooperation with the GAMM – cal systems, and geometric quantization Information: contact C. Bennewitz, G. Committee for Discretization Methods in Invited Speakers: K. Abe (Matsumoto), Gudmundsdottir or A. Melin, Centre for Solid Mechanics A. Bette (Stockholm), M. Damnjanovic Mathematical Sciences, Lund University, Site: Mathematisches Seminar of (Beograd), K. Fujii (Hokkaido), K. Fukui Box 118, S-221 00 Lund, Sweden Christian-Albrechts-Universität Kiel (Kyoto), P. Holod (Kiev), M. Karasev e-mail: [email protected] Deadlines: for abstracts, 15 June 1999 (Moscow), M. Puta (Timisoira), M. Spera URL: http://www.maths.lth.se/garding80.html Information: contact Jan Valdman, tel: (Padova) 19–25: Topology and Dynamics: (+49)-431-880-1421; fax: (+49)-431-880- Programme: one-hour plenary lectures Rokhlin Memorial, St Petersburg, 4464 by the invited speakers; 30-minute con- Russia e-mail: [email protected] tributed talks Information: contact M. Zvagel’skii, URL: http://www.numerik.uni-kiel.de/cc Advisory Committee: P. Gilkey (Oregon), 191011 Steklov Institute of Math. /work99. G. Marmo (Naples), J. Rawnsley (POMI), nab. reki Fontanka 27, St 27–1 September: Fourth International (Warwick), W. Schempp (Siegen), G. Petersburg, Russia Conference on Geometry and Tuynman (Lille), I. Vaisman (Haifa) e-mail: [email protected] Applications, St. Constantine, Bulgaria Sponsors: the Bulgarian Academy of URL: http://www.pdmi.ras.ru/EIMI/1999 Information: Sciences, California State University /rokhlin/ URL: http://hopf.uoregon.edu/~gilkey/dirbul (Chico, USA), the Bulgarian National [For details, see EMS Newsletter 31] garia/bulgariaconf.html Science Fund, and the European Mathematical Society 20–26: Eleventh International Congress 29–4 September: Linear series and Proceedings: to be published of Logic, Methodology and Philosophy lower dimensional varieties, Bedlewo, Accommodation costs: approximately of Science, Kraków, Poland Poland $30–35 full board at GUP Hotel Information: Information: Site: GUP Hotel, St. Constantine URL: http://www.uj.edu.pl/Phils/congress/ e-mail: [email protected] Information: 22–29: Summer School on Quantum URL: http://www.im.uj.edu.pl/~workshop/ e-mail: [email protected] or Groups, Hesselberg, Germany [For details, see EMS Newsletter 31] [email protected] Information: contact Steffen Koenig, 30–1 September: Sixth International URL: http://www.csuchico.edu/math/conference Fakultät für Mathematik, Universität Symposium on Generalized Convexity /index.shtml Bielefeld, D–33501 Bielefeld, Germany and Monotonicity, Karlovassi, Samos, 3–7: Summer School on Differential e-mail: [email protected] Greece Geometry, Coimbra, Portugal URL: http://www.mathematik.uni-bielefeld. Information: contact T. Vigli-Papadaki, Information: contact Francisco J. de/~sek/summerseries.html Department of Mathematics, University Craveiro de Carvalho, Universidade de [For details, see EMS Newsletter 31] of the Aegean, Karlovassi 83200, Samos, Coimbra, Portugal 23–29 International Conference on Non- Greece; tel: (+30)-273-33914/34750; e-mail [email protected] linear Partial Differential Equations, fax: (+30)-273-33896 [For details, see EMS Newsletter 31] Lviv, Ukraine e-mail: [email protected] URL: http://kerkis.math.aegean.gr/~gc6/ 5–8: Conference Moshe Flato, Dijon, Information: France e-mail: [email protected] GC6.htm [For details, see EMS Newsletter 31] [in honour of Moshe Flato, 1937–1998] 23–4 September: Generalized Dirac Scope: the many domains of mathemat- Operators and their Geometric 30–3 September: International ics, mathematical physics and physics that Conference in Honour of Jean Leray, were close to Moshe Flato’s heart

EMS June 1999 25 CONFERENCES Speakers: Yakir Aharonov, Louis Boutet e-mail: [email protected] [email protected] de Monvel, Alain Connes, Ludwig URL: http://www.ms.mff.cuni.cz/gd99/ [For details, see EMS Newsletter 31] Faddeev, Boris Fedosov, Sergio Ferrara, [For details, see EMS Newsletter 31] 21–24: AIRO ’99, Annual Conference of Jürg Fröhlich, Christian Fronsdal, 15–23: Advanced Course on Integral the Operational Research Society of Simone Gutt, Maxim Kontsevich, Bert Geometry, Centre de Recerca Italy, Naples, Italy Kostant, Elliott Lieb, Wilfried Schmid, Matemàtica Information: Jacques Simon, Leon Takhtajan Speakers: R. Langevin (Dijon), URL: http://www.airo.org/airo99/ Organisers: Daniel Sternheimer, Jacques Introduction to integral geometry; R. 22–29: Operators on Banach spaces and Simon, Wilfried Schmid, Jean-Claude Schneider (Freiburg), Integral geometry: Cortet Banach algebras, Mussomeli, Sicily, measure theoretic approach and stochastic Italy Information: contact Laboratoire Gevrey applications de Mathématique Physique, Université de Scope: an instructional conference aimed Information: at graduate students and younger col- Bourgogne, BP 47870, 21078 Dijon URL: http://crm.es/info/acig/acig.html Cede, Dijon Cedex leagues, but open to anyone interested e-mail: [email protected] 16–22: Fourth International Workshop Programme: three 7-lecture courses in URL: http://www.u-bourgogne.fr/monge/cmf/ on Differential Geometry and its English, tutorials, and written material Applications, Brasov, Romania Lecturers: K. B. Laursen (Copenhagen) 5–11: XX International Seminar on Information: and P. Aiena (Palermo), Local spectral theo- Stability Problems for Stochastic e-mail: [email protected], ry; J. Eschmeier (Saarbrucken), Invariant Models, Lublin-Nalêczòw, Poland [email protected], subspaces; H. G. Dales (Leeds), Banach Information: K. Kubacki, Institute of [email protected] or algebras and cohomology Mathematics UMCS, Pl. Marii Curie- [email protected] Organisers: Gianluigi Oliveri (Oxford), Sklodowskiej 1, 20-031 Lublin, Poland [For details, see EMS Newsletter 31] and H. G. Dales (Leeds) e-mail: [email protected] Information: URL: http:stabil.umcs.lublin.pl/ or URL: 20–23: EPSICODE ’99: International Conference on Numerical Methods for e-mail: [email protected] or http://bernoulli.mi.ras.ru/ [email protected]. [For details, see EMS Newsletter 30] Transport-Dominated and Related Problems, Castle of Wendgräben, near URL: http://www.wolfson.ox.ac.uk/operators/ 6–10: Second Meeting on Quaternionic Magdeburg, Germany Structures in Mathematics and Physics, Scope: discretization techniques: FDM, October 1999 Rome, Italy FEM, FVM, spectral methods, collocation 4–8: ParaOpt VI, 6th International Programme committee: D. V. methods; solution of the discrete algebra- Conference on Parametric Optimization Alekseevsky (Moscow), K. Galicki (New ic problems: multigrid, domain decompo- and Related Topics, Dubrovnik, Croatia Mexico), P. Gauduchon (Palaiseau), S. sition, parallelization; analytical Information: Marchiafava (Rome), S. Salamon approaches: asymptotic expansions, URL: http://www.math.hr/dubrovnik/index. (Oxford) Shishkin-type decompositions; error esti- htm Organisers: S. Marchiafava, P. Piccinni, mates and adaptive approaches; model- 5–9 Géométrie des équations diffeéren- M. Pontecorvo ling and applications Site: Università di Roma ‘La Sapienza’, tielles, Luminy, France Invited speakers: V. F. Butuzov Scope: bifurcation theory of dynamical Università ‘Roma Tre’, Italy (Moscow), C. Canuto (Torino), P. W. Note: Proceedings of the First Meeting systems, Hilbert’s 16th problem on limit Hemker (Amsterdam), R. B. Kellogg cycles, finiteness properties of analytic can be found in the e-library of EMS: (Maryland), G. Lube (Göttingen), R. URL: http://www.emis.de/proceedings/QSMP families of functions, Bernstein inequali- Rannacher (Heidelberg), H.-G. Roos ty, centre-focus problem, Arnold-Hilbert 94/index.html (Dresden), G. I. Shishkin (Ekaterinburg), Information: problem on Abelian integrals, Abel equa- E. Süli (Oxford), R. Verfürth (Bochum), tions and Pugh’s problem, Liènard equa- URL: http://www.mat.uniroma3.it/users/max P. Wesseling (Delft) /meeting/meeting.html tions Organising committee: Lutz Tobiska Organisers: J.-P. Francois (Paris), R. 6–21: EMS Summer School in Applied (Magdeburg), Martin Stynes (Cork, Roussarie (Dijon) Mathematics: Numerical Simulation of Ireland), Lutz Angermann (Magdeburg), Site: C. I. R. M. (Centre International de Flows, Heidelberg and Freiburg, Volker John (Magdeburg) Rencontres Mathématiques) Germany, and Zürich, Switzerland Conference proceedings: to be published Information: contact J.-P. Francois, Information: as a special issue of Computing; articles will Equipe Géométrie différentielle, e-mail: [email protected] be collected after the conference and Systèmes dynamiques, applications, UFR 6–17 December: Mathematical reviewed in a standard way 920, Mathématiques, B.C. 172, Tour 46, Developments in Solid Mechanics and Registration fee: DM 80 5ème étage, Université P.-M. Curie, Paris Materials, Cambridge, UK Accommodation fee: DM 140/165 for a VI 75252, Paris, France; Information: double/single room per night (including fax: (+33)-1-44275345 URL: http://www.newton.cam.ac.uk/ full-board lodging) e-mail: [email protected] Deadlines: abstracts and registration, 14–18: International Conference on past; submission of manuscripts, 26 6–9: New Trends in the Calculus of Analytic Methods of Analysis and November 1999 Variations, Lisbon, Portugal Differential Equations (AMADE), Minsk, Information: Scope: calculus of variations, shape opti- Belarus e-mail: [email protected] misation, non-convex problems, free dis- Information: contact AMADE, magdeburg.de continuity problems and other related Department of Mathematics and URL: http://david.math.uni-magdeburg.de/ areas Mechanics, Belarusian State University, EPSICODE99 Programme committee: L. Mascarenhas Fr. Skaryny Avenue 4, 220050 Minsk 50, and J. Matos (Lisbon) Belarus 20–26: International Symposium on Organisers: CMAF/UL and IST e-mail: [email protected] or Classical Analysis, Kazimierz Dolny, Grants: some financial aid is available for [email protected] Poland selected students [For details, see EMS Newsletter 31] Information: contact T. Mazur, Information: contact CMAF/Univ. Department of Mathematics, Technical 15–19: GD’99 Seventh International Lisboa, Av. Prof. Gama Pinto 2, 1649-003 University, Malczewskiego 29, 26–600 Lisboa, Portugal Symposium on Graph Drawing, Prague, Radom, Poland; Czech Republic e-mail: [email protected] fax: (+48)-48-26333 or (+48)-48-23969 URL: http://www.math.ist.utl.pt/~ntcv99/ Information: e-mail: [email protected] or

26 EMS June 1999 CONFERENCES November 1999 Concept Laboratories Limited, HW Bonet (Valencia), J. Cerdà (Barcelona), H. Communications Limited, Racal-Airtech Jarchow (Zürich), M. Maestre (Valencia), 2–5: Workshop on Hilbert’s 10th prob- Limited, Vodafone Limited, The J. Schmets (Liège) lem, relations to arithmetic and algebra- Institution of Electrical Engineers Organisers: R. M. Aron (USA), K. D. ic geometry Proceedings: to be refereed and pub- Bierstedt (Paderborn), J. Bonet Theme: the relation between decidability lished (Valencia), J. Cerdà (Barcelona), H. problems, arithmetic and algebraic geom- Site: Royal Agricultural College, Jarchow (Zürich), M. Maestre (Valencia), etry Cirencester, UK J. Schmets (Liège) Aim: to bring together number theorists, Deadlines: abstracts, 1 July 1999; full Local organising committee: C. algebraic geometers and logicians in papers, 1 September 1999 Fernàndez, A. Galbis, P. Galindo, D. order to provoke discussions and set Information: Garcia, M. López Pellicer, V. Montesinos, directions for future research related to e-mail: [email protected] A. Peris (all UPV or UV) Hilbert’s original question URL: http://www.ima.org.uk/mathematics/con Sponsors: Technical University of Programme: selected lectures presenting ferences.htm Valencia (UPV), University of Valencia recent results in the field, and three or Organisers: (UV). four series of instructional lectures on January 2000 Proceedings: to be published in the topics from amongst the following: work 17–22: Workshop on Computational series North-Holland Mathematical Studies on Hilbert’s 10th problem, for various Stochastics, Aarhus, Denmark Site: Technical University of Valencia, rings and fields, over the past decades; Aim: computational stochastics is a new Spain some model-theoretic aspects and related and expanding area of stochastics, deal- Information: contact: K. D. Bierstedt or decidability problems, decidability for ing with computational methods of J. Bonet, Univ. Paderborn, FB 17, Math., certain generic diophantine problems analysing complex mathematical and sta- D-33095 Paderborn, Germany or and for fragments of arithmetic; the alge- tistical models. The workshop intends to Universidad Politècnica de Valencia, braic geometric structure of Diophantine reveal and discuss the potential strength Departamento de Matemática Aplicada, families, Mazur’s conjectures on the and impact of this new discipline in a vari- E-46071 Valencia, Spain topology of rational points; computation- ety of applications e-mail: [email protected] al aspects, work of Rojas on (un)com- Programme committee: Soren Asmussen URL: http://math-www.uni-paderborn.de/ putability of bounds for integral points (Lund), Eva B. Vedel Jensen (Aarhus) VLC2000 and the \exists\exists\forall\exists dio- Organisers: StocLab (Laboratory for 10–14: Third European Congress of phantine problem, complexity of dio- Computational Stochastics) and Mathematics, Barcelona, Spain phantine geometry MaPhySto (Centre for Mathematical Theme: Shaping the 21st century Scientific committee: Jan Denef, Physics and Stochastics), University of Organisers: Societat Catalana de Leonard Lipschitz, Thanases Pheidas, Jan Aarhus Matemátiques, under the auspices of the Van Geel Site: University of Aarhus European Mathematical Society Note: all who are interested are invited to Deadlines: registration, 15 November Information: contact Societat Catalana de apply, but the number of participants will 1999; submission of contributed papers, 1 Matemátiques, Carrer del Carme, 47, E- be limited; an updated list of participants October 1999 08001 Barcelona; is available at the URL below Information: contact Eva B. Vedel tel: (34 3) 270 16 26; fax (34 3) 270 11 80 Information: contact Jan Van Geel or Jensen, Department of Mathematical e-mail: [email protected] Karim Zahidi, University of Gent, Sciences, University of Aarhus, Ny URL: http://www.iec.es/3ecm/ Department of Pure Mathematics, Munkegade, DK–8000 Aarhus C, [For details, including satellite confer- Galglaan 2, B–9000 Gent, Belgium; Denmark ences, see First Announcement in EMS fax: (+32)-9-264-49-93 e-mail: [email protected] Newsletter 31] email: [email protected] URL: http://www.maphysto.dk/events/Comp URL: http://cage.rug.ac.be/~hilbrt10/hilbert Organisers: Stoc2000/ August 2000 10.html Organisers: 21–25: IMACS 2000, Lausanne, Organisers: June 2000 December 1999 Switzerland 13-16 First AMS-Scandinavian [International Association for 20–22 Seventh IMA International International Mathematics Meeting, Mathematics and Computers World Conference on Cryptography and XXIII Scandinavian Congress of Congress] Coding, Cirencester, UK Mathematicians, Odense, Denmark Scope: scientific computation, applied Theme: the future of coding and cryptog- Organisers: AMS and IMADA, Odense mathematics and simulation raphy University Scientific committee: R. Vichnevetsky Topics: all aspects of the theory and Information: contact Hans J. Munkholm, (President, USA), J. Flaherty (USA), J. applications of cryptography and coding, Odense University, Campusvej 55, DK Butcher (New Zealand), R. Beauwens including source coding, data compres- 5230 Odense M, Denmark, (Belgium), A. Iserles (Cambridge), N. sion, channel coding, error control cod- tel: (+45)-655-72309 / (+45)-659-32691 Kuznetsov (Moscow), R. D. Russell ing, combined coding and modulation, e-mail: [email protected] (Canada) coding for multiple-access, coding for URL: http://www.imada.ou.dk/~hjm/AMS. Organisers: IMACS & EPFL multi-media, quantum coding, multi- Scand.2000.html Site: EPFL, Lausanne, Switzerland functional coding, sequence design, cryp- Deadlines: for proposals for the organ- tographic algorithms, public key cryptog- Organisers: July 2000 ised session, mini-symposia and keynote raphy, authentication, key management, speakers, submit as soon as possible; for data integrity, secure and reliable proto- 3–7: Functional Analysis Valencia 2000, contributed papers, 15 September 1999 cols, interaction between cryptography, Spain Information: contact Prof. Robert Owens, coding and combinatorics [on the occasion of the 70th birthday of IMACS Congress 2000, DGM-IMHEF- Confirmed speakers: S. Blake-Wilson Professor Manuel Valdivia; satellite con- LMF, Swiss Federal Institute of (Canada), L. Knudsen (Norway), S. ference to the Third European Congress of Technology, CH–1015 Lausanne, McGrath (Limerick), G. Zemor (France) Mathematics in Barcelona, 10–14 July] Switzerland; Organising committee: M. Walker Programme: about 15 invited plenary lec- tel: (+41)-21- 693-35-89; (Chairman), M. Darnell (Leeds), P. G. tures on various topics in functional fax: (+41)-21-693-36-46 Farrell (Lancaster), M. Ganley, J. Gordon, analysis; contributed 25-minute talks in e-mail: [email protected] B. Honary (Lancaster), C. Mitchell parallel sessions URL: http://imacs2000.epfl.ch (London), F. Piper (London) Programme committee: R. M. Aron Sponsors: Codes & Ciphers Limited, (USA), K. D. Bierstedt (Paderborn), J. EMS June 1999 27 RECENT BOOKS Book Review

and this continued for a whole decade. abroad to attend conferences and those Prime case of The main opposition to German who went were carefully selected by the mathematicians came, as might he political hierarchy. numbers indivisible expected, from France. A country where Germany’s East/West division also Michael Atiyah intellectuals feature prominently in pub- caused problems, as did the question of lic life was inevitably going to find it more China and Taiwan. These mirrored simi- Mathematics without Borders: difficult to disentangle politics from sci- lar problems at the United Nations. One A History of the International ence. It is remarkable how many eminent might have thought that scientists could Mathematical Union, by Olli Lehto French mathematicians of the period also solve their problems of cooperation more Springer, 399 pp, £26 held high public office. Paul Painlevé was easily than the politicians. For mathe- ISBN 0-387-98358 9 prime minister, Emile Borel minister for maticians, at least, the opposite was usu- “It makes me very happy that after a long the navy, Raymond Poincaré (cousin of ally the case. The China/Taiwan issue is hard time all of the mathematicians of the mathematician Henri Poincaré) was instructive. At the UN, realpolitik eventu- the world are represented here. This is as president of the republic. The dominant ally won the day, but the IMU had the it should be and as it must be for the figure, and the most hostile to German luxury of moral scruples. Although its prosperity of our beloved science ... It is a mathematicians, was Emile Picard. He statutes had been carefully drafted so as complete misunderstanding of our sci- was president of the International not to refer to nation states, it took near- ence to construct differences according to Research Council from 1919 to 1931, ly 30 years to devise a formula acceptable peoples and races, and the reasons for honorary president of the IMU (1929-32) to the IMU, China and Taiwan. The com- which this has been done are very shabby and permanent secretary of the French bination of mathematical precision and ones. Mathematics knows no races ... For Academy of Sciences from 1916. oriental subtlety was a hard nut to crack. mathematics, the whole cultural world is The French position did not go unop- a single country.” The speaker, who A unique difficulty faced the IMU at posed, particularly in Britain, the United the time of the planned Warsaw congress received a standing ovation for this forth- States and Scandinavia. G. H. Hardy, the right affirmation of the scientific ethos, of 1982. Martial law had been declared leading British mathematician, was an and the country was in turmoil. Many in was the great German mathematician early and outspoken opponent, as might David Hilbert. The occasion was the the West felt that the congress should be have been expected from a staunch sup- cancelled as a political protest. But the Eighth International Congress of porter of Bertrand Russell’s pacifist stand Mathematicians at Bologna in 1928, the Polish mathematicians who had worked and his subsequent troubles with Trinity so hard in preparation, and who were not first postwar congress to which German College, Cambridge. The Americans, responsible for the actions of the commu- mathematicians had been invited. who were becoming increasingly impor- nist government, were understandably The tortuous politics behind this event tant, had little sympathy with the French keen to hold the congress. Eventually it and, more generally. the inter-relation attitude. Eventually Picard had to con- was decided to postpone the congress by between politics and science, is the main cede defeat, and the Bologna Congress, one year. It was successfully held in 1983, theme of this account by Olli Lehto of the presided over by Salvatore Pincherle, was by which time the political situation was history of the International Mathematical the turning point. The IMU itself, as improving. Union. It covers in essence the whole of opposed to the congress, was not so for- the 20th century, and, by focusing on the tunate. Its internal politics led to its There are those who believe, honestly role of key individuals, it brings to life demise in 1932, despite heroic efforts by but perhaps naively, that science should what might otherwise be a dry academic its last president, the British mathemati- and can be insulated from international study. cian William Henry Young. politics. In reality this is not always easy, Formal international cooperation in The lessons of history are sometimes and genuine ethical dilemmas occur. For mathematics started at the end of the heeded. The political mistakes of 1918 instance the Japanese were planning to 19th century and culminated in the First were not repeated in 1945. Germany was host the 1990 congress at a time when International Congress in Zurich in 1897. not ostracised, and this applied also in UN sanctions against South Africa might The major role of France and Germany the scientific sphere. The US was now the have prevented South African mathe- was reflected in the fact that the second dominant power, and American mathematicians from attending. The problem congress took place in Paris in 1900 and maticians under Marshall Stone took the was solved, with honour on all sides, but the third in Heidelberg in 1904. The lead in organising the postwar congress it was a close call. Paris congress holds a special place in at Harvard in 1950 and in setting up a Lehto, as secretary of the IMU for the history of mathematics because it was new IMU. The statutes of the IMU were seven years and as organiser of the there that Hilbert set out his famous list clear and explicit: no country was barred. Helsinki congress in 1978, has recorded of problems for the century – the possi- Even in France, attitudes in 1945 were an eventful century of international ble repetition of which in the year 2000 different from 1918. The leading French mathematical organisation and has both fascinates and intimidates the world mathematician Henri Cartan (a future enlightened the official records with sen- community. president of IMU), whose family had suf- sitive accounts of what went on behind The world war of 1914-18 put an end fered grievously in the war, was one of the the scenes. While primarily addressed to to these four-yearly congresses, and its first to visit Germany to meet and assist the mathematical community, who will be aftermath left a legacy of hostility that his mathematical colleagues. familiar with the main actors, the hook poisoned the air in political and scientific If the French-German problem had should attract a wider audience interested circles. The International Research been resolved, the second half of the 20th in the way in which politics and science Council, covering the whole of science century saw other political divisions, and interact. and giving birth to specialised bodies the IMU had to struggle with these. For This review first appeared in the Times Higher such as the IMU. was set up in the imme- many years Russia proved a difficult part- Educational Supplement, 12 March 1999, diate postwar years, and it specifically ner. This was particularly unfortunate excluded Germany and its allies. The because Russia had a great and continu- and is reprinted with permission. IMU and the closely associated interna- ing mathematical tradition. In the early Sir Michael Atiyah, OM, was formerly Master, tional congresses were equally affected, days post-1945 few Russians were allowed Trinity College, Cambridge. 28 EMS June 1999 RECENT BOOKS Recent books edited by Ivan Netuka and Vladimír Souèek

Books submitted for review should be sent to 42511-1 Welsh, Approximate counting. Each article is Ivan Netuka, MÚUK, Sokolovská 83, 186 75 This book contains the proceedings of the of substantial length and presents useful Praha 8, Czech Republic. 4th International Congress of Geometry information and a collection of problems held in May 1996 at Thessaloniki, Greece. directed not only at specialists. Y. Abramovich, E. Avgerinos and N. C. It includes versions of the six invited ple- Congratulations to the editor and organis- Yannelis, eds., Functional Analysis and nary lectures, together with fifty contribu- ers for the meeting and its proceedings. Economic Theory, Springer, Berlin, 1998, tions to the programme of the congress. (jnes) 296 pp., DM 149, ISBN 3-540-64495-4 The topics of the plenary lectures (by N. K. In July of 1996, a conference on non-linear Artémiadis, W. Benz, P. M. Gruber, N. A. Belleni-Morante and A. C. McBride, analysis and its applications in engineering Kapoileas, R. Osserman and I. R. Applied Nonlinear Semigroups, Mathemat- and economics was held in Greece on the Shafarevic) were taken from hyperbolic ical Methods in Practice, John Wiley & Sons, occasion of the birthday of Ch. Aliprantis. geometry, convex geometry, minimal sur- Ltd., Chichester, 1998, 273 pp., £50, ISBN 0- This book contains contributions in both face theory and the theory of algebraic 471-97867-1 mathematics and economics. In the first varieties. Individual contributions cover a The aim of this book is to introduce to a part, there are mathematical papers con- broad spectrum of geometrical problems non-expert the method of solving abstract cerning disjointness-preserving operators, taken from different areas of geometry. Cauchy problems (ACP) via (linear and positive isotropic random vectors, a topo- Some of the contributions are written in non-linear) semigroup theory. It can serve logical approach to fuzzy measures, the German and French. (vs) to students as a first introduction to the ranges of additive correspondences, a theory. The prerequisities needed are just characterisation of the behaviour of back- M. Artin, Algebra, Birkhäuser Advanced a basic knowledge of real analysis and vec- ward minimal vectors, non-linear ortho- Texts. Basler Lehrbücher, Birkhäuser, Basel, tor spaces; any necessary functional analy- morphisms and central operators, finitely 1998, 705 pp., DM 88, ISBN 3-764-32927- sis and Lebesgue integration is sum- generated vector sublattices, the second 0 marised in the book. Chapters 2-5 present dual of the space of all compact operators This is a reprint of the 1993 German trans- the theory of strongly continuous semi- on a Banach space, topological transitivity lation of the original English version groups of linear operators and its relation and recurrence, regular and order bound- (1991). The book is a systematic treatment to strong solutions of ACPs, mild solutions ed operators. The second part contains of classical parts of algebra (matrices, of semilinear ACPs, dissipative and m-dis- seven papers in economics. (jl) groups, vector spaces, linear mappings, sipative (non-linear) operators and semi- bilinear forms, representations of groups, groups of contractions generated by them, G. E. Andrews, The Theory of Partitions, rings, modules, fields, and Galois theory). relations to strong solutions, perturbations Cambridge Mathematical Library, Cambridge These parts and some others (such as the and weak solutions. Included are a number University Press, Cambridge, 1998, 255 pp., axioms of Peano or solutions to the exer- of examples. The last chapter (34 pages) £19.95, ISBN 0-521-63766-X cises), and especially the manner of the contains three (more sophisticated) equa- This is a paperback edition of the 1976 exposition, give a special flavour to the tions that model particle transport (a semi- classical treatise on the theory of number text, making it a very popular and linear inhomogeneous problem, mild solu- partitions, a topic lying on the borderline favourite textbook. Moreover, some years tion), the diffusion of a contaminant (an between number theory and combinatorics ago, I had the pleasure of listening to a lec- affine operator describing inhomogeneous that was founded by Euler and cultivated ture of Professor Artin in Paris. Comparing boundary conditions, strong solution), and by Ramanujan, Hardy and many others. Its my impressions of the lecture and the the combustion of a solid fuel (m-dissipa- content is characterised best by the titles of book, I have the feeling that both book and tive operator, strong solution). the chapters: the elementary theory of par- lecture were made with the same vivid Each chapter is accompanied by a list of titions, infinite series generating functions, colours streaming from the complex per- exercises (hints are added to more difficult restricted partitions and permutations, sonality of the author. (lbe) ones). Some of the fundamental theorems compositions and Simon Newcomb’s prob- (such as Hille-Yosida) are stated without lem, the Hardy-Ramanujan-Rademacher R. A. Bailey (ed.), Surveys in proof but with references; nevertheless, all expansion of p(n), the asymptotics of infi- Combinatorics, 1997, London Mathematical proofs in the book are worked out in nite-product generating functions, identi- Society Lecture Note Series 241, Cambridge detail. The book contains one page of ref- ties of the Rogers-Ramanujan type, a gen- University Press, Cambridge, 1997, 338 pp., erences. (ef) eral theory of partition identities, sieve £24.95, ISBN 0-521-59840-0 methods related to partitions, congruence This book presents the proceedings of a K. Bichteler, Integration – A Functional properties of partition functions, higher- British Combinatorial Conference. It con- Approach, Birkhäuser Advanced Texts, dimensional partitions, vector and multi- tains nine contributions that cover some of Birkhäuser, Basel, 1998, 193 pp., DM 78, partite partitions, partitions in combina- the main advances in contemporary com- ISBN 3-7643-5936-6, ISBN 3-8176-5936-6 torics, and computations for partitions. binatorics: J. H. Conway, M13 (this includes This book presents Lebesgue integration Almost all of these areas have seen new dis- a new construction of this Mathieu group), theory based on a modified Daniell’s coveries and developments in the last K. Edwards, The harmonious chromatic num- approach. The first chapter is devoted to a twenty years. To identify some of them, the ber and the achromatic number, C. Lam, review of basic notions, such as the author has added an introduction and a Computer construction of block designs, C. E. Riemann integral and the theorem of list of recent references (each chapter has Praeger, Finite quasiprimitive graphs, B. A. Stone-Weierstrass. The theory starts in its own list of references). There is no Reed, Tree width and tangles: a new connec- Chapters 2 and 3 with an elementary inte- doubt that this book will continue to serve tivity measure and some applications (this is gral (a linear map defined on a lattice ring as a basic and indispensable source of one of the best introductions to Robertson- of bounded functions on some set). Using information for everyone interested in this Seymour-Thomas theory), A. Schrijver, a Daniell mean seminorm, this elementary fascinating subject. (jnes) Minor-monotone graph invariants (centred integral has a straightforward extension to about Colin de Verdier variations, as devel- the extended integral. The notion of mea- N. K. Artémiadis and N. K. Stephanidis oped by Lovász, Schrijver and his stu- surability is then motivated by Littlewood’s (eds.), Proceedings of the 4th International dents), T. Szönyi, Some applications of alge- principles. The fourth chapter contains the Congress of Geometry, Thessaloniki 1996, braic curves in finite geometry and combina- study of classical Banach Lp-spaces and the Aristotle University of Thessaloniki, torics, W. T. Trotter, New perspectives on last chapter deals with products and Thessaloniki, 1997, 440 pp., ISBN 9-607- interval orders and interval graphs, and D. images of measures, signed measures, dis- EMS June 1999 29 RECENT BOOKS tributions of measurable functions and D. M. Clark and B. A. Davey, Natural Equations, London Mathematical Society, maps, convolution and interpolation. The Dualities for the Working Algebraist, Lecture Note Series 255, Cambridge University text includes exercises and an appendix Cambridge Studies in Advanced Mathematics Press, Cambridge, 1999, 424 pp., £27.95, where answers and hints to the majority of 57, Cambridge University Press, Cambridge, ISBN 0-521-59699-8 them can be found. 1998, 356 pp., £40, ISBN 0-521-45415-8 This volume is based on lectures presented This book is intended for beginning The natural dualities between the concrete at the second international conference on graduate students with a basic knowledge categories K and H are created by a ‘schiz- symmetries and integrability of difference of real analysis. It might also be useful to ophrenic object’, an object carrying two equations (SIDE II) at the University of advanced mathematicians and everybody structures, the first making it an object of K Kent at Canterbury in July 1996. It con- who wish to become acquainted with this and the second an object of H – for exam- tains 33 articles and a list of conference approach to the theory of the Lebesgue ple, the two-point Boolean algebra and the participants. integral. (jl) two-point Boolean space in the case of The contributions cover the following Stone duality, or the two-point distributive topics: special functions and difference R. Bix, Conics and Cubics, Undergraduate lattice and the two-point Priestley space in equations (discrete Painlevé equations, dif- Texts in Mathematics, Springer, New York, the case of Priestley duality. In the mono- ference– and q-difference orthogonal poly- 1998, 289 pp., DM 98, ISBN 0-387-98401-1 graph, only natural dualities with finite nomials, separation of variables), algebraic This is an elementary textbook containing schizophrenic objects are examined; aspects (quantum algebras and representa- the theory of real conics and cubics in the Pontryagin duality remains beyond the tion theory, associated special functions), real projective plane. It is addressed main- scope of the monograph, although its computational and numerical aspects (for- ly at prospective and current teachers at restricted variant is mentioned. mal theory of orthogonal polynomials, secondary schools. Each chapter begins The authors present a general theory soliton cellular automata, symplectic and with historical remarks on the topics it con- which, besides its beauty, is of use when volume-preserving integrators, integrable tains and a discussion of related geometri- examining varieties and quasivarieties of versus non-integrable discretisations in cal problems. For a study of real conics and universal algebra determined (by means of computation), symmetry aspects (symme- cubics, the author uses homogeneous coor- products, subalgebras and isomorphic tries of difference equations, similarly dinates and applies the Bezout theorem to copies) by a finite universal algebra M. reductions, integration techniques through intersections of curves. Some classical They create a category of structured symmetries), analytic aspects (analysis of results, such as Pascal’s theorem and the Boolean spaces – the category obtained by difference equations, isomonodromic dual correspondence introducing non-empty powers and closed subobjects deformation theory for discrete systems, envelopes of conics, are presented. An of the underlying set of M, endowed with asymptotics of orthogonal polynomials), interesting part of the book is the theory of the discrete topology and some additional geometry (discrete curves and surfaces, cubics, giving most known results. (jbu) structure consisting of operations (total connections with discrete soliton systems, S. D. Chatterji, Cours d’Analyse, Vol. 3, and partial) and relations; M is then a visualisation techniques) and applications Equations différentielles ordinaires et aux schizophrenic object of these two cate- (neural networks, coding theory and cryp- dérivés partielles, Presses Polytechniques et gories. In this approach, the first category, tology, data compression, mathematical Universitaires Romandes, Lausanne, 1998, the quasivariety of universal algebras and biology and economics, integrable algo- 755 pp., sFr 108, ISBN 2-880-74350-8 their homomorphisms, is the centre of rithms). All these subjects are highly inter- This third volume of the Cours d’Analyse interest, and the second category, the cate- connected. gives a detailed introduction to ordinary gory of the structured Boolean spaces, is The contributions are written in such a and partial differential equations, as well created in order to get dualities with ‘nice way as to give a brief overview of the state as to other parts of analysis useful in properties’. In the ‘dual category’ of the of the art whilst reporting some original physics. It arose from a course delivered by structured Boolean spaces, it is often easi- research in the subject area. The reviewer the author for ‘future ingénieurs, mathé- er to solve some problems that are of inter- is convinced that this book will form an maticiens et physiciens’ at the Ecole poly- est in the original category. The authors inspiration for further research and so technique fédérale de Lausanne. show the fruitfulness of this idea in some help to establish the links between the var- In 160 pages, the fundamentals of ordi- examples. ious communities working on discrete sys- nary differential equations are presented The theory itself offers nice and sophis- tems. (kn) (the general existence and uniqueness the- ticated procedures on how to create an orems and linear equations). About 400 additional structure on the discrete space G. A. Edgar, Integral, Probability, and pages are then devoted to Hilbert space on the underlying set of a given finite alge- Fractal Measures, Springer, New York, theory, orthogonal expansions, and opera- bra M to get a nice connection between the 1998, 286 pp., 36 fig., DM 69, ISBN 0-387- tors on Hilbert spaces, including unbound- corresponding categories. Starting from 98205-1 ed operators, spectral theory, language of ‘pre-dualities’ which can always be obtained This book is a loose continuation of the quantum mechanics, Fourier and Laplace by laying all the algebraic relations on the author’s text Measure, Topology, and Fractal transforms and distributions. The last part discrete space, the authors present some Geometry. (about 170 pages) deals with partial differ- necessary and/or sufficient conditions to The first chapter summarises basic facts ential equations. Physical motivation is improve it and to diminish the number of from measure theory, with an emphasis on given and basic problems for elliptic, para- operations and relations in the additional outer measures. Hausdorff and packing bolic and hyperbolic equations are studied. structure of the Boolean spaces without measures are studied in detail and various Harmonic function theory, the Dirichlet destroying an already existing duality, and notions of dimension are introduced. Also, problem and eigenvalues of laplacians are obstacles for these procedures for some local fractal measures are considered and also treated in detail, and special chapters finite algebras M. Nice dualities are the geometry of fractals is investigated, fre- treat the heat equation and the wave equa- obtained for the varieties of Heyting alge- quently using suitable densities. tion. There are plenty of well-chosen exer- bras, Kleene algebras, De Morgan alge- The second chapter discusses the theory cises, mainly of a computational character. bras, Stone algebras, Post algebras, proper of integration. The approach to the inte- Historical comments and bibliographical subvarieties of the variety of Abelian gral of a non-negative function with remarks form another nice feature of the groups, and many others. respect to a measure is based on the idea of book. Although this monograph is very com- the ‘area’ under the graph (formally intro- The three volumes of Cours d’Analyse prehensive, it is written in a readable clear duced, of course, by means of a product of represent an important addition to the style and can be recommended to the measure in question and one-dimen- existing textbooks on mathematical analy- researchers and to students of advanced sional Lebesgue measure). The integration sis and will be appreciated by students of courses. (vt) theory developed covers the standard mathematics and physics, as well as univer- material on the abstract Lebesgue integral sity teachers interested in mathematical P. A. Clarkson and F. W. Nijhoff (eds.), as well as Radon-Nikodym derivatives, the analysis. (in) Symmetries and Integrability of Difference Riesz Representative Theorem, narrow 30 EMS June 1999 RECENT BOOKS convergence of measures, and properties disordered media, or on curve detection in study on the classical, as well as on some of the space of Borel probability measure 3D dot patterns using Voronoï neighbour- recently discovered, properties of these on a metric space. hoods. spaces – for example, the results on com- Chapter 3 deals with topological and The proceedings will be certainly useful plemented subspaces of the space J, the fractal dimension, the M. Riesz capacity for mathematicians in pure or applied result on dentability in JT*, the results on approach to fractal dimension, fractal mathematics, or with orientations towards fixed points, isometries, etc. The presenta- measure, pointwise dimension, iterated computer science (as computer graphics, tion makes the text accessible to graduate function systems, self-affine graphs and image recognition, artificial intelligence), students, and the text is a good reference self-similar measures. physics, biology, astronomy, geography, book for researchers in Banach spaces and The next chapter is an introduction to molecular biology, radiation physics, cos- related fields. (vz) probability theory (including the law of mology, chemical engineering or physical large numbers) needed in the final chapter chemistry. It can also be recommended to R. Friedman, Algebraic Surfaces and on probability and fractals. The chaos post-doctoral students with the above Holomorphic Vector Bundles, Universitext, game is described and the dimension of interests. (spor) Springer, New York, 1998, 328 pp., DM 88, self-similar measures is investigated. ISBN 0-387-98361-9 Special attention is paid to random Cantor A. Facchini, Module Theory, Progress in This book presents a comprehensive and sets, and further statistical self-similarity Mathematics 167, Birkhäuser, Basel, 1998, contemporary overview of the theory of and statistically self-affine graphs are dis- 285 pp., DM 138, ISBN 3-7643-5908-0 and complex surfaces and vector bundles on cussed. The dimension of paths of 0-8176-5908-0 them. Complex surfaces can also be con- Brownian motion is evaluated and a multi- The main result of the book is a presenta- sidered as interesting examples of 4- fractal decomposition is briefly mentioned. tion of a negative answer to the Krull and dimensional real manifolds, important in Each chapter is accompanied by a Warfield problems, that the Krull-Schmidt mathematical physics. Their theory has ‘Remarks’ section with further relevant Theorem does not hold for finite direct also been intensively developed in recent information and bibliographical indica- sums of artinian and uniserial modules. On years, in connection with the Donaldson tions (there are 273 references). This book the other hand, a weaker form of the Krull- theory and the Seiberg-Witten theory. is recommended for anybody who wants to Schmidt Theorem for finite sums of biuni- In the first part, a brief and nice intro- learn the mathematics of fractals. (in) form modules is proved. This applies to duction to the theory of algebraic surfaces uniserial modules, since each uniserial is given, including curves on surfaces, P. Engel and H. Syta (eds.), Voronoï’s module is biuniform. In general, finitely coherent sheaves and the birational geom- Impact on Modern Science I, II, Proceedings generated serial modules are determined, etry of surfaces. of the Institute of Mathematics 21, Institute of not up to one permutation of isomorphic The stability of bundles and their ele- Mathematics, Acad. Sci. Ukraine, Kyiv, 1998, summands, but up to two permutations of mentary properties are studied in the next 274 pp. and 225 pp., US$50, ISBN 966-02- monogeny and epigeny equivalent sum- part. Ruled and elliptic surfaces are stud- 0643-7 and 966-02-0644-5 mands. Moreover, the author presents cer- ied in detail, and vector bundles and their G. Voronoï is one of the most cited mathe- tain results for the case of infinite direct geometrical properties are described. maticians. These volumes are the proceed- sums of uniserial modules. Special attention is paid to the structure of ings of the second conference devoted to The author gives his attention to the moduli space of bundles on a surface and the various aspects of mathematical work class of serial rings, especially to the sub- their local and global properties. For ruled of G.Voronoï. The conference was held in class of serial rings that have Krull dimen- surfaces and elliptic surfaces X, it is possi- Kyiv in 1998 (the first one was held in sion. He presents a detailed description of ble to present the given surface as a fibra- 1993). quotient rings of serial rings and he stud- tion over a base curve. Such a fibration The first volume consists of two parts. ies also the class of serial rings that are iso- allows us to study bundles over X by study- The first (historical) part contains two morphic to endomorphism rings of artin- ing their restriction to fibres of the fibra- mathematically oriented contributions: a ian modules. tion. In particular, a description of the sin- description of the mathematical contribu- This book is written in an attractive and gular fibres of this fibration and a classifi- tions of Voronoï during his Warsaw period fresh mathematical style. Each topic is cation of stable bundles on them are used (1894-1908) and the connections between arranged well and lucidly. The author has for understanding stable rank 2 vector Voronoï’s summation formula and the made important contributions to the study bundles over elliptic surfaces. geometry of quasicrystals. The remaining of direct sum decompositions and many of Results from the earlier parts of the contributions of this part are formed by a the main results in this book include his book are used for an alternative proof of short (14 pp.) illustrated biography of own work. (jze) Bogomolov’s inequality for stable bundles Voronoï. Of interest are fragments of and also for a discussion of the classifica- Voronoï’s diary, in its Russian original and H. Fetter and B. Gamboa de Buen, The tion of algebraic surfaces using moduli an English translation. The second part, James Forest, London Mathematical Society spaces of stable bundles. entitled Development of Voronoï’s research in Lecture Note Series 236, Cambridge University Each chapter ends with a number of modern mathematics, contains surveys on Press, Cambridge, 1997, 255 pp., £27.95, exercises containing further results of the various aspects of such classical results as ISBN 0-521-58760-3 theory. The book can be recommended to Voronoï’s congruence on Bernoulli num- The James space J consists of all sequences everybody interested in the topic. (jbu) bers and its summation formula in analytic of real numbers x = {ai} for which x = number theory. sup 1/√2|(ap1 – ap2)² + (ap1 – ap3)² + … + M. Giaquinta, G. Modica and J. Soucek, ½ The second volume also has two parts. (apm–1 – apm)² + (apm – ap1)²| < ∞ with lim an Cartesian Currents in the Calculus of The first part, entitled Investigations in par- = 0, where the supremum is taken over all Variations: I, Cartesian Currents, II, allelohedra and Voronoï domains, contains ten choices of m and p1 < p2 < … < pm. The Variational Integrals, Ergebnisse der contributions in these areas. The last part, James tree space JT is then obtained from the Mathematik und ihrer Grenzgebiete, A Series of Applications in the natural sciences, includes space J by replacing the index set (the inte- Modern Surveys in Mathematics, Vols. 37/38, contributions on application of Voronoï’s gers) by an infinite tree. Both spaces are Springer, Berlin, 1998, 711 and 697 pp., DM tessellation to detect a crystalline nucleus very important in Banach space theory, 229 each volume, ISBN 3-540-64009-6 and in the analysis of computer simulation of separable and non-separable, linear and 3-540-64010-X crystallization process, on computational non-linear. For example, J is non-reflex- Any graph of a smooth function u: Ω→RN, porosimetry, on Voronoï’s polyhedron ive, J** is isometric to J, the codimension where Ω is an open subset of Rn, is an n- analyses for characterizing the local envi- of J in J** is 1, and J × J is not isomorphic dimensional surface in Rn × RN which can ronments of atoms in the supercooled to J. The space JT is a separable Banach be endowed with a natural orientation. metal liquids and glasses, a geometrical space with non-separable dual, such that The oriented graph induces an n-dimen- n N method of analysis of the statistical ensem- JT contains no isomorphic copy of l1. sional current in R × R which we identi- bles of the trapping sites for electrons in The book contains a comprehensive fy with the graph. Limit currents of smooth EMS June 1999 31 RECENT BOOKS graphs are currents in the ‘weak closure’ of tion to geometry of plane algebraic curves. (mb) smooth graphs. A list of basic properties of It is designed as a first text for undergrad- limit currents is used to define Cartesian uates in mathematics, as well as a text for K. Grove and P. Petersen (eds.), currents. The spaces of Cartesian currents postgraduate students in engineering and Comparison Geometry, Mathematical in the calculus of variations lead us to hope physical sciences. The material contained Sciences Research Institute Publications 30, that they may serve when the usual func- is standard, the only exception being that Cambridge University Press, Cambridge, 1997, tion spaces are not effective enough. The real curves are studied first (for motiva- 262 pp., £30, ISBN 0-521-59222-4 authors devoted about ten years of their tion) and an extension of the theory to the This volume is a beautiful, comprehensive intensive and systematic research to devel- case of a general follows later. There is also and up-to-date collection of expository op the theory of Cartesian currents. This a section that shows the relation between and research articles, written by leading book contains the result of their investiga- the theory of algebraic curves and planar experts in the field. The survey articles are tions, as well as all the background needed kinematics (e.g., special planar motions). written by U. Abresch, W. T. Meyer and many related topics. Only a small part of the book is devoted to (Injectivity radius estimates and sphere theo- The monograph is divided into two general polynomial algebra theory. rems), M. T. Anderson (Scalar curvature and thick volumes. The first volume contains a The theory of affine conics, especially geometrization conjecture for 3-manifolds), T. self-contained introduction to geometric the affine classification and their affine H. Colding (Aspects of Ricci curvature), R. E. measure theory, starting from general invariants, is studied in more detail. For a Greene (A genealogy of noncompact manifolds measure theory and including the topics of general affine curve of arbitrary order, tan- of nonpositive curvature), Y. Otsu (Differential area and co-area, fine properties of W1,p- gents at a point, the multiplicity of the geometric aspects of Alexandrov spaces), P. functions, BV spaces and sets of finite point and intersection numbers for the Petersen (Convergence theorems in perimeter, general and integer multiplicity pair of curves are defined and discussed. Riemannian geometry) and S. Zhu (The com- rectifiable currents, deformation and clo- In relation to rational curves, Diophantine parison geometry of Ricci curvature). The sure theorems, degree theory, and conti- equations are mentioned. This enables the research articles are witten by G. Perelman nuity of gradient minors and their approx- author to present some applications of and A. Petrunin. (ok) imation properties. The main aim of the algebraic geometry in number theory. volume is to study the class of Cartesian In the second part, a natural extension H.-C. Hege and K.Polthier, Visualization currents. Deep closure, compactness and of the theory to projective algebraic curves and Mathematics. Experiments, Simul- structure theorems are established, and is given. All standard questions (properties ations and Environments, Springer-Verlag, particular interest is paid to Cartesian cur- of singularities, tangents and intersection Berlin, 1997, 386 pp., 230 fig., DM 138, rents between manifolds, which naturally numbers) are also discussed for projective ISBN 3-540-61269-6 carry induced homology and cohomology curves. One of the global results, Bezout’s This book is a collection of contributions maps. Among the main topics let us men- theorem for curves in complex projective which were presented at the international tion flat chains, the Hodge-Kodaira- plane, is presented. Some special types of workshop ‘Visualization and Mathematics’, Morrey decomposition theorem, Poincaré- complex projective algebraic curves are held in June 1995 in Berlin. The aim of the Lefschetz and de Rham dualities, intersec- mentioned – for example, cubics together workshop was to show how mathematics is tion and indices. with their natural group structure. There important and helpful for visualisation and In the second volume, the theory of are many examples illustrating the theory computer graphics, and vice versa. The Cartesian currents is applied to problems and many exercises at the end of each book contains several parts that cover main in the calculus of variations. Minimisation chapter. (jbu) topics of current research interest in this of the energy functional in non-linear area: visualising mathematics, geometric (finite) elasticity leads to investigation of M. Grey, M. Mezzino and M. A. Pinsky, algorithms and experiments, visualisation polyconvex and quasiconvex integrands. Introduction to Ordinary Differential algorithms and data structures, visualisa- Existence theorems for minimisers are Equations with Mathematica. An tion environments, and visualization and obtained in the classes of weak diffeomor- Integrated Multimedia Approach, The simulation techniques. This book gives a phisms. These are Cartesian currents Electronic Library of Science, Springer-Verlag, very nice and interesting overview on this which are ‘well invertible’ in the class of New York, 1997, 890 pp., DM 128, ISBN 0- interdisciplinary area, and it is recom- Cartesian currents. The spaces of weak dif- 387-94481-8 mended to everybody. (ml) feomorphisms are also studied as topics of This book deals with traditional methods independent interest. Minimisation of the of solving ordinary differential equations. P. C. Hemmer, H. Holden and S. K. Dirichlet integral among functions with Its advantage is that it includes an intro- Ratkje (eds.), The Collected Works of Lars values in manifolds leads to (weakly) har- duction to the software package Onsager (with commentary), World Scientific monic maps; some results are specific to Mathematica which is used here to avoid Series in 20th Century Physics 17, World the sphere-valued maps. The energy func- routine and time-consuming calculations. Scientific, Singapore, 1996, 1075 pp., GBP tional of liquid crystals is investigated with The book is not only a guide to solving 68, ISBN 9-810-22563-3, ISBN 9-810- the Oseen-Frank density. The minimal ODEs, but the theory of ODEs is followed 22718-3 surface problem is studied with an empha- by many examples. Mathematica can be This is a complete edition of papers, short sis on the non-parametric problem – that used without extra knowledge – all the communications, and printed discussion is, minimisation among ‘graphs’. reader needs is found in the book. remarks (from conferences, etc.) by Lars These volumes represent a comprehen- The book is divided into 21 chapters Onsager, a physicist about whom Lev D. sive treatment of an important direction in and two appendices. These chapters dis- Landau said that “while the work of other modern calculus of variations. Updated cuss first-order differential equations (exis- theorists of his (Landau) generation pre- systematic presentation of a large part of tence and uniqueness of solution), second- sented no real challenge to him, he could geometric measure theory is also valuable. order linear differential equations, in par- not envisage himself accomplishing Some parts are of particular interest to ticular with constant coefficients, numeri- Onsager’s solution of the Ising model”. specialists in Sobolev spaces, BV-spaces cal solutions of differential equations, the The book starts with a bibliographical and applied real analysis. The book is Laplace transform, systems of linear differ- memoir by H. Christopher Longuet- indispensable for mathematicians in the ential equations, the stability of non-linear Higgins and M. E. Fisher, followed by field and for mathematical libraries. (jama) systems, Frobenius and power series solu- autobiographical commentary and the tion of second-order equations, and appli- Nobel Lecture by Lars Onsager (The motion C. G. Gibson, Elementary Geometry of cations of ODEs. of ions; principles and concepts). The rest of Algebraic Curves. An Undergraduate This book is suitable for students spe- the book is divided into sections reflecting Introduction, Cambridge University Press, cialising in mathematics and other disci- various scientific interests of Onsager. Cambridge, 1998, 250 pp., £15.95, ISBN 0- plines. As a bonus, the reader gets a Each section is accompanied by a com- 521-64140-3 and 0-521-64641-3 ‘Multimedia resource kit for Introduction mentary written by a leading present spe- This textbook is an elementary introduc- to ODE with Mathematica’ on CD-ROM. cialist in the field. 32 EMS June 1999 RECENT BOOKS The sections of the book are: irre- impressive book which aspires to become field. Many examples make the presenta- versible processes (commentary by P. an important monograph, a reference tion more accessible to newcomers to this Mazur), the Ising model (commentary by book as well as a textbook for more area. (vz) C. Domb and C. N. Yang), electrolytes advanced students. 615 pages of the main (commentary by W. Ebeling and J.-C. text, plus 220 pages devoted to four N. L. Johnson and S. Kotz (eds.), Leading Justice), electrons in metal (commentary appendices (the index takes 37 pages), Personalities in Statistical Sciences. From by A. B. Pipard), colloids (H. N. W. show the extent of the material that the the Seventeenth Century to the Present, Lekkerkerker and T. Odijk), dielectrics (G. book covers. Further, it is clear from the Wiley Series in Probability and Statistics, J. Stell), helium II and vortex quantization organisation of the book that the authors Wiley & Sons, Inc., New York, 1997, 399 pp., (R. J. Donelly), off-diagonal long range have much experience in presenting the £39.95, ISBN 0-471-16381-3 order and flux quantization (P. W. subject. They have found ways of making a .Johnson and Kotz co-edited the interna- Anderson), turbulence (A. Chorin), ion reader quickly familiar with parts of the tionally acclaimed ten-volume Encyclopedia recombination (G. Weiss), fluctuation theo- theory, without requiring a lot of prelimi- of Statistical Science, published by Wiley. ry (H. MacKean), ice and water (J. F. naries. This will doubtless stimulate fur- Their work inspired them to publish a Nagle), biology (J. F. Nagle), and Mathieu ther, more difficult, readings in the book. chronicle of lives and achievements of the functions – L. Onsager’s thesis (R. Askey). There are many interesting examples and most influential personalities in the field, Three of the articles appear in German, exercises (with hints if necessary) which will spanning nearly four centuries. This book and the rest are in English (or an English substantially improve the knowledge of a includes more than 110 names, with texts translation of the original text). reader and which make the text more partially written by 75 experts from The variety of subjects covered by the attractive. around the world, and contains many book is really impressive, and most of the At the beginning of each chapter the authentic photos and illustrations. I find articles represent a seminal contribution of reader is told which prerequisites are the book extremely useful for students, the author to the corresponding field of needed and where to find them, and at the who can find when, and in which situa- physics. They are still extremely relevant end there are references for additional tions, famous results connected with names for the contemporary researchers working reading. The authors have included many of individual persons were originally in these fields. (mz) remarks, comments, and postscripts at the found. It is interesting that many persons end of each chapter to clarify the main now considered as Americans were of J. Hilgert, J. D. Lawson, K.-H. Neeb and text, and have tried to make the book as European origin and that many of them E. B. Vinberg (eds.), Positivity in Lie self-contained as possible. For this purpose had a wide range of scientific interests, Theory: Open Problems, de Gruyter they have included appendices on abelian being originally educated as pure mathe- Expositions in Mathematics 26, Walter de groups, covering spaces and groups, a maticians, physicists, astronomers, econo- Gruyter, Berlin, 1998, 290 pp., DM 258, primer of category theory, and selected mists, biologists and geneticists. This again ISBN 3-11-016112-5 results in topology and topological groups. illustrates that statistics has deep roots in This series of 15 papers is based on the The book deals with compact topologi- other sciences. conference ‘Positivity in Lie theory’, which cal groups, written more from the point of The statistical personalities are classi- was held in December 1996 at the view of general topology than from that of fied into seven sections: forerunners (23 Mathematical Research Institute in algebraic topology. Nevertheless, much people), statistical inference (24), statistical Oberwolfach. This conference was a meet- information about algebraic topology and theory (19), probability theory (17), gov- ing of mathematicians working in various homological properties of compact groups ernment and economic statistics (17), branches of mathematics but applying sim- can be found. The representation theory of applications in medicine and agriculture ilar ideas – namely, the ideas of distin- compact groups is presented from a gener- (8), and applications in science and engi- guishing positive elements. The papers al point of view, so we cannot expect to neering (6); the interests of some persons presented in this collection are divided find lists of representations of all the clas- lay in several of these categories. The indi- into four overlapping groups: harmonic sical groups. Lie groups play a very impor- vidual entries are more concerned with analysis, representation theory, control tant role in the whole book, but this is not lives of persons than with the technical theory, and a fourth group of various top- a textbook on Lie groups. Not only does details of their work that can be found ics such as probability theory and algebra- the book present a lot of material, but more easily in the literature. Only four ic semigroups. The main aim of this collec- there are many results that have previous- women are included, some of them doing tion is to present a a compact text intro- ly appeared only in articles. The book will pioneering work (such as Florence ducing contemporary research in fields probably also be useful to non-specialists in Nightingale). I find the book fascinating where positivity methods are applied. All the field. If one is looking for a notion or a and recommend it to every statistician and articles are organised so as to introduce result, one can find and understand it with- probabilist. As Karl Pearson is quoted in the main definitions, give the necessary out reading the book systematically from the preface: “It is impossible to understand references, and present open problems. the very beginning. We expect that the a man’s work unless you understand some- We agree with the editors that ‘the level of book will be on the shelves of many math- thing of his environment.” (jju) presentation is chosen in such a way that a ematicians, as well as many students of Editor’s note. This review appeared in the graduate student with a sound knowledge mathematics. (jiva) last number of the Newsletter with the of basic Lie theory should be able to grasp wrong heading. We apologise for this the gist of the problem’. In order to pre- S. Janson, Gaussian Hilbert Spaces, error. sent information about new developments, Cambridge Tracts in Mathematics 129, they have set up a website: http://lie.math. Cambridge University Press, Cambridge, 1997, L. P. Kadanoff, From Order to Chaos. tu-clausthal.de/\~{}Hilbert/Problembook. 340 pp., £40, ISBN 0-521-56128-0 Essays: Critical, Chaotic and Otherwise, In general, all the articles in this collec- A Gaussian Hilbert space is a linear space World Scientific Series on Nonlinear Science tion are carefully and clearly written, and of random variables. It involves both prob- (A) 1, World Scientific, Singapore, 1994, 555 the results presented are very attractive. I ability theory and Hilbert space theory, pp., £45, ISBN 9-810-21197-X and 9-810- can imagine that many mathematicians and thus has many applications ranging 21198-8 will read at least one article from this inter- from stochastic processes, quantum field This is a collection of selected papers and esting collection. (jiva) theory and partial differential equations to essays by the author. The book is divided Banach space theory. The book contains a into four parts, with a new foreword and K. H. Hofmann and S. A. Morris, The well-written study on some of these topics. introductory essay to each part of the book, Structure of Compact Groups, de Gruyter The book contains chapters on written by the author especially for this vol- Studies in Mathematics 25, Walter de Gruyter, Gaussian spaces, Wiener chaos, Gaussian ume. After a general introduction (essay: Berlin, 1998, 835 pp., DM 278, ISBN 3-11- stochastic processes, limit theorems, the worlds of science), there are four main 015268-1 Malliavin calculus and transforms. The topics in the book: Fundamental issues in This is, from several points of view, a very text provides a good orientation in the hydrodynamics, condensed matter and field the- EMS June 1999 33 RECENT BOOKS ory (essay: from level to level); Scaling and Banach algebras, compact operators and The book is a nice introduction to phase transitions (essay: on the joys of cre- their Riesz-Schauder theory and weakly Riemannian geometry, containing basic ation), Simulations, urban studies, and social compact operators). Then follows a chap- theory as well as several advanced topics. systems (essay: models and arguments) and ter on Schauder bases (unconditional The basic notions and results from Turbulence and chaos (essay: questions with- bases, equivalent bases, the Orlicz-Pettis Riemannian geometry (covariant deriva- out answers) theorem, bases and duality and James’s tives and Riemann and Ricci curvature ten- This book includes both the famous space J). sors) are introduced at the beginning; seminal papers of Kadanoff (often shaping The last chapter deals with basic notions these quantities are computed for several the above disciplines in recent decades, of the geometry of Banach spaces (rotun- interesting Riemanian manifolds. such as the papers from the 1960s on the dity and smoothness, uniform rotundity, A chapter is devoted to the theory of renormalisation group, and a number of uniform smoothness and their generalisa- hypersurfaces in Euclidean space, where articles from recent years. The newly tions). There are four appendices, includ- classical results, such as the fundamental added introductory essays are also ing the basic properties of metric spaces, lp theorem of hypersurface theory and the extremely interesting. The book is an spaces and ultranets. Gauss-Bonnet theorem, are presented. A invaluable source of information and inspi- The book is sprinkled with examples, remarkable part of the book describes the ration on a variety of important problems historical notes and citations of original Bochner technique and its extension to in modern physics. (mz) sources. There are over 450 exercises that forms using the Clifford multiplication. provide the reader with some practice, In the next chapter, these results are L. Manivel, Fonctions symmétriques, present supplementary examples and used for a classification of compact mani- polynômes de Schubert et lieux de counter-examples, and extend the theory folds with non-negative curvature opera- dégénérescence, Cours Spécialisés 3, Société presented in the text. tor. There is also a brief introduction to Mathématique de France, Paris, 1998, 179 This book can be warmly recommended the theory and classification of symmetric pp., ISBN 2-85629-066-3 to graduate students and to anybody who spaces, together with a discussion of This book is divided into three parts. In wishes to become acquainted with the basic Grassmanians and complex projective the first two parts, the theory of symmetric elements and deeper properties of Banach spaces). For these spaces, the curvature functions, Schur polynomials and Schubert space theory. (jl) and holonomy of connections are comput- polynomials are developed; Schubert poly- ed. nomials were defined by A. Lascoux and M. Mezard, G. Parisi and M. A. Virasoro, There are also three appendices con- M.-P. Schützenberger in 1982. Some ideas Spin Glass Theory and Beyond, World taining the Stokes theorem and related de of S. Fomin and A. Kirillov in the mid- Scientific Lecture Notes in Physics 9, World Rham and Cech cohomology, Cartan for- 1990s led to an interesting approach to the Scientific, Singapore, 1988, 461 pp., £20, malism for the connection and curvature subject. The third part is devoted to ISBN 9-971-50115-5 and 9-971-50116-3 and spinor calculus on Riemannian spin Schubert varieties inside Grassmannians This book provides a self-contained treat- manifolds. Each chapter ends with discus- and flag manifolds. One of its culminating ment of the physical theory of spin glasses. sions and suggestions for further study, points is the theorem of Fulton. The main body of this theory was devel- together with corresponding references. The book is carefully written; however, oped between 1977 and 1985, in a consid- This book can be recommended to any- we think that the presentation deserves a erable part due to the efforts of the authors body interested in modern Riemannian more detailed treatment of the classical of this book. geometry. (jbu) results of M. Demazure. The reader will The volume is divided into three parts. surely appreciate the ‘rhythm’ of the text: Each part starts with a general introduc- H. A. Priestley, Introduction to ‘exercise – definition – example – exercise tion and a more detailed exposition of the Integration, Clarendon Press, Oxford, 1997, – example – proposition’. The appendix main ideas. A collection of related reprints 306 pp., £40, ISBN 0-198-50124-2 on singular homology makes the book of original papers then follows, so that the This book is designed primarily as an more accessible for a less prepared reader. reader can find more detailed information undergraduate or introductory graduate (lbe) and more calculations. Part 1 (Spin glasses) textbook. It offers a unified account of develops the essence of the replica method integration theory, the stress being on R. E. Megginson, An Introduction to and the TAP approach and explains the functions on R or Rk, rather than on set Banach Space Theory, Graduate Texts in breaking of the replica symmetry; apppli- functions. The theory is accompanied by a Mathematics 183, Springer, New York, 1998, cations to the study of the spin glass phase wealth of well-chosen examples and exer- 596 pp., DM 134, ISBN 0-387-98431-3 and the cavity method are also treated in cises illustrating the use of Lebesgue inte- The book is an extensive graduate text detail. Twenty-four of the original impor- gration. There are also brief chapters on Lp devoted to basic notions of Banach space tant articles are then reprinted. Part 2 spaces, on Fourier series (convergence theory. The first chapter presents the basic (Optimization) deals with combinatorial questions, in particular), on orthogonal concepts of the theory (normed linear and optimisation problems, simulated anneal- systems and on Fourier transforms. The Banach spaces, linear operators, dual ing, and some analytical results, followed final chapter is an invitation to the use of spaces and reflexivity, quotient spaces, by four reprints of original articles. Part 3 integration in probability theory. direct sums, separability) as well as Hahn- is devoted to biological applications, in The exposition starts with a simplified Banach extension theorems (including particular to brain modelling, learning Lebesgue-style integral for continuous Helly’s theorem) and other fundamental and a study of the Hopfield model. The functions on a compact interval in R based principles of functional analysis (the proofs book concludes with seven reprints related on step functions (no null sets). This are based on Zabreiko’s lemma). This to these subjects. replaces the more traditional Riemann chapter culminates with a proof of James’s The fact that the book is a 1993 reprint integral. Then the one-dimensional sequential characterisation of reflexivity. of the original 1987 edition confirms that Lebesgue integral is introduced via monot- The second chapter deals with weak the subject is still important, and this vol- onic sequences of step functions. topologies and includes such topics as vec- ume remains a very useful source of rele- Integration on Rk is sketched as an exten- tor topologies (also metrisability condi- vant information on the progress achieved sion of the theory explained in great detail tions), primers of locally convex spaces, by theoretical physicists in the field. It can in R. The two-dimensional Fubini and weak topology, weak* and bounded weak* be helpful also to mathematicians trying to Tonelli theorems are proved, but the proof topologies, James’s weak compactness the- develop a mathematically rigorous coun- of the change of variables theorem is orem, the Krein-Milman theorem, Bishop- terpart of this theory. (mz) sketched only for R2. Phelps theorems and subreflexivity. The book nicely illustrates the power of The next chapter is devoted to a deeper P. Petersen, Riemannian Geometry, the Lebesgue theory and provides a rigor- study of bounded linear operators (proper- Graduate Texts in Mathematics 171, Springer- ous practical guide to the use of integrals. ties of adjoint operators, projections and Verlag, New York, 1998, 432 pp., DM 89, It can be recommended to mathematics complemented subspaces, elements of ISBN 0-387-98212-4 students and teachers of mathematical 34 EMS June 1999 RECENT BOOKS analysis. (in) Research Institute for Mathematical useful for anybody interested in the sub- Sciences at Kyoto University. Plenary lec- ject. It is beautifully written and can be V. Maz’ya and T. Shaposhnikova, Jacques tures were given by E. Bombieri, P. D. T. A. warmly recommended to students in engi- Hadamard, A Universal Mathematician, Elliott, J.-H. Evertse, J. Friedlander, A. neering or mathematics. (kn) American Mathematical Society, Providence, Granville, K. Hashimoto, A.Ivic, H. 1998, 574 pp., £52, ISBN 0-821-80841-9 Iwaniec, M. Jutila, Y. Kitaoka, Y. C. A. Rogers, Hausdorff Measures, This is a fascinating book on the life and Motohashi, M. R. Murty, P. Sarnak, H.-P. Cambridge Mathematical Library, Cambridge work of J. Hadamard (1865–1963). In fact, Schlickewei, R. Tijdeman, M. Walschmidt, University Press, Cambridge, 1998, 195 pp., it is also a book on mathematics and math- and T. D. Wooley. Speakers in parallel ses- £17.95, ISBN 0-521-62491-6 ematicians from the last quarter of the sions were A. Akiyama, M. Amou, R. C. The first edition of this well-known and 19th century until today –extremely rich Baker, R. Balasubramanian, J. Brüdern, H. beautiful book appeared in 1970. material collected, ordered and presented Diamond, S. Egami, S, Gonek, G. Greaves, Chapter 1 gives a nice account of basic in an interesting, attractive and readable M. Hata, A. J. Hildebrand, M. Hindry, N. (outer) measure theory with special atten- form. Hirata-Kohno, M. N. Huxley, S. Kanemitu, tion to the study of non-σ-finite measures. The first half of the book is devoted to M. Katsurada, K. Kawada, A. Laurinikas, E. Chapter 2 develops the most general Hadamard’s life. Childhood, school-years, Manstavius, K. Matsumoto, H. Mikawa, L. aspects of the theory of Hausdorff mea- education, marriage, first results in mathe- Murata, V. K. Murty, M. Nagata, A. Perelli, sures. In particular, it is proved that in matics, colleagues, friends, international J. Pintz, B. Ramakrishman, W. Schwarz, T. some metric spaces each Souslin set of pos- contacts, teaching, le séminaire Hadamard, N. Shorey, C. L. Stewart, K.-M. Sang, C. itive Hausdorff measure µh contains a com- hobbies, activities during the war, political Viola, D. Wolke, E. Yoshida, J. Yu and T. pact set of finite positive µh-measure. commitments, travelling, emigration, fam- Zhan. Chapter 3 contains a general survey of ily tragedies – all are offered with much applications of Hausdorff measures and documentation: interviews, correspon- J. R. Norris, Markov Chains, Cambridge detailed accounts of two special topics. The dence, recollections, jokes, myths, over 300 Series in Statistical and Probabilistic first is devoted to applications to the theo- photographs and illustrations, all creating Mathematics, Cambridge University Press, ry of continuous fractions and the second an authentic and colourful picture. The Cambridge, 1998, 237 pp., £16.95, ISBN 0- one to a study of general non-decreasing account of Hadamard’s life is intelligible to 521-63396-6 continuous functions (and corresponding a wide readership, and only a necessary This is a paperback edition of the book Lebesgue-Stieltjes measures). minimum of Hadamard’s mathematical published in 1997 (for a review, see EMS The book is almost self-contained and is achievements is included in the first part of Newsletter 26, December 1997, p. 33). (in) written with notable clarity and precision, the book. so that bright students can read it by them- The second half deals with a detailed H. L. Resnikoff and R. O. Wells, Jr., selves. Mathematicians who need to know analysis of Hadamard’s contribution to Wavelet Analysis. The Scalable Structure of about Hausdorff measures can find clear mathematics – namely to function theory, Information, Springer, New York, 1998, 435 statements, clear proofs and a good guide number theory, geometry, analytical pp., DM 120, ISBN 0-387-98383-X to the basic literature. mechanics, calculus of variations, function- This book introduces the reader to the This second edition contains a new al analysis, mathematical physics, PDEs ideas and methods that lie behind the the- appendix (16 pp.) on ‘dimension prints’ - a and other areas of analysis, algebra, set ory of compactly supported wavelets. The notion introduced by the author in 1988 to theory, topology, and also to the psycholo- authors relate them to previously known distinguish between different sets with the gy of invention. Most of the more than 30 methods in mathematics and engineering, same Hausdorff dimension. Very useful is a sections (divided into eight chapters) is in show how they can be practically used in a new foreword (21 pp.) written by K. J. the form of essays (or short survey papers) digital signal processing and computing Falconer containing a survey of recent on individual mathematical topics. The environment, and illustrate their potential developments of the subject and new exposition is clear, accessible and nicely for mathematical engineering by describ- applications of Hausdorff measures with a written, connecting Hadamard’s mathe- ing several successful applications in band- long list of references. (lz) matics with further developments, fre- width management. quently up to results of current research The book consists of four parts. Part I, A. J. Scholl and R. L. Taylor (eds.), Galois interest. The scalable structure of information, Representations in Arithmetic Algebraic At the end of the book, there is a list of describes the multi-scale nature of infor- Geometry, London Mathematical Society 62 mathematical objects in which mation in many aspects of the real world. Lecture Note Series 254, Cambridge University Hadamard’s name appears and an exten- Part II, Wavelet theory, presents the alge- Press, Cambridge, 1998, 493 pp., £29.95, sive bibliography: 406 of Hadamard’s pub- braic and analytic theories of wavelet ISBN 0-521-64419-4 lications, 62 publications about Hadamard matrices, scaling and wavelet functions, This volume is based on the symposium and his work, and 430 references related to wavelets systems, and the corresponding Galois representation in arithmetic algebraic the text. An incredible amount of work has multi-resolution analysis of square-inte- geometry held in Durham in July 1996. had to be undertaken in order to produce grable functions on a given space. Turning There were six expository courses at the such a book. The authors have done an from the continuous to the discrete, Part symposium on the following topics: Galois excellent job and the result deserves much III, Wavelet approximation and algorithms, module structure, Shimura varieties in attention from professional mathemati- shows how a properly selected set of mixed characteristic, p-adic comparison cians and historians of science, as well as wavelets can be used to represent a wide theorems, the work of Kato on the Birch- from students with an interest in mathe- variety of signals efficiently and effectively Swinnerton-Dyer conjecture, polyloga- matics. This book is warmly recommended by means of a variety of algorithms useful rithms, rigid analysis and modular forms. to everybody who likes mathematics. (in) for implementation of wavelet methods in There were also fourteen research semi- the discrete world. A theory of wavelet- nars. Y. Motohashi (ed.), Analytic Number based differentiation is developed and the As the title indicates, the contents are Theory, London Mathematical Society Lecture wavelet-Galerkin method is used to formu- devoted to topics of interplay between Note Series 247, Cambridge University Press, late and develop single-scale and multi- algebraic number theory and arithmetic Cambridge, 1997, 382 pp., £27.95, ISBN 0- scale numerical algorithms for solving algebraic geometry. There are ten contri- 521-62512-2 elliptic boundary value problems. Part IV, butions to the volume – both expository This volume arose from the 39th Wavelet applications, presents a variety of and research articles. Readers can find Taniguchi International Symposium on applications of wavelets to problems in here carefully written reports on subjects Mathematics which, under the title Analytic data compression and telecommunica- which have recently attracted a lot of atten- Number Theory was held in May 1996, tions. tion; for example, expositions by B. Erez organised by N. Hirata-Kohno, L. Murata This book contains very rich material on Geometric trends in Galois modules theory and Y. Motohashi as a conference at the concerning the analysis of wavelets and is (32 pp.), B. Mazur on Open problems regard- EMS June 1999 35 RECENT BOOKS ing rational points on curves and varieties (28 remaining thirteen chapters divide into recommended to readers who do not want pp.), B. Moonen on Models of Shimura vari- three parts. The first part, Basic solution to be cheated by misused statistics, as well eties in mixed characteristics (84 pp.) and P. techniques, is devoted to classical tech- as to researchers who wish to publish Schneider on Basic notions of rigid analytic niques, as local methods, Skolem one, etc. results of their statistical analysis correctly. geometry (11 pp.) provide carefully written The reader finds here a description of var- The fresh style of the book make it suitable reports on these topics. From the rest, let ious tools (ternary quadratic forms, contin- as a supplement to classical statistical text- us mention a long paper The eigenvalues ued fractions and the basis reduction algo- books. (ja) (115 pp.) by R. Coleman and B. Mazur, A. rithm) that play an important role in the Goncharov’s Mixed elliptic motives (76 pp.), development of the subject. S. M. Srivastava, A Course on Borel Sets, J.-P. Serre’s La distribution d’Euler—Poincaré Part 2, Methods using linear forms in loga- Graduate Texts in Mathematics 180, Springer, d’un groupe profini (33 pp.) and A. J. rithms, deals with Thue-Mahler-type equa- New York, 1998, 261 pp., DM 98, ISBN 0- Scholl’s Introduction to Kato’s Euler systems tions; and the recent algorithms of Bilu 387-98412-7 (82 pp). The volume can be recommended and Hanrot or Tzakanis and de Weger are The main objects of the exposition are the to those interested in recent trends in described here. The effective theory of S- essential parts of classical descriptive set arithmetic algebraic number theory and unit equations and unit equations follows theory, the theory of Borel sets and mea- geometry. (šp) ideas first developed by K. Gyory, com- surable selections. The book is intended to bined with other methods (such as sieve be introductory, and it is possible to use it M. Šilhavý, The Mechanics and methods). The author’s own algorithm for to study even at undergraduate level. It is Thermodynamics of Continuous Media, unit equations and discriminant-form self contained, and the needed prerequi- Texts and Monographs in Physics, Springer- equations of Mahler type are also present- sites on set theory and theory of metric Verlag, Berlin, 1997, 504 pp., 24 fig., DM ed here. spaces are thoroughly explained in the 128, ISBN 3-540-58378-5 In part 3, Integral and rational points on early chapters. Only an understanding of This book covers a broad range of mathe- curves, the author surveys the most impor- the possible applications, indicated often matical theories and techniques used in tant methods from the theory of rational in the form of remarks, requires knowl- the field of rational mechanics. The main and integral points on elliptic curves. edge from topology, algebra, measure the- topics are balance equations, basic laws of Curves of genus greater than 1 are also ory, etc. Methods like universal sets, pre- thermodynamics, constitutive theory, ther- taken into consideration. well-ordering, and scales are explained. modynamic equilibrium and thermody- Besides the description of the modern Methods that use games, recursive func- namics. It also contains an explanation of methods in this rapidly developing theory, tions and forcing are not included. basic principles of geometry and kinemat- many historical notes and exercises for The presentation is systematic, and the ics, together with necessary parts of alge- solutions accompany the text. All this theory of Borel sets is split into two parts: bra and analysis. together predestines the book to be rec- one that does not need the theory of ana- The first part formulates the basic bal- ommended not only to interested students lytic and co-analytic sets, and another that ance equations for various quantities. This but also to active researchers in the subject. depends deeply on these crucial notions. part presents a lot of material formerly (spor) The part on selections and uniformisations accessible only in research papers. In the that concludes the book contains many second part, the author introduces axioms H. F. Spirer, L. Spirer and A. J. Jaffe, known results in the subject, and so for this for the foundations of thermodynamics, Misused Statistics, Second Edition, Revised topic, as well as for the Borel set theory, which are based on his results (together and Expanded, Popular Statistics 7, Marcel the monograph can serve also as a good with J. Serrin). A detailed mathematical Dekker, Inc., New York, 1998, 263 pp., ISBN reference book. (ph) analysis of entropy and the second law of 0-8247-0211-5 thermodynamics is presented in a way Statistics is a science of collecting, R. F. Streater, Statistical Dynamics: A which is free from the usual ambiguities. analysing, and interpreting data. There Stochastic Approach to Nonequilibrium The third part covers constitutive equa- are many reasons why the results may not Thermodynamics, Imperial College Press, tions, and includes a discussion of irre- be presented correctly. The most impor- World Scientific, Singapore, 1995, 275 pp., versible linear thermodynamics. The tant categories of statistical misuses are: £17, ISBN 1-860-94002-1 and 1-860- fourth part is, in a sense, the central part of lack of knowledge of the subject matter, 94004-8 the book. Standard topics in non-linear poor quality of the basic data, incorrect or This is a book on stochastic dynamics, of continuum mechanics are discussed in an incorrectly applied statistical methodolo- models of statistical mechanics. It consists understandable and comprehensive way. gy, misleading presentation of results, of two parts of roughly equal size and par- The last part is devoted to dynamics. incorrect conclusions from statistical allel organisation (275 pages in total). The The book is excellent, and covers a very results, and deliberate suppression of data. first part develops the dynamics of classical broad area (usually treated as separate top- The authors illustrate statistical misuses statistical models, using the ‘field point of ics) from a unified perspective. The author on a number of real examples taken from view’, while the second part is devoted to has clearly tried to reduce the mathemati- newspapers and scientific journals. A con- C*-algebras and quantum probability. The cal tools to a minimum so as to make the siderable deal of the material is devoted to material is given in a self-contained form, book accessible to readers from the physics problems connected to surveys and pools, and the student is not assumed to have a community (a more mathematical treat- because such topics appear in newspapers prior knowledge of probability theory. ment can be found in his papers). It will be very frequently. Teachers will read with The first part consists of six chapters: very useful for both mathematicians and interest the part of the book about how to Introduction, Probability theory, Linear physicists. (jsou). predict which of several applicants will be a dynamics (reversible and random dynam- good student. It is shown that typical ics and Markov chains), Isolated dynamics N. P. Smart, The Algorithmic Resolution of scores of standardised tests used as one of (the Boltzmann map and the ‘heat parti- Diophantine Equations, London the criteria for admission have small corre- cle’), Isothermal dynamics (the Legendre Mathematical Society Student Texts 41, lation with the grade point average which Transform), and Driven (open) systems. Cambridge University Press, Cambridge, 1998, the student will earn in the admitting insti- The second part starts with an introduc- 243 pp., £16.95, ISBN 0-521-64156-X and tution. The reason may be applicants with tion to C*-algebras and quantum probabil- 0-521-64633-2 low scores are not admitted, and so there ity. The contents of subsequent chapters This book presents an up-to-date summary are no data to verify the hypothesis that are roughly parallel to the first part of the of the latest developments in the so-called their study would not be successful. book, with a return to some harder prob- constructive theory of Diophantine equa- The first edition of the book became lems of classical dynamics in the last chap- tions, an area of number theory that has very popular. The authors updated the ter. recently undergone very important devel- examples and added many new ones, so This book contains a wealth of useful opments. that more that 50% of the second edition is information. Many interesting applications After an introductory chapter, the new or revised material. The book can be (such as activity-led reactions and chemical 36 EMS June 1999 RECENT BOOKS kinetics) are discussed. Basic concepts, Kadomtsev-Petviashvili equation is estab- The reader is supposed to have a basic such as entropy, are thoroughly explained, lished in Chapter 7, and the last chapter knowledge of partial differential equa- with an emphasis on useful technical (Representation of Palais-Smale tions, Sobolev spaces technique and linear details, lemmas and sharp bounds instead sequences) describes the loss of compact- functional analysis. Being very nicely writ- of aiming for the maximum possible gen- ness in some variational problems. ten, the book will certainly be of use as a erality for each result. Interesting histori- Material used in the previous text is briefly textbook for advanced graduate students. cal and other remarks are scattered and transparently explained in four It will be extremely useful to researchers in throughout the text. The results are pre- appendices (the superposition operator, partial differential equations and non-lin- sented in a way that minimises the require- variational identities, symmetry of min- ear functional analysis. (oj) ments on the mathematical preparation of imisers and topological degree). the reader. This makes the book attractive for a wide range of physicists and mathematicians. (mz)

A. N. Whitehead and B. Russell, Principia Mathematica to *56, 2nd edn., Cambridge Mathematical Library, Cambridge, 1997, 410 pp., £ 32.50, ISBN 0-521-62606- Positions available at the 4 This book contains the abridged text of Volume 1 of Principia Mathematica (the Max-Planck-Institute famous work on the foundations of mathematics). Here one finds material for an introductory study of logic and the philos- for ophy of mathematics. It is a paperback edition, suitable for students. Mathematics in the Sciences Nowadays there are modern books on mathematical logic that use more ‘efficient’ axiomatic systems. But it may happen that in Leipzig after finishing such a course, one does not have an understanding of both the historical background and the circumstances connected with the development of the branch and possible different ways of reasoning. Project: Mathematical Biology To avoid such a situation, a study of this book can be recommended because it also one Postdoctoral position (3 years) describes the foundations of mathematics as it was at the beginning of the century. Because of that, the book may also be one PhD-position (2 years) interesting for a wider group of mathematicians and philosophers. (kcu) Extension of both contracts is possible.

M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and its Applications 24, Birkhäuser, Boston, 1998, Candidates are expected to have good 159 pp., DM94, ISBN 0-8176-3913-6 and 3- 7643-3913-6 knowledge in Analysis and/or As the title indicates, the book is devoted to basic minimax theorems. These theo- Stochastics and should be interested in rems are explained in a unified manner starting in each case from a quantitative Mathematical Modelling in Biology. deformation lemma. In each chapter, the theory is used as a tool for many applications (the semilinear Dirichlet problem, the semilinear Schrödinger equation, a The Max-Planck-Society is an Equal treatment of the generalised Kadomtsev- Petviashvili equation, etc.) Opportunity Employer and encourages In Chapter 1, the mountain pass theorem and its applications are studied. A applications of minorities and disabled. linking theorem is explained and applied to the semilinear Dirichlet problem in Chapter 2. Invariant functionals with infi- nitely many critical values are considered Applications should be sent before 25 in Chapter 3 (the Fountain theorem). The notion of a Nehari manifold, developed in June, 1999 to the Max-Planck-Institute Chapter 4, is then used to prove the existence of nodal solutions. A minimax theo- for Mathematics in the Sciences (MIS), rem proved in Chapter 5 (Relative category) is applied to the problem with critical Inselstr. 22-26, D-04103 Leipzig, non-linearities. degree theory by Kryszewski and Szulkin and generalised Germany. linking theory is considered in Chapter 6. The application to the semilinear Schrödinger equation is given. The existence of solitary waves of the generalised EMS June 1999 37 Professor in Mathematics, Stockholm

Stockholm University invites applications for a position as Professor in Mathematics at the Department of Mathematics, Faculty of Natural Sciences.

Stockholm, the capital of Sweden, with a population of about one million inhab- itants, is a major cultural and scientific centre.

When appointing a professor of the state university system of Sweden, special emphasis is given to both research competence and teaching competence. Consideration is also given to administrative skills, in particular, leadership ability. Proficiency in Swedish (Scandinavian) or English is necessary. Wherever appropriate, a willingness to learn Swedish is assumed.

Salary is negotiable. The University is an Equal Opportunities employer, and since most professors at the Faculty of Natural Sciences are men, applications from female candidates are particularly welcome. Since the position is a full-time job, residence in the Stockholm area is necessary.

Informal inquiries may be made to the Head of the Department, Dr. Torbjörn Tambour (phone: (+46)-8-164516, e-mail: [email protected]), or to the Dean of the Sub-Faculty of Mathematics and Physics, Professor Torsten Ekedahl (phone: (+46)-8-164526, e-mail: [email protected]).

Applications, quoting reference no. 611-1484/99, should be sent to the Registrar, Administration Office, Stockholm University, S-106 91 Stockholm, Sweden. They must reach the Registrar’s Office no later than 15 September 1999. The following items, all in four copies, should be included: 1. Curriculum vitae. 2. Bibliography (numbered). 3. Description of the candidate’s research achievements and teaching experience and leadership ability (5-10 pages). 4. ‘Letter of intent’. 5. Photocopies of relevant graduation diplomas. 6. Research publications of the candidate’s own choice, numbered according to the bibliography. (Please observe, however, that only one copy of each research publication referred to should be sent to the University administration. Three additional copies of item 6 are to be sent later, upon notifi- cation from the University, to the Expert Members of the Appointments Board.)

38 EMS June 1999