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. 34 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] December 1999 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University Reymonta 4 EMS News : Committee and Agenda ...... 2 30-059 Kraków, Poland Editorial by EMS Secretary David Brannan ...... 3 e-mail: [email protected] KATHLEEN QUINN Introducing the Editorial Team : Part 2 ...... 7 Open University [address as above] EMS Executive meeting in Zurich ...... 8 e-mail: [email protected] Felix Klein Prize ...... 10 SPECIALIST EDITORS 3ecm Barcelona: Second Announcement ...... 12 INTERVIEWS Steen Markvorsen [address as above] EMS Poster Competition ...... 14 SOCIETIES EMS Council Meeting in Barcelona: Second Announcement ...... 15 Krzysztof Ciesielski [address as above] Interviews - Jan van Maanen...... 16 EDUCATION Vinicio Villani Interviews - Olavi Nevanlinna ...... 18 Dipartimento di Matematica Interviews - Ian Frigaard ...... 19 Via Bounarotti, 2 1999 Anniversaries : Laplace and Poincaré ...... 20 56127 Pisa, Italy e-mail: [email protected] 1999 Anniversaries : Neugebauer ...... 23 MATHEMATICAL PROBLEMS 1999 Anniversaries : Zariski ...... 24 Paul Jainta C.I.M.E. Summer Courses 2000 ...... 25 Werkvolkstr. 10 D-91126 Schwabach, Germany Societies Corner : Kharkov Mathematical Society ...... 26 e-mail: [email protected] Societies Corner : Luxembourg Mathematical Society ...... 26 ANNIVERSARIES EMS - WiR Summer School ...... 28 June Barrow-Green and Jeremy Gray Open University [address as above] Education Section ...... 29 e-mail: [email protected] Forthcoming Conferences ...... 30 and [email protected] and Recent Books ...... 36 CONFERENCES Kathleen Quinn [address as above] Personal Column ...... 43 RECENT BOOKS Ivan Netuka and Vladimir Sou³ek Designed and printed by Armstrong Press Limited Mathematical Institute Unit 3 Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK Charles University phone: (+44) 23 8033 3132; fax: (+44) 23 8033 3134 Sokolovská 83 Published by European Mathematical Society 18600 Prague, Czech Republic ISSN 1027 - 488X e-mail: [email protected] and [email protected] ADVERTISING OFFICER NOTICE FOR MATHEMATICAL SOCIETIES Labels for the next issue will be prepared during the second half of February 2000. Martin Speller Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, Department of Mathematics P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: [email protected] Glasgow Caledonian University Glasgow G4 0BA, Scotland INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER e-mail: [email protected] Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, OPEN UNIVERSITY Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: PRODUCTION TEAM Please include the name and full address (with postal code), telephone and fax number (with coun- Kathleen Quinn, Liz 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 December 1999 1 EMS NEWS EMS News: Committee and Agenda EXECUTIVE COMMITTEE EMS Agenda PRESIDENT (1999–2002) Prof. ROLF JELTSCH 2000 Seminar for Applied Mathematics 31 January ETH, CH-8092 Zürich, Switzerland Nominations to the Secretariat for delegates of individual members e-mail: [email protected] contact: EMS Secretariat, e-mail: [email protected] VICE-PRESIDENTS February – March Prof. ANDRZEJ PELCZAR (1997–2000) Voting for delegates of individual members Institute of Mathematics contact: EMS Secretariat, e-mail: [email protected] Jagellonian University 15 February Raymonta 4 Deadline for submission of material for the March issue of the EMS Newsletter PL-30-059 Krakow, Poland contact: Robin Wilson, e-mail: [email protected] e-mail: [email protected] 1 March Prof. LUC LEMAIRE (1999–2002) Deadline for submission of nominations for the Felix Klein prize Department of Mathematics contact: EMS Secretariat, e-mail: [email protected] Université Libre de Bruxelles 24 – 25 March C.P. 218 – Campus Plaine Executive Committee Meeting, hosted by the Polish Mathematical Society and the Institute of Bld du Triomphe Mathematics of the Polish Academy of Sciences, Bedlevo, near Poz•an (Poland) B-1050 Bruxelles, Belgium 15 May e-mail: [email protected] Deadline for submission of material for the June issue of the EMS Newsletter SECRETARY (1999–2002) contact: Robin Wilson, e-mail: [email protected] Prof. DAVID BRANNAN 13 – 20 June Department of Pure Mathematics EMS lectures by Prof. Dr. George Papanicolaou (Stanford, USA) The Open University 13–16 June: ETH, Zurich (Switzerland): Financial mathematics Walton Hall 18–20 June: University of Crete, Herakleion, Crete (Greece): Time reversed acoustics Milton Keynes MK7 6AA, UK contact: David Brannan, e-mail: [email protected] e-mail: [email protected] 17 – 22 June TREASURER (1999–2002) EURESCO Conference in Mathematical Analysis at Castelvecchio Pascoli (Italy): Prof. OLLI MARTIO Partial Differential Equations and their Applications to Geometry and Physics Department of Mathematics Organiser: J. Eichhorn, Greifswald (Germany), e-mail: [email protected] P.O. Box 4 [This series of conferences is financed by ESF.] FIN-00014 University of Helsinki 3 – 7 July Finland ALHAMBRA 2000: a joint mathematical European–Arabic conference in Granada (Spain), e-mail: [email protected] promoted by the European Mathematical Society and the Spanish Royal Mathematical Society ORDINARY MEMBERS contact: Ceferino Ruiz, e-mail: [email protected] website: www.ugr.es/~ruiz/ Prof. BODIL BRANNER (1997–2000) 6 July Department of Maathematics Executive Committee Meeting in Barcelona (Spain) Technical University of Denmark 7 – 8 July Building 303 Council Meeting in Barcelona (Spain) DK-2800 Kgs. Lyngby, Denmark contact: EMS Secretariat, e-mail: [email protected] e-mail: [email protected] 10 – 14 July Prof. DOINA CIORANESCU (1999–2002) Third European Congress of Mathematics (3ecm) in Barcelona (Spain) Laboratoire d’Analyse Numérique contact: S. Xambó–Descamps, e-mail: [email protected] website: www.iec.es/3ecm/ Université Paris VI 24 July – 3 August 4 Place Jussieu EMS Summer School in Edinburgh (Scotland): New analytic and geometric methods in inverse problems 75252 Paris Cedex 05, France Organiser: Erkki Somersalo (Otaniemo, Finland), e-mail: [email protected] e-mail: [email protected] 15 August Prof. RENZO PICCININI (1999–2002) Deadline for submission of material for the September issue of the EMS Newsletter Dipto di Matem. F. Enriques contact: Robin Wilson, e-mail: [email protected] Universit à di Milano 17 August – 2 September Via C. Saldini 50 EMS Summer School at Saint–Flour, Cantal (France): Probability theory I-20133 Milano, Italy Organiser: Pierre Bernard (Clermont–Ferrand, France), e-mail: [email protected]–bpclermont.fr e-mail: [email protected] Autumn Prof. MARTA SANZ-SOLÉ (1997–2000) Fifth Diderot Mathematical Forum, on Mathematics and Telecommunication. Facultat de Matematiques Date and programme to be announced. Universitat de Barcelona contact: Jean-Pierre Bourguignon, e–mail: [email protected] Gran Via 585 22 – 27 September E-08007 Barcelona, Spain EURESCO Conference at Obernai, near Strasbourg (France): e-mail: [email protected] Number Theory and Arithmetical Geometry: Motives and Arithmetic Prof. ANATOLY VERSHIK (1997–2000) Organiser: U. Jannsen, Regensburg, e-mail: [email protected] P.O.M.I., Fontanka 27 EURESCO Conference at San Feliu de Guixols (Spain): 191011 St Petersburg, Russia Geometry, Analysis and Mathematical Physics: Analysis and Spectral Theory e-mail: [email protected] Organiser: J. Sjöstrand, Palaiseau (France), e-mail: [email protected] EMS SECRETARIAT 30 September Ms. T. MÄKELÄINEN Deadline for proposals for the 2001 EMS Lectures Department of Mathematics contact: David Brannan, e-mail: [email protected] P.O. Box 4 14 – 15 October FIN-00014 University of Helsinki Executive Committee Meeting in the UK, hosted by the London Mathematical Society Finland 15 November tel: (+358)-9-1912-2883 Deadline for submission of material for the December issue of the EMS Newsletter fax: (+358)-9-1912-3213 contact: Robin Wilson, e-mail: [email protected] telex: 124690 Summer 2001 e-mail: [email protected] In the summer of 2001 there will be an EMS Summer School on Fluids at Charles University, website: http://www.emis.de Prague. Details to be announced. 2 EMS December 1999 EDITORIAL from G. H. Hardy on the death of his sis- ‘lost pages’.) ter completely transformed the Society’s Council also wrung its hands at intervals financial position, so that covering print- over the losses being made by its new ing costs was no longer a serious problem. Bulletin. Its format of review articles and EditorialEditorial In 1961 the LMS started to translate book reviews as well as research articles Uspekhi Matematicheskii Nauk (as Russian meant that while mathematicians would by Mathematical Surveys) in conjunction with subscribe personally or would read a lot of the British Library; in 1964 it was a found- pages in each issue, they had trouble per- EMS Secretary ing co-sponsor of the Journal of Applied suading libraries to subscribe – even at its Probability; and in the late 1960s it began very low price. It also began to appear David Brannan translation of the Transactions of the Moscow later and later, encouraging libraries who (Milton Keynes, UK) Mathematical Societies, in conjunction with subscribed not to pay on time! But after a the AMS. Then in 1968 it started two book period of problems, its losses were sta- series, the Monographs (originally with bilised, the Editor got it back on schedule, Academic Press, and then Oxford and Council decided that the losses were It all happened like this ... University Press when Academic Press affordable – they would be covered by the moved most of its UK activities to USA) profits on the Proceedings and Bulletin, and The start of my interest in publications and the Lecture Notes (with Cambridge ascribed to the furtherance of the Society’s After gaining my PhD in London, I spent University Press) – which in 1982 spawned mission in its Royal Charter to publish and 1967-68 in the USA. There I spent a lot of a third series, the Student Texts. And in disseminate mathematics. time talking to a friend, Walter Schneider, 1969 the LMS started the Bulletin. In 1973 the Society decided that it about classical potential theory, approxi- At first the Society had two Secretaries, needed to advertise to members the 1974 mation, Vietnam, the state of the world, who edited the journals. Then in 1937 a International Congress of Mathematicians and other important matters – one of separate office of Editor was created; since in Vancouver. (This was the first ICM at which was the benefits to a Mathematics a reorganisation in 1969, the journals have which the Society had a reception for Department of a good mathematics each had two Editors. For many years till members, to enable members to meet each library. From there it was a short step to the early 1970s, one Editor per journal had other and for foreign members to sign the just how one could build a good mathe- an automatic seat on the Council; and LMS Membership Book – the original matics library even when university money Publications Committee consisted of a 15- book, still in use since 1865). For many was short. minute meeting before the monthly years the Society had posted to members a Then in 1970 I was at a college in Council meeting; a list of all the papers monthly postcard listing the monthly London whose library lacked some impor- accepted but not yet published was laid on meeting of the Society in London. But now tant journals for my interests. I thought of the Council table at each meeting. Things it decided to launch a ‘proper’ LMS the idea of starting up a new mathematics are so much more professional now! – but Newsletter. I took a sheet of A4 paper from journal, and using ‘exchange’ copies to the system matched the needs of the time. my desk, folded it over into A5 size, pen- build up our library. Talking to mathe- cilled a page layout design on it, and sent maticians elsewhere in London, one told The 1970s this off to Pat Hodgson asking him to print me that it wasn’t that easy to do so and I I was on LMS Council from 1971 to 1981. the new Newsletter “like this”. The should forget the idea, but that the During this time the LMS operated from a Newsletter has appeared every month London Mathematical Society was looking shared office in the Royal Astronomical for a new Secretary if I was interested in Society in Burlington House in Piccadilly, burning off excess energy. I thought this London. For most of these years it had sounded worth exploring, and six months one 0.8-time employee, Mrs Shalit, who later was elected Secretary. Two years later did all the routine administration that the the job was divided into two – into a Council Society needed; in 1981 Susan Oakes took and General Secretary and a Meetings and up this post as full-time LMS Administrator, Membership Secretary – since the LMS had and has been a wonderful ambassador for entered an expansionary phase in its activ- the Society in addition. I spent most of my ities. time as Council Secretary dealing with Council meetings and the dozens of ‘little What did the LMS publish? things’ that needed to be done to keep the The LMS was founded in 1865, and began Council affairs smooth. to publish its Proceedings immediately These were the last days of the ‘hot with the firm C. F. Hodgson in north metal’ printing process at Hodgson’s, and London. Things must have been difficult Council spent time wondering about the financially for a small society, and in 1874 future of its publishing. It agonised over Lord Rayleigh gave the LMS £1,000 to what was going to be the medium for its support the printing bills. In 1926, at the journals in future – would it be Microfiche urging of G. H. Hardy, the society started or would it be Microfilm? Fortunately publishing its Journal. During the second Council never decided to switch from the world war, the Proceedings was moved from printed page, since both media turned out Hodgson’s in London to Oxford not to be the future after all. University Press. As recently as 1953 the In late 1973 there was one of a series of LMS Council was having anguished ‘oil crises’, together with a collapse in the debates over the projected large annual UK stock market and an increase in the (except August) since October 1973, and deficit on its two journals and considering UK inflation rate to 28%. LMS Council goes from strength to strength – it is a approach industry for support. discussed the fact that if it paid off its bills good size so that you can sit and read it Post Sputnik, the 1960s were a period of and printed all the journal issues for which cover to cover easily, and it has a lot of major expansion in science: new universi- it had taken advance subscriptions, its net interesting digestible information. ties were founded world-wide, and their worth was only around £75,000; so as an Nowadays it is of course the main benefit libraries needed long runs of journals. emergency measure it cut the sizes of the that LMS members receive for their sub- The LMS launched a major reprinting Proceedings, Journal and Bulletin by one- scription. programme over ten years or so to reprint third immediately. (Over the next 20 years In 1979 I moved from London to the the Proceedings and Journal; the income they increased in size again, but it took Open University in Milton Keynes. I was from this and the money that it received many years before they fully regained their pretty busy with a new job, organising a EMS December1999 3 EDITORIAL NATO Instructional Conference in The Bulletin and Journal went to had to reach agreement with IOP over the Durham, and as LMS Secretary. Shortly Cambridge University Press, and the differing refereeing arrangements stan- before my period of office ended I was the Newsletter to Armstrong Press in dard in mathematics journals and in Acting Meetings and Membership Southampton. Unfortunately there was physics journals (e.g. was timeliness more Secretary as well as the Council and considerable disruption to subscribers, important than complete accuracy? how General Secretary for six months, so dur- since in the chaos the journal subscription many referees? should the academic ing this heavy load I looked forward to lists were only recovered incomplete by the Editors-in-Chief see all papers that were to ‘release’ in summer 1981! Society to pass to CUP; this took two years be accepted? and so on). The LMS still My first LMS Council meeting in June to return to normal. However around this had just one employee, whereas IOP had 1971 was the last Council meeting attend- time the Bulletin reached break-even point, over 150 (and 24 journals!); how could we ed by J. A. Todd who had served a contin- and never made a deficit again! ensure that the venture would be fully uous 20-year period. But in the mid- equal? and that financially each side would 1970s, Council was alarmed by the fact that From the frying pan into the fire not be ‘ripped off’ by its new unfamiliar if its whole membership was elected annu- In 1986 I rejoined LMS Council as partner? I had the job of buying a small ally by the small number of members who Publications Secretary when my predeces- company ‘off the shelf’, changing its name bothered to vote, it would be quite easy for sor John Pym went abroad on leave. to LMS Publishing Ltd., changing its a small group of members acting in con- Council had become much more business- Articles of Association, and writing a con- cert to elect their own nominees unrepre- like since 1981, meetings much longer, tract between LMSPL and IOP that sentative of the wishes of the members and business involved a much more out- ensured fair and equal liabilities and assets generally. So it had introduced a system ward-looking approach than in the 1970s. to each partner; I was the Company of a mixture of one-year and two-year A completely new period of my life had in Secretary of LMSPL, responsible for its terms for ‘ordinary’ Council members, fact started! only business – handling the business with a 6-year continuous office maximum; affairs of Nonlinearity, together with the and a 10-year maximum period for Nonlinearity LMS Treasurer (who was also the LMSPL Officers, who continued to be elected The incoming President was Christopher Treasurer, of course). The LMS felt that annually to make sure that the Officers did Zeeman. He had the idea of the LMS try- the whole venture was extremely risky, and not begin to behave undemocratically! ing to increase its membership in the that it was not in the business of starting a Applied Mathematics community and cov- new journal often whereas IOP started, Back again! ering all mathematics, recognising the sold and bought journals just like a com- In summer 1982 I was approached about inherent unity of the subject (even today a mercial publisher; so LMSPL was to be the possibility of taking on joint Editorship rather too radical approach in some quar- used to insulate general LMS financial of the Proceedings. Having had a year’s ters!). One component in his strategy was resources from this very uncertain threat. break, I agreed readily, and enjoyed a real- to launch a new journal in applied mathe- The contract between LMS and IOP was ly interesting period of four years (1983- matics, tentatively titled Transactions of the signed after the first issue had appeared, 86) as Editor with Don Collins. Editing a LMS. He did a lot of work on this; but at things were happening so quickly at that large research journal is a really varied and the point of contacting possible Editors to time! interesting role, not fully understood by help in the planning, he discovered that In the event, things went brilliantly. We anyone who has not tried to do the impos- the Institute of Physics was planning to had chosen a subject area that was growing sible themselves! launch a new journal with some of the explosively quickly, with much interest We had all the usual problems: same putative Editors! After preliminary from the two subject communities. IOP – authors complaining that their wonderful discussions, it was decided that LMS and handled the practical publishing and dis- papers had not been understood by the IOP should join forces, to harness the joint tribution arrangements extremely smooth- referee energies of the mathematics and physics ly, the Managing Editors nominated by the – referees doing superficial work communities; and that non-linear mathe- two owners worked together like a dream, – referees failing to respond to appeals to matics and related areas should its subject the Editorial Advisers formed a good referee papers sent to them area. The title Nonlinearity was adopted as coherent group meeting once a year but – agonising over which papers each month its title on the suggestion of Mike Berry. gelling by e-mail discussions, and the sup- we would be forced to reject simply Nonlinearity was a baptism of fire for an ply of excellent papers from both areas because we did not have sufficient space to incoming Publications Secretary! I took picked up very quickly – causing LMSPL publish them over in July 1986 and the first issue and IOP regular problems over how quick- – trying to explain to authors and Editorial appeared in March 1988. Meantime we ly to expand the journal from quarterly to Advisers why really good papers had been bimonthly! After two years the journal had rejected in spite of a glowing referee’s covered its launch costs for the LMS, and report had an excellent subscription list base for – at other times wondering how to fill the the future. The business side continued to pages in an issue give the owners an annual headache in – wondering whether recently we had quite view of their different pricing structures enough of area X and so we should posi- and philosophies; and I regularly worried tively try to cut back a bit on papers in X in whether I would go to prison for not sub- the next few issues; mitting the LMS annual accounts on time and so on. to Companies House! But all this was In 1985 I had a view from Publications minor – overall the launch of this great Committee of the LMS Treasurer and new journal had gone like a dream. The Publications Secretary coping with the very journal is instantly recognised on library difficult problems of the bankruptcy of shelves from its green and orange cover, Hodgson’s who had worked for the Society and even non-readers look at the superb since 1865. As subscription income was front-cover designs; both the LMS and received by Hodgson’s on behalf of the IOP should justifiably be proud of this col- Society, the LMS found itself with signifi- laboration. cant publishing commitments to sub- scribers but without the corresponding From the USSR to the Russian income. In the event the two Officers Federation extricated the LMS from this extremely One of the first things I had to do when difficult situation brilliantly, with a rela- becoming LMS Publications Secretary in tively small financial loss to the Society. July 1986 was to find a successor to Kurt 4 EMS December 1999 EDITORIAL Hirsch as editor of Russian Mathematical opening ceremony. That was a great occa- my ten-year stint as LMS Publications Surveys, as he died abroad quite unexpect- sion with much deserved celebration! (I do Secretary! edly. Having taken advice but without hav- regret that we were never able to set up a ing ever met him, I rang up Eric Primrose series of publications jointly between the Money (Hirsch’s deputy) and asked him to take it EIIM and the LMS.) A major part of the Publications Secretary’s on. Eric was a great Editor, and had a I made a point of visiting Moscow each job was to handle the annual debate on the wonderful relationship with his authors year to keep an eye on possible future pricing of the journals. As the Treasurer and translators; for example, long before developments, and in 1992 was able to used to say, this had to be ‘got right’ - but agree a new contract for RMS on behalf of nobody ever knew what the right decision the LMS and BL in Moscow. But things was until about two years later when they had now changed – the contract was not saw its effect! How could you predict with VAAP but with the Russian Academy major international financial crises that of Sciences and its Department of affected university funding across the Mathematics. I believe strongly in the ben- globe? or currency fluctuations (after all, efits of personal contact, and continued to financial professionals cannot predict this visit Moscow. Then in 1994 I heard that reliably!)? or the cost of paper? or the the Academy was interested in discussing costs in the printing industry? or postage with the LMS the possibility of some form costs? of joint ownership of the translation jour- Given that universities were ‘rationalis- nals Izvestiya: Mathematics and Sbornik: ing’ their journal subscriptions, circulation Mathematics; the Academy had decided to of virtually all journals was declining. move from its previous arrangement with What strategy should the LMS adopt? the AMS. In the event, a multi-partnership Should the LMS each year increase prices arrangement was arranged, involving the by X% to compensate for its anticipated Academy, its Department of Mathematics, decline in subscription + Y% to allow for the Editorial Board of each, the LMS, and production and distribution cost increases Turpion – a body set up in both London ± Z% to allow for the variation in the and Moscow to enable such international exchange rates of the pound and the US scientific publishing collaborations. In dollar (North America being the largest 1997 a similar ownership arrangement was single market)? In the case of Nonlinearity, agreed for RMS as well. should it increase the price to match the This collaboration features the mathe- increase in size of the journal? Every May maticians in the UK and Russia being in and June I used to talk to our printers and full academic and financial control of the publishers about their anticipated costs for e-mail made communications with Russia venture, on a partnership model that is the year ahead, talk informally to commer- easy, Eric used to return helpful comments most successful; I think that each side is cial publishers about their pricing plans (a on translating Russian into English to his really happy with it; a key ingredient is the carefully guarded strategic commercial panel of translators within Russia; several arrangements for regular face-to-face decision to them, of course), agree with the of them have told me how much they meetings of they key people at each level. Treasurer a strategy for what we thought appreciated and learned from his wise sug- It must be a model for future collabora- the LMS should do, then negotiate the gestions. tions. I have to say that the UK editors detail of this through LMS Publications Then in 1987 there was a problem over (Eric Primrose on RMS, Gerald Gould on Committee, LMS Finance Committee and the renewal of the contract for RMS – Sbornik and Dave Johnson on Izvestiya) LMS Council – and then finalise negotia- negotiations (handled by the British were a brilliant team of Editors to work tions with our various partners! This was a Library, our joint partners in RMS) had with – as were their Russian counterparts. really interesting and testing experience collapsed. The Russian ‘non-governmen- After my 10-year term as LMS annually, to say the least. tal body’ VAAP [Soviet Copyright Agency] Publications Secretary ended, I was asked Overall the LMS tried to increase prices that handled contractual matters in to stay on a while as Deputy to the incom- less than commercial publishers, mindful Moscow planned to transfer translation ing Publications Secretary, Chris Lance; I of its learned society obligations to the rights to some 14 translation journals in stayed on for 18 months, with the principal which BL had a share to someone else. task of handling the Russian translation This was a severe crisis, rescued only by a programme. I was very sad when Eric died speedily arranged visit by Edwin Shelock shortly after that, in late 1998: he left many (Royal Society of Chemistry) and others to friends in Britain and Russia. Moscow. But it meant that I knew I need- I did not agree with every view put at ed to adopt a more active role in RMS LMS Council of the LMS Russian ventures! affairs than the LMS had traditionally – but Council was tremendously supportive taken in the past. of these complex international collabora- In 1989, Edwin Shelock, now Chairman tions, often giving me significant authority of ALPSP (see below), set up a visit for 17 to conduct negotiations in Moscow and British publishers to visit VAAP in Moscow sign a contract without having to refer to discuss problems in existing collabora- things back to London (they must have had tions or opportunities for future collabora- strong nerves!). The ventures did not tions. Eric and I went, learned a lot about make large profits for the LMS; but the Soviet publishing and mathematical Council supported them since they cov- set-ups, and made useful contacts in VAAP, ered their costs and represented a signifi- the Academy of Sciences of the USSR, and cant contribution to disseminating mathe- the Steklov Institute in Moscow. matical research and to supporting Around the same time, John Coates Russian colleagues. Council also backed (LMS President) was involved with Ludwig up its commitment by setting up a travel Faddeev in the setting up of the Euler fund to enable mathematicians in the UK International Institute of Mathematics in and Russia to visit each other for short Leningrad (now St Petersburg), and I was research visits. fortunate enough to be invited to visit the Nonlinearity and the Russian translation One of the books in the LMS-AMS History of EIIM and then in 1992 to attend its formal programme were the main visible fruits of Mathematics series. EMS December 1999 5 EDITORIAL mathematics community. We cannot have of value to ‘small learned societies’ like the and punctuation, so that even readers new got our pricing decisions too far wrong LMS (that is, as well as the big commercial to the field or readers whose native lan- because, in spite of our cautious approach, publishers, the big Engineering Institutes, guage is not English can read and under- our subscription levels declined less quick- etc.). My two-year spell on the ALPSP stand the mathematics without difficulty or ly than most mathematics journals and our Council taught me a lot about publishing ambiguity arising surpluses rarely declined. These surpluses and publishers! Amongst other things I myth 2: authors will do the TeX typeset- were fed back into general LMS funds; and learned that the ‘amateur’ LMS approach ting work for a journal, so the journal type- were used to support its meetings, confer- to journal pricing was in fact generally at setting costs will be nil or negligible ences, visiting fellowships, and general least as successful as the ‘professional’ myth 3: individual journals will be avail- running costs. approach of the commercial publishers; able indefinitely on the Editor’s server or and I grew to believe (and to tell Council his/her University server and can be Innovation colleagues) that the LMS should itself accessed at any time In spite of my tendency to conservatism, expand its publishing activities in a major myth 4: editors do their work at zero cost, every so often an obvious development or way, though of course it is up to my succes- as their universities absorb the cost. innovation came along. Thus in the early sors to decide what they will actually do! In fact, quality costs money: 1990s a member suggested that the LMS – to ‘technically edit’ manuscripts into a launch a series of books in the History of Since then version (fit to publish) that readers can Mathematics. It turned out that the AMS Over the decade 1986-96 LMS assets understand was thinking along similar lines, and in increased from £2M to £6M, with publish- – to prepare the electronic files, whether due course we launched a joint LMS-AMS ing profits rising from £200K to £500K per for paper, server, or both series in the area. Its objective is to publish year. The Society had expanded to two – to create accessibility of the material (that books in which the working mathematician full-time staff, and did a large amount of is, its distribution in the short term) will have an interest and at a price that business in relation to mathematics in UK; – to maintain its accessibility in the long (s)he can afford. And I had to create a con- it became simply too cramped, even term tract with the AMS. . . though it had moved in the early 1990s so that publishers (whether commercial, A major development was on the tech- into a large office of its own in the Royal learned societies or universities) will con- nical side of journals. In the 1970s print- Astronomical Society building. LMS tinue to have to charge for mathematics ers stopped using ‘conventional’ hot-metal Council decided to seek more appropriate journals. Nevertheless, the mathematical handsetting and moved to computer-dri- premises, both for the work of the Society community owes it to itself, and to its suc- ven typesetting. This was more economi- and as an investment. cessors, to agree a ‘system’ that will make cal, but still had the problem that items It purchased two adjacent properties in mathematics research literature available could fall on the floor from the fonts or Russell Square, near Euston Station, in now and into the indefinite future at a from the glue on the printer’s film failing. 1998 (see EMS Newsletter 31); in the new price that enables as many as possible Then along came TeX, followed by premises it now has around seven staff – research libraries to afford to buy the key LaTeX, followed by a whole range of ver- from an Executive Director through a journals. The community does not seem to sions of each and so-called improved vari- Publications Manager to a receptionist. be succeeding in this goal, yet. ants from many sources! The enthusiasts How did the LMS ever cope in the past? I suspect that there will continue to be a for these developments being adopted at Also, in 1997 the LMS launched a new market for both paper and electronic ver- once by the LMS were vocal, but our print- purely electronic journal – the LMS Journal sions of journals for years to come, as each ers were certainly less skilled in it than our of Computation and Mathematics. This excit- format has its own role – mathematicians authors! ing new venture had been in planning for like to read papers slowly and carefully! – It took many years before we were able some years, but its launch was delayed until and that paper (backed up, admittedly, by (with CUP) to introduce the option of we had the right academic objectives and secondary, regularly-refreshed electronic LaTeX files being submitted to the LMS technical systems in place to start a new files) will continue to be the principal for the Bulletin and the Journal, and it took journal that the LMS would continue to archiving format for some centuries yet. even longer for the Proceedings. The con- publish indefinitely – its objective with all But neither I nor my 1999 readers know tinuing problems of incompatibility its publishing ventures. Rumour has it that whether I’m right or wrong. between versions and dialects plague every most electronic journals find it difficult to mathematics journal – TeX developers attract authors, particularly authors of “Would you be interested . . . ?” please note! papers of sufficient quality to publish. Then out of the blue in 1998 I was asked if Universities continue to regard printed I’d be willing to be nominated for the post And other things besides! journals in many subjects (including math- of EMS Secretary. Though I had been an What else did I do? Well, trouble-shoot ematics) as more authoritative, as better EMS member for years, I was not entirely generally – the job was effectively that of refereed, and as a better guide to the qual- clear what the EMS actually did, but Director of a small publishing house – or ity of existing and prospective staff. While thought it seemed like an interesting chal- so it seemed! (No doubt that is why the appointments and promotions are affected lenge and I agreed. LMS now has a full-time Publications by this view, electronic journals will find it My first EMS Executive Committee Manager, rather an academic doing it in hard to break the mould of conventional meeting in late 1998 in Copenhagen, as a the corners of his time.) I was responsible publishing. visitor before taking office in January for identifying and appointing Editors, The fratricidal debate over the cost or 1999, showed how different was the nature Technical Editors and Editorial Advisers non-cost of electronic journals seems to me of the EMS from the LMS – the EMS has a for the journals and book series, subject to to be a dead-end debate. (Interesting con- coordinating role for nations across Council approval. This was sometimes tributions to the question appear in Europe totally unlike what the LMS does. quite difficult, to get a good balance ‘Electronic publishing and electronic pub- But what was a major agenda item at that between efficiency and academic standing! lications in mathematics’, Progress in Executive Committee meeting? – the first – and sometimes I had to ‘thank various Mathematics 169 (1998), 315-337.) There issue of, and the contract for JEMS, the people for their services’ (non-native are real costs involved in producing a qual- new Journal of the EMS! This business English speakers should replace this ity mathematics research journal, whether seemed strangely familiar . . . phrase by ‘fire various people for not paper or electronic; and, in my view, there doing their job’). are a number of myths around that sup- And finally I also became involved in the Association port the flawed view that electronic jour- Do I yet know how my EMS role will work of Learned and Professional Society Publishers nals should be free or priced at minimal out? – not really! Do I look forward to [ALPSP], an interesting body that celebrat- cost: finding out? – very much indeed. Good luck ed its 25th birthday last year. It runs a myth 1: all authors write clearly in good to the European Mathematical Society in the series of courses, seminars and conferences grammatical English with proper spelling coming millennium! Ad multos annos! 6 EMS December 1999 EMS NEWS Introducing the Editorial Team : part 2

Ivan Netuka (Recent books editor) received (the equivalent of) a Ph. D. in Mathematics in 1972 at Charles University, Prague, Czech Republic, where he has taught at the Faculty of Mathematics and Physics and is now Professor in the Mathematical Institute of Charles University. His mathematical interests lie in analysis, both classical and abstract and in the history of mathematics. He has made contributions to the field of potential-theoret- ic methods applied to boundary value problems for partial differential equations, and particularly in classical and abstract potential theory.

Vladimír Sou³ek (Recent books editor) grad- uated at Charles University, Prague, in 1968 and has worked at the Faculty of Mathematics and Physics, Charles University since 1969. He received here (the equivalent of) a Ph. D. in 1974, and is currently Professor in the Mathematical Institute of Charles University. His research interests lie in global analysis and differential geometry, with connections to mathematical physics. They are centred around an investigation of properties of invariant differential operators on homogenous spaces and their curved ana- logues. In particular, he has contributed to the development of Clifford analysis (func- tion theory for solutions of the Dirac equa- tion).

Paul Jainta (Problems Corner editor) teaches mathematics and physics at Adam-Kraft Gymnasium, Schwabach, Bavaria. He has been involved with various mathematical com- petitions in Germany, and last year was appointed manager and secretary of the ‘Landeswettbewerb Mathematik Bayern e.V’. In February 1998 he was elected Vice- President of the association ‘Begabtenförderung Mathematik e.V’ (Fostering mathemat- ically gifted youngsters). Another of his fields of activity is popularising mathematics. Apart from the Problem Corner in this Newsletter, he writes a column called ‘Werkstatt Mathematik’ in the German mathematics journal ‘Wurzel’.

Jeremy Gray (Anniversaries editor) has a BA in mathematics from Oxford University, and obtained his PhD in mathematics from the University of Warwick in 1981. He is presently a Senior Lecturer in Mathematics at the Open University, UK. His main area of research is the history of mathematics in the nineteenth century, particularly the growth of complex func- tion theory and algebraic geometry. In 1998 he was an invited plenary speaker for the History of mathematics section of the International Congress of Mathematicians in Berlin.

Vinicio Villani (Education editor) is Professor of Mathematics Education in the Department of Mathematics, University of Pisa, Italy. He has been President of the Italian Mathematical Union. He has worked in the theory of functions of several complex variables. Currently his interests are mainly devoted to mathematics education, and specifically to aspects con- cerning the teaching-learning process of geometry at secondary and tertiary level, as well as teacher preparation. He has been Chairman of the International Programme Committee appointed for the ICMI Study ‘Perspectives on the Teaching of Geometry for the 21st Century’ and editor of the resulting book with the same title, published in 1998.

EMS December 1999 7 EMS NEWS of the Prize Committee will be publicised separately. The first Klein Prize will be awarded at the 3ecm in July 2000. The Group on Relations with European EMSEMS Institutions intends to form a strategy towards both DGXII and DGXIII of the EU, and to establish contacts with appro- ExExecutiveecutive CommitteeCommittee priate new EU commissioners. V. Capasso, J.-P. Pier and O. Martio were added to the Group’s membership. The Group was meetingmeeting asked to campaign against plans to cancel the network programmes in the 6th Zurich (Switzerland), 9 – 10 October 1999 Framework Programme. The Executive Committee agreed to invite ERCOM, as a committee of EMS, to send a letter oppos- Officers’ reports provided by EMIS. ing the cancellation of network pro- The President reported briefly on recent Committees grammes. contacts with SIAM, GAMM and CICIAM. R. Piccinini was elected chair of the EMS The Treasurer proposed the investment of Summer Schools Committee for 2000–03, and World Mathematical Year 2000 60000 euro of the Society’s reserves in a D. Cioranescu was appointed a member of It was reported that a new resolution on Finnish financial fund, and this was agreed this committee. Emilia Mezzetti, World Mathematical Year 2000 was to be by the Committee. The Committee agreed University of Trieste, was elected to chair presented to the November meeting of to invite the Council meeting in July 2000 the Committee on Women and Mathematics. UNESCO. The EMS was heavily involved to reconsider the level of membership fees. O. Barndorff Nielsen was elected to chair in the international preparation for this, ERCOM for the years 1999-2002. Claude via the activities of its Publicity Officer Report of the former President Lobry has agreed to chair the Committee on Mireille Chaleyat-Maurel – for example, (J.-P. Bourguignon) Developing Countries, and A. Henault, M. S. via the WMY calendar of events, the Plans for an exciting conference on the Narasimhan, A. Pelczar and M. Roberts Alhambra conference in July 2000, and its Mathematics of the Alhambra in Granada as a were elected members of the committee. J. support for a pan-European campaign to satellite meeting for 3ecm in July 2000 are Bruening, M. Chaleyat-Maurel, J. raise public awareness of Mathematics by a almost complete. Davenport, I. Diaz, A. Quarteroni and K.- poster campaign in European cities and O. Widman were elected members of the related actions during the European Projects Committee on Special Events, chaired by J.-P. Science and Technology Week The EU has funded LIMES (Large Bourguignon. The Committee for the The EMS ran a poster competition for Infrastructure in Mathematics – Enhanced Support of Eastern European Mathematicians use for WMY2000. The Prize Committee Services) within its Fifth Framework was granted an additional sum of 5000 of M. Chaleyat-Maurel, R. Brown, B. Programme with the aim of improving the euro for the year 2000. Branner and V. L. Hansen had decided on service of Zentralblatt-MATH and establish- The 4th Diderot Mathematical Forum on the following awards. The posters will be ing it as a widely used infrastructure in ‘Mathematics and Music’ will be held on forwarded to professional designers for use mathematics. The project will probably 3–4 December 1999, in Lisbon, Paris and in the WMY2000 campaign, and the start in April 2000. The partners in the Vienna. It is hoped that the 5th Diderot names of the original designers will be vis- project are likely to be FIZ Karlsruhe, Mathematical Forum will be on ible in the final version of each poster. MathDocCell Grenoble, TU Berlin, Telecommunications. Eidetica (Amsterdam), DTV (Copen- It was agreed to change the name of the Summer schools hagen), SIBA (Lecce), USC/CESGA Committee on Applications of Mathematics to The Society had held two summer schools (Santiago de Compostela), HMS (Athens) the Committee for Applied Mathematics. Its in 1999: the EMS-CIME summer school in and the EMS. mission statement was accepted as follows: Martina-Franca, Italy, and the EMS-WiR The Committee discussed a proposed “Applied Mathematics and Pure summer school in Heidelberg, Germany. project Euclid designed to help indepen- Mathematics are two sides of the same Both had been very successful, and had dent mathematics publishers make the coin, they need each other. The received financial support from UNESCO- transition to the electronic scene, and to Committee sees its role in promoting Roste as well as the EMS; ESF had also act as a catalyst for the mathematics pub- Applied Mathematics as a whole through given financial support to Heidelberg. lishing community to arrive at a commit- and within EMS, since applications cannot The EMS was planning two summer ment to use a common metadata standard. be separated from the mathematical meth- schools in 2000, one of which had already It decided that the Society should be ods. The Committee, instead of compet- received EU financial support. (For infor- involved in this project. ing, wants to cooperate with other, some- mation on these, see the EMS Agenda, There was some preliminary discussion times more specialised, societies on the page 2.) One application to hold a 2001 of the possibility that the Society become a European and international level and with summer school, from Charles University in mathematics publishing house in its own applications-oriented member societies Prague, was approved. It was hoped that right. It was agreed that the Society should especially in further improving the public another 2001 proposal was in the pipeline. organise a meeting of the non-commercial and political awareness about the impor- The Committee expressed the wish to have publishers of mathematics journals pro- tance of mathematics to cultural, economic the EMS summer schools move around duced in Europe during 3ecm in Barcelona and social development.” Europe. in July 2000. It was agreed to establish a four-yearly It was agreed to provide a front-page prize, the Felix Klein Prize, in conjunction STOA Subcommittee of the European link on EMIS to COMPUSCIENCE, a between the EMS and the Institute for Parliament database produced by FIZ Karlsruhe in Industrial Mathematics in Kaiserslautern, STOA (Scientific and Technological close co-operation with Zentralblatt-MATH. to be financed by the latter. The intention Options Assessment), a group in the This covers a part of computer science is to award the prize to a young scientist European Parliament, has invited expres- which is closely related to area 68 of (normally under the age of 38) or to a sions of interest in membership of a panel MATH, complements the offer in comput- small group of young persons (each under for research into science/mathematics poli- er science provided by INSPEC, and has its 38 years), for using sophisticated methods cy questions. R. Jeltsch, J.-P. Bour- users mainly near the borderline between for solving a concrete industrial problem guignon, H. Engl and L. Lemaire were mathematics and informatics. This will to the industry’s satisfaction. The detailed appointed to an ad hoc EMS group to inves- complement the data base access already rules for the Prize and mode of operation tigate this idea. 8 EMS December 1999 EMS NEWS tents list of JEMS. Cooperation between EMS and other mathematical societies EMS Newsletter Plans for joint events of EMS and SIAM are It was agreed to offer institutions that are under discussion. R. Jeltsch, H. Engl, O. not EMS members to subscribe to the Martio and D. Cioranescu were appointed Newsletter; the arrangements for this will to an ad hoc committee to progress a possi- be publicised shortly. ble joint meeting in 2001. The Executive Committee discussed the EMS Lectures possibility of cooperation and/or a reci- It was reported that the three sets of EMS procity agreement between the EMS and 1999 Lectures had been very successful. the American Mathematical Society, and between the EMS and the Australian Publicity material Mathematical Society. The Committee It was agreed to print a new brochure for also discussed possible future cooperation the Society in time for 3ecm at Barcelona. with the European Regional Committee of (The current brochure was printed in the Bernoulli Society. 1996.) A poster with the Society’s Agenda Anatoly Vershik (left) & Renzo Piccinni (right) for the year 2000 will also be prepared. European Mathematical Congresses The Committee felt that the ‘visibility’ The Committee received a progress report of the EMS is enhanced by having booths on 3ecm, describing the scientific pro- at mathematics meetings. The EMS will gramme, financial matters and social pro- have booths at various meetings in 2000, gramme. Everything seems to be progress- including the AMS Annual Meeting in ing well, and the Committee believed that Washington, and at 3ecm. the Congress should be a mathematically exciting event that should attract very wide And finally . . . participation. The Committee expressed their heartfelt Bids for holding 4ecm in summer 2004 thanks to the Swiss Mathematical Society were discussed by the Committee, and a for supporting its meeting in Zurich, and recommendation will be made to the to R. Jeltsch and A. Rast for making such Council meeting in July 2000. efficient arrangements for the accommo- dation, preparation of papers, social pro- EMS Council meeting in Barcelona in gramme, transport and other arrange- July 2000 ments for the meeting. Things had been The Catalan Mathematical Society has just perfect. offered its help with the local arrange- David Brannan & Doina Cioranescu ments. David A Brannan

Executive Committee elections The terms of office of one Vice-President (A. Pelczar) and of three ordinary mem- bers (B. Branner, M. Sanz-Solé and A. Vershik) terminate in 2000. A. Pelczar will have served 8 years, and cannot be re- elected. The ordinary members can be re- elected, and have expressed their willing- ness to continue in service. It was agreed that the composition of the Executive Committee is important, in order to ensure a proper balance of areas of mathematics and geography. This will be discussed again at the next Executive Committee meeting in March 2000.

EMS Council meeting in 2002 The ICM 2002 will be held in Beijing. The Committee discussed whether to identify a Carles Casacuberta & Tuulikki Mäkeläinen site in Europe to be presented to members as an alternative to a meeting in Beijing; this will also be discussed again in March 2000.

Future Executive Committee meetings Likely dates for meetings in 2000 are: 23- 26 March in Poland; 6 July in Barcelona; and 13–15 October in the UK.

JEMS, Journal of the EMS It was agreed to appoint a number of addi- tional associate editors to widen the fields covered by JEMS. Member societies will be asked if they are willing to collect pay- ments for JEMS with their subscriptions; and as a promotional measure, the EMS Newsletter should continue to print the con- Some of the Executive Committee relax after a busy weekend EMS December 1999 9 NEWS geodesy, and technical mechanics (kine- matics, graphical statics). The number of subjects was extended in following years to include numerical and graphical methods, FFelixelix KleinKlein PPrizerize insurance mathematics and statistics, hydrodynamics and aerodynamics. The advent of such specialised teaching in The idea of a Felix Klein prize was born on education that was remote from practica- applied mathematics made the establish- the first day of the ICIAM99 meeting in lity, set in motion an anti-mathematics ment of corresponding subject areas neces- Edinburgh (see EMS Newsletter 33) during movement. In order to change the public sary, and eventually led to the creation of a discussion between the winner of the image of mathematics and create greater the first professorships in Germany in 1999 Pioneer prize, Helmut Neunzert, awareness for the usefulness of modern applied mathematics. Not only was Klein and the president of the EMS. Two days mathematical methods, Klein not only successful in convincing government min- later, Heinz Engl, Chair of EMS’s Applied turned his own research to applied mathe- istries, he also gained support for his plans Mathematics Committee, joined in and a matics and application-oriented themes, from heads of industry. Within the frame- first draft of the specifications was com- but also smoothed the way for others with work of the ‘Göttinger Vereinigung zur pleted. The executive committee diverse measures. His valuable results on Förderung der angewandten Physik und approved the wording of the draft at its the application of mathematics were aptly Mathematik’, affluent circles supported meeting in Zurich on 9–10 October. described by Richard von Mises Klein’s endeavours with over 2 million Renate Tobies’s article shows why the (1883–1953), founder of the journal Goldmarks between 1898 and 1920. name Felix Klein was chosen. The first call Zeitschrift für angewandte Mathematik und The decision to produce a journal for nominations can be found below. Mechanik, thus: devoted to applied mathematics was a fur- “A good part of [Klein’s] work on linear ther element of Klein’s programme. For Why a Felix Klein Prize? differential equations must be counted this, in 1900 the already-existing Zeitschrift Nowadays, mathematics plays an ever- here . . . for the main part they are con- für Mathematik und Physik was transformed greater role – often the decisive role – in cerned with so-called oscillation theories, and became what is acclaimed as the pre- finding solutions to numerous technical, which are crucial to problems of stability cursor of the Zeitschrift für angewandte economical and organisational problems. and eigenfrequencies of mechanical (and Mathematik und Mechanik. In order to In order to encourage such solutions and other) systems. A few treatises deal with change the public image of mathematics it to reward exceptional research in the area questions relating to geometrical optics, was not sufficient to limit activities to the of applied mathematics, the EMS decided, [such as] the theory of refraction in optical universities. Klein strove in an interna- in October 1999, to establish the Felix instruments. It is within various areas of tional context – in 1908 at the Fourth Klein Prize. mechanics, however, that Klein has ven- International Congress of Mathematicians The mathematician Felix Klein tured deepest into applied areas. He suc- in Rome, he was elected as Chairman of (1849–1925) is generally acknowledged as ceeded in promoting the kinematics of the International Commission of a pioneer with regard to the close connec- rigid bodies by developing English Mathematical Instruction – for a reform of tion between mathematics and applica- research which was virtually unknown in the teaching of mathematics ‘from primary tions that lead to solutions to technical Germany at the time (Robert Ball, defini- school to university’. Special emphasis was problems. Klein’s success in his efforts to tion of spiral or ‘dyname’) . . . and he placed on nurturing close relations open up modern mathematical methods searched for related areas in ‘technical between high-level science and perspicu- and theories to wider circles was based on mechanics’, i.e. direct solutions to real- ous applications-oriented mathematics. his international reputation as a renowned world problems. . . The outstanding teach- The fact that the group of Göttingen’s mathematician. His contributions to pure ing material originating from the lectures mathematicians achieved international mathematics include not only the well- in Göttingen by Klein and Sommerfeld on renown was due, in a great measure, to known systematisation of geometrical the theory of rigid bodies reaches . . . into Klein’s programme to develop mathemat- fields in his Erlanger Programm (1872), but technical problems dealing with gyro- ics in all directions and enable results of covered nearly all fields of mathematics. scopes and gyro-compasses, yawing of ves- pure mathematical research to flow into These contributions were collected in three sels, etc. Together with K. Wieghardt, applied areas combining the interests of volumes in his Gesammelte Mathematische Klein published a theory of stresses in academe and industry. Klein implement- Abhandlungen (1921–23). David Hilbert plane-truss assemblies based on an imagi- ed an adroit appointment policy (David (1862–1943), whom Klein supported and native combination of Maxwellian recipro- Hilbert, Ludwig Prandtl and Carl Runge) whose call to Göttingen he arranged in cal figures and Airy stress functions – a the- to achieve an ideal balance in the combi- 1895, was impressed with Klein’s striking ory which has proved its fruitfulness up nation of theory, application and numeri- geometrical perception. Hilbert empha- until the present time for dealing with cal mathematics. Close cooperation sised Klein’s outstanding results in the area problems occurring in the statics of struc- between scientists and their students pro- of automorphic functions and the scientif- tures” (Richard von Mises, ‘Felix Klein’, duced valuable contributions for the devel- ic vision that was evident in the undertak- ZAMM 4 (1924), 87–88). opment of mathematics and its applica- ing Encyklopädie der mathematischen However, in order to bring about tions. Wissenschaften mit Einschluss ihrer change, it was not sufficient for Klein alone Scientists who can prove, in a promi- Anwendungen (1895–1935), a comprehen- to yield up research results. Numerous nent and commendable way, that mathe- sive work of international authorship. and diverse scientific measures were neces- matical theory and mathematical models When the Berlin mathematicians – who sary to activate the long-neglected (in lead to practical solutions of problems, and over a long period had remained sceptical Germany) areas of applied mathematics. who thereby contribute to and influence of Klein’s application-oriented endeavours Around the turn of the century, Klein suc- the future growth of the mutual stimula- – elected him as corresponding member ceeded, together with many allies, in tion of theory and practice, are following to the Berlin Academy of Science in 1913, bringing about much improved conditions in the footsteps of Felix Klein and are wor- their election recommendation stated: for the development of applied mathemat- thy candidates and eligible for the award of ‘Klein [is] one of the few mathematicians ics. the Felix Klein Prize. who is still capable of an overall view of One of these developments was a new mathematics’ (full citation in Tobies, examination curriculum which was passed The above was written by Renate Tobies, from the 1999). in 1898 and which introduced and regulat- Department of Mathematics, University of Klein was aware that abstract-oriented ed – for the first time at a Prussian univer- Kaiserslautern, who is habilitated in the History of pure mathematics was in danger of becom- sity – the teaching of applied mathematics. Mathematics and has published five books, three of ing isolated. In the 1890s engineers and The course programme included a choice which include material on Felix Klein, and a number technicians, who lamented a mathematical of core subjects in descriptive geometry, of essays. [English translation by A. Rast-Margerison] 10 EMS December 1999 NEWS Felix Klein Prize Description of the award Prize history The award comprises a certificate contain- The first prize will be awarded in the year Specifications ing the citation and a cash prize, the 2000. amount of which is to be determined by Principal guidelines the endowing Institute for Industrial Prize fund The prize, established in 1999 by the EMS Mathematics in Kaiserslautern in consulta- The endowing Institute for Industrial and the endowing organisation, the tion with the presidents of EMS and ECMI. Mathematics in Kaiserslautern is responsi- Institute for Industrial Mathematics in Normally, the prize sum will be approxi- ble for managing the prize fund as well as Kaiserslautern, is awarded to a young sci- mately 5000 euro. its administration, should such a fund be entist or a small group of young scientists established. (normally under the age of 38) for using Award presentation sophisticated methods to give an outstand- The prize is presented every four years at Changes to these specifications ing solution, which meets with the com- the European Congress of Mathematics. A All changes to these specifications must plete satisfaction of industry, to a concrete representative of the endowing Institute have the approval of the EMS Executive and difficult industrial problem. for Industrial Mathematics in Committee and the endowing Institute for Kaiserslautern or the president of EMS Industrial Mathematics in Kaiserslautern. Selection procedures for composing the presents the award. The recipient is invit- prize committee ed to present his or her work at the con- Approved by the EMS Executive Committee at The prize committee consists of six mem- ference. its meeting in Zurich, 9–10 October 1999. bers, with one designated as “Chair”. The prize committee is composed of the follow- ing people. Three committee members are chosen 2000 : by unanimous agreement of the president of EMS and the chair of the Applied World Mathematical Year Committee of the EMS. The endowing Mireille Chaleyat-Maurel Institute for Industrial Mathematics in Kaiserslautern elects two members to the The year 2000 will be a crucial year for mathematics and math- prize committee, at least one of whom ematicians. For eight years the mathematical community has should be a representative from industry. known that this year, the first (or last) of the century and the The European Consortium for millennium, has been declared World Mathematical Year by Mathematics in Industry, ECMI, elects one the International Union of Mathematics. This decision, taken under the presidency member to the prize committee. The prize of Prof. J.-L. Lions, is supported by UNESCO, whose support has been confirmed by committee constitutes itself. a vote in General Assembly. A solemn declaration, called ‘Déclaration de Rio’ pro- Appointments to the prize committee poses three main lines of actions centred on mathematics: should be made at least eighteen months – the major challenges in mathematics for the 21st century; before the prize award date. – mathematics and development; Tenure of the Prize Committee – the image of mathematics among the general public. From the date of appointment to the Prize The first theme is mostly directed toward the mathematics community that wants its Committee, the members serve until the conjectures turned into theorems with simple proofs – short, elegant and accessible to prize is awarded. If no prizewinner is cho- all. This past century has witnessed the establishment of Fermat’s last theorem, that sen, the duties of the committee are com- had baffled people for over 300 years. Hopefully, at the end of the next century, peo- pleted. ple will speak of ‘Riemann’s theorem’ no longer as a hypothesis! During 2000 a com- Rules of Operations mittee, directed by Prof. V. -I. Arnold, is assessing the work accomplished during the A prize committee will be appointed every 20th century and prospecting for the coming century; a synthetic work is in prepara- four years. If no prize is awarded, the tion on these topics. award date moves ahead four years. The second theme involves the applications of mathematics and problems raised by The prize committee determines its own teaching mathematics. This point will be emphasised at the 2000 International procedures and rules of operations. Congress of ICMI in Tokyo. The third theme is aimed at teaching mathematics to a general public not always Nomination of the Award willing to learn. This calls for great creativity and originality from mathematicians, in There are no restrictions on eligibility the domain of communication and media such as: introducing mathematical sections other than those specified in the Principal and exhibitions in science museums, developing movies, videos and books, and Guidelines. organising conferences that popularise mathematics; all initiatives are welcome. In The prize committee is responsible for this direction, an idea proposed some years ago by the European Mathematical solicitation and evaluation of nominations. Society is already under way: posters on mathematical topics in subway stations and in Nominations may be made by anyone, cars and other forms of public transportation. A similar campaign has already been including members of the prize committee developed for poetry. Many European cities are willing to participate in this cam- or by candidates themselves. It is the paign, and some have already started to do so. The EMS has sponsored a poster con- responsibility of the nominator to provide test for this mathematical metro campaign – see page 14. all relevant information to the prize com- The year 2000 is also very important for the European Mathematical Society, mittee, including a resumé and documen- because its third Congress 3ecm will be held in Barcelona in July. The announced tation of the benefit to industry and the programme shows that it should be as successful as the Congresses of Paris and mathematical method used. Budapest. We hope that, for this event, many mathematicians will join the EMS. The nomination for the award should There is still time to propose mathematical congresses, workshops, conferences and be reported by the prize committee to the exhibitions. World-wide events can be announced in the WMY 2000 newsletter: just EMS president at least three months ask the Editorial Committee at WMY 2000, Institut Poincaré, 11, rue Pierre et Marie before the date of the award. The nomi- Curie, 75005 Paris, France. For European events, please contact the author of this nation for the award must be accompanied note [e-mail: [email protected]] or the EMS Newsletter editor. For national events, we by a written justification and a citation of urge national societies to create a Year 2000 Committee and to publish information about 100 words that can be read at the in their newsletters. award date. In conclusion, all European mathematicians should become involved with World The prize is awarded to a single person Mathematical Year 2000, and should participate, actively and at all levels, to every- or to a small group and cannot be split. thing that may contribute to the development of mathematics and its impact on world-wide problems of education, society and economy.

EMS December 1999 11 3ecm 3r3rdd EurEuropeanopean CongrCongressess ofof MathematicsMathematics

Shaping the 21st Century Barcelona, 10 – 14 July 2000 Second announcement

The Second Announcement of the 3ecm Studi di Udine) practice [Hélyette Geman, Université will soon be mailed to those who have pre- • Alexander B. Givental (University of de Paris IX and ESSEC] registered through the Congress web site. California at Berkeley and Caltech) • Quantum computing [Sandu Popescu, It will contain detailed instructions for reg- • Alexander Goncharov (Brown University of Cambridge] istration, grant requests, information on University, Providence) • Free boundary problems [José accommodation, and other features of the • Alexander Grigor’yan (Imperial Francisco Rodrigues, Universidade de Congress. Here we present a summary of College, London) Lisboa] the relevant information that is currently • Michael Harris (Université Paris 7 • Symplectic and contact geometry and available. Denis Diderot) Hamiltonian dynamics [Mikhail B. • Kurt Johansson (Kungl Tekniska Sevryuk, Russian Academy of Sciences] Plenary Lectures Högskolan, Stockholm) • Curves over finite fields and codes • Robbert Dijkgraaf (Universiteit van • Konstantin M. Khanin (Heriot-Watt [Gerard van der Geer, Universiteit van Amsterdam) University, Edinburgh, Isaac Newton Amsterdam] • Hans Föllmer (Humboldt-Universität Institute, Cambridge, and Landau • Wavelet applications in signal pro- zu Berlin) Institute, Moscow) cessing [Andrew T. Walden, University • Hendrik W. Lenstra, Jr. (University of • Pekka Koskela (Jyväskylän Yliopisto) of London] California at Berkeley and Universiteit • Steffen L. Lauritzen (Aalborg Leiden) Universitet) Round Tables • Yuri I. Manin (MPI für Mathematik, • Gilles Lebeau (École Polytechnique, The following list of topics has been agreed Bonn) Palaiseau) by the Round Table Committee. • Yves Meyer (École Normale • Nicholas S. Manton (University of • Mathematics teaching at the tertiary Supérieure de Cachan) Cambridge) level • Carles Simó (Universitat de Barcelona) • Ieke Moerdijk (Universiteit Utrecht) • What is mathematics today? • Marie-France Vignéras (Université • Eric M. Opdam (Universiteit Leiden) • The impact of mathematical research Paris 7 Denis Diderot) • Thomas Peternell (Universität on industry and vice versa • Oleg Viro (Uppsala Universitet and Bayreuth) • The impact of new technologies on POMI St Petersburg) • Alexander Reznikov (University of mathematical research • Andrew J. Wiles (Princeton University) Durham) • Building networks of cooperation in • Henrik Schlichtkrull (Københavns mathematics Parallel Lectures Universitet) • How to increase public awareness of • Rudolf Ahlswede (Universität • Bernhard Schmidt (Universität mathematics Bielefeld) Augsburg) • Shaping the 21st century • François Baccelli (INRIA and École • Klaus Schmidt (Universität Wien) Normale Supérieure, Paris) • Bálint Tóth (Budapesti Müszaki Call for Software, Video and Multi-media • Volker Bach (Universität Mainz) Egyetem) As has already been announced, a session • Viviane Baladi (Université Paris-Sud on mathematical software will take place XI) Mini-Symposia during the Congress. In this session, • Joaquim Bruna (Universitat Autònoma The following list of topics was chosen by mathematical software systems relating to de Barcelona) the Scientific Committee. all fields of mathematics, and applicable to • Xavier Cabré (Universitat Politècnica The speakers at each mini-symposium will a variety of purposes, will be presented. de Catalunya, Barcelona) be selected by the corresponding Chair The scheduled length of a presentation • Peter J. Cameron (Queen Mary and (listed in brackets below). (including discussion) is 30 minutes. Westfield College, London) • Quantum chaology [Sir Michael Berry, Submissions must be received by the • Ciro Ciliberto (Università degli Studi University of Bristol] organisers before 1 February. They may di Roma ‘Tor Vergata’) • Computer algebra [Wolfram Decker, be made electronically by using the form • Zoé Chatzidakis (CNRS and Université Universität des Saarlandes] provided on the web site http://www.iec. Paris 7 Denis Diderot) • Mathematics in modern genetics es/3ecm/mathsoft.htm, or by e-mail to • Gianni Dal Maso (SISSA, Trieste) [Peter Donnelly, University of Oxford] [email protected] with the single • Jan Denef (Katholieke Universiteit • String theory and M-theory [Michael word mathsoft in the Subject field. Leuven) Douglas, Rutgers University] The organisers also plan to produce a • Barbara Fantechi (Università degli • Mathematical finance: theory and DVD containing both short videos and 12 EMS December 1999 3ecm multi-media with mathematical content. Satellite Activities 3 – 9 July: Summer School on This DVD will be exhibited in general pub- The following list of satellite activities has Mathematical Aspects of Evolving lic sessions. Submissions of contributions been acknowledged by the Executive Interfaces, Funchal, Portugal for this DVD may be made from all areas of Committee by October 1999. Proposals Contact: Pierluigi Colli (Università di mathematics, and must be received by the for further satellite congresses or other Pavia), [email protected]. organisers before 1 February. Submission mathematical events will be welcome until Web site: http://maei.lmc.fc.ul.pt. forms are available at http://www.iec.es/ 1 February. 3ecm/video.htm, where additional 4 – 6 July: Catop 2000, a Conference on detailed information can be found. The Categorical Topological Methods, address [email protected] may be used 26 June – 1 July: Summer School on Fribourg, Switzerland to contact the organisers of this comple- Interactions between Algebraic Contact: H.-P. Künzi (Universität Bern), mentary activity or to ask any related ques- Topology and Invariant Theory, [email protected]. tions. Ioannina, Greece Contact: Nondas Kechagias (University of 4 – 7 July: First Euro-Mediterranean Call for Posters Ioannina), [email protected]. Topology Meeting, Bellaterra, Barcelona, All registered participants will have the Web site: http://www.uoi.gr/conf_sem/topol Spain opportunity to present their mathematical ogy2000/. Contact: Carlos Broto (Universitat work in the form of a poster. Decisions on Autònoma de Barcelona), euro-mtm acceptance will be made by the Organising 29 June – 1 July: 2nd International @mat.uab.es. Committee on the basis of an abstract Conference on Symmetry and Web site: http://mat.uab.es/euro-mtm. which should reach the organisers before 1 Antisymmetry in Mathematics, Formal March. Abstracts submitted after this date Languages and Computer Science, 3 – 5 or 5 – 7 July: cem 2000, Congrés will not be considered. Acceptance will be Brasov, Romania d’Educació Matemàtica, I Jornades confirmed before 20 March. Contact: Gabriel V. Orman (Transylvania d’Educació Matemàtica a Catalunya. Abstracts should conform with the fol- University), [email protected]. Mataró, Barcelona, Spain lowing instructions. It is strongly recom- Contact: Xavier Vilella (FEEMCAT), vilella mended that abstracts be submitted elec- 29 June – 4 July: Workshop on @pie.xtec.es. tronically by using the form provided in Bifurcation, Symmetry and Patterns, the web site http://www.iec.es/3ecm/ Porto, Portugal. 5 – 8 July: 6BLM, 6th Barcelona Logic posters.htm. Abstracts may also be sent by Contact: Jorge Buescu (IST, Lisboa), Meeting, Barcelona, Spain e-mail to [email protected], with the [email protected]. Contact: Josep Maria Font (Universitat de Subject field containing exclusively the rel- Barcelona), [email protected]. evant section number (see the list of sec- 3 – 7 July: Functional Analysis Valencia tions at the web site). Abstracts should 2000, an international functional analy- 6 – 8 July: IX Fall Workshop on preferably be written in English, and pre- sis meeting on the occasion of the 70th Geometry and Physics (Special Session), pared in LaTeX using only standard com- Birthday of Professor Manuel Valdivia. Vilanova i la Geltrú, Spain mands and AMS macros, symbols and Valencia, Spain. Contact: Miguel C. Muñoz-Lecanda fonts. Contact: José Bonet (Universidad (Universitat Politècnica de Catalunya), Politécnica de Valencia), vlc2000@mat. [email protected]. Grants upv.es or Klaus D. Bierstedt (Universität Web site: http://www-mat.upc.es/dgdsa/geo The organisers of the 3ecm will award Paderborn), [email protected]. mphys2000.html. grants of either partial or full support to Web site: http://www.upv.es/VLC2000/. attend the Congress. The aim of these 6 – 8 July: New Women in Mathematics: grants is to promote the participation of 3 – 7 July: 6th International Conference an International Forum for Women young researchers in mathematics, with on Harmonic Analysis and Partial Starting in Mathematical Research, special attention to their professional situ- Differential Equations, El Escorial, Barcelona, Spain ation and their country of origin. Madrid, Spain. Contact: Laura Fainsilber (University of Financial support will be offered in the fol- Contact: Eugenio Hernández (Universidad Gothenburg), [email protected]. lowing ways. Autónoma de Madrid), eugenio.hernan Web site: http://www.math.helsinki.fi/EWM/. A. Grants of 25,000 PTA covering the [email protected]. registration fee. 17 – 19 July: Distributions with Given B. Grants of 30,000 PTA covering accom- 3 – 7 July: Alhambra 2000, a Joint Marginals and Statistical Modelling, modation expenses at university resi- Mathematical European-Arabic Barcelona, Spain dences. Conference, Granada, Spain Contact: Carles M. Cuadras (Universitat de C. Grants up to 35,000 PTA for travel Contact: Ceferino Ruiz (Universidad de Barcelona), [email protected]. expenses. Granada), [email protected]. Web site: http://www.ugr.es/~alhambra 17 – 22 July: Colloquium on Lie Theory Mathematicians working in Catalonia can 2000/. and Applications, Vigo, Spain apply only for type A grants. Contact: Ignacio Bajo, Esperanza Mathematicians working in Spain but out- 3– 7 July: EVEQ 2000, International Sanmartín (Universidad de Vigo), clieta@ side Catalonia can apply for type A and/or Summer School on Evolution Equations, dma.uvigo.es. type B grants. Mathematicians working Prague, Czech Republic Web site: http://www.dma.uvigo.es/~clieta/ abroad can apply for all types. Contact: Hana Petzeltová (Academy of index. People interested in obtaining financial Sciences, Prague), [email protected]. support are requested to fill in an applica- tion form which can be found at the 3ecm 3 – 7 July: Colloquium on Number Contact Addresses web site http://www.iec.es/3ecm. Applic- Theory, Debrecen, Hungary Congress e-mail: [email protected] ations should be submitted before 31 Contact: Attila Pethö (Lajos Kossuth Congress web site: http://www.iec.es/3ecm/ January. Decisions will be taken before 10 University), [email protected]. or http://www.si.upc.es/3ecm/ March. Grant holders should confirm their Mailing address: Societat Catalana de registration before 1 April. The registra- 3 – 7 July: Conference on Algebraic K- Matemàtiques, Institut d’Estudis Catalans tion fees of people with type A grants will Theory and Homotopy Theory of Carrer del Carme, 47 E-08001 Barcelona, be paid by the organisers. Grants of type Schemes, Toulouse, France Spain B and C will be paid to their holders on Contact: Max Karoubi (Université Paris 7 Phone: (+34)-93-270-16-20 arrival at the Congress. Denis Diderot), [email protected]. Fax: (+34)-93-270-11-80 EMS December 1999 13 NEWS

EMSEMS PPosteroster CompetitionCompetition rresultsesults Vagn Lundsgaard Hansen

In the spring of 1999, the European [Durand receives the first prize for a series Mathematics (a flower picture which is Mathematical Society announced a compe- of seven posters that deal with Sunflower actually a rotational invariant Willmore tition to encourage the idea of creating seeds and Fibonacci sequences, Animals surface), The World is different with posters with a mathematical theme that with a spotted body, The Nautilus shell Mathematics (a ‘world pretzel’, in the form would catch the eye and be representative and the golden mean, Viruses and knots, of a double torus, that exhibits the various of mathematics and its uses. Such ideas Escher’s Circle Limit III (hyperbolic plane) continents).] can prove valuable in many situations as a and the Big Bang, Fractal geometry in Runner-up: Wolfgang Joppich, Institute for way of presenting mathematics to the pub- many situations, and Snowflakes and chaos Algorithms and Scientific Computing-GMD- lic. The direct reason for the competition theory.] SCAI, Sankt Augustin, Germany, for an was, however, to get ideas for suitable Second prize: Andreas Frommer, Stefanie applied mathematics poster on numerical posters to be displayed in subways and Krivsky and Petra Zöllner, Bergische weather forecasting. other public places, as one of the events Universität, Gesamthochschule Wuppertal, Many of the ideas for posters are suitable during the World Mathematical Year 2000. Fachbereich 7 (Mathematik), Gauss-Strasse 20, for use in other contexts as well, such as In the announcement of the competition, 42097 Wuppertal, Germany postcards, mugs, T-shirts etc. The the EMS offered prizes for the three best [Frommer, Krivsky and Zöllner receive the European Mathematical Society hopes to proposals, but naturally the hope was to second prize for a series of five posters obtain permission from the proposers to get more good proposals than those that divided into two concepts: three posters on make all such uses of their ideas as may be would finally be selected for a prize . . . and Mathematical thinking, which deal with of benefit to mathematics and may the EMS was not disappointed! The bridges of Königsberg, Primes and enhance the public understanding of our The deadline for submission of propos- twin primes, The Four Colour Theorem, subject. If permissions are granted, the als was 1 May 1999. Twenty-six proposals and two posters on Advertising mathemat- EMS will allow the use of the ideas in all were received, many containing multiple ics as being the foundation of high tech in worthy contexts. suggestions for posters. Altogether the jury everyday life, which deal with It was an unusual and exiting experience appointed by the Executive Committee of Tomography: the brain, Mathematical car for the jury in the competition. We feel the EMS to evaluate the proposals had crash test.] certain that we selected some very good about 100 posters to consider. Third prize: Nadja Kutz, Fachbereich proposals, but we also know that there are The jury consisted of Bodil Branner Mathematik, Sekr. MA 8-5, Technische other very valuable ideas in the total col- from the Executive Committee, and Universität Berlin, Str. des 17. Juni 136, lection. Early in the evaluation procedure, Ronnie Brown, Mireille Chaleyat-Maurel 10623 Berlin, Germany the jury realised that it is difficult for math- and Vagn Lundsgaard Hansen (Chair) [Kutz receives the third prize for a series of ematicians to judge what will catch the from the EMS committee on WMY 2000. posters with short slogans. She submitted attention of the general public in connec- It was a difficult task for the jury to three posters: Play with Mathematics (a tion with mathematics. But nevertheless, it come up with a decision. If a poster is to baby holding a model of a doubly discrete is important to try, for the future of math- be both instantly attractive to a lay person, smoke ring flow in her hand), Grow with ematics. and also signal an important math- ematical message to a person reflecting on the poster, fruitful ideas are not particularly easy to come by. In several proposals, the graphics were attractive but the mathematical message was too sim- ple. In other proposals the mathe- matical content was substantial, but the graphics were not sufficiently appealing to the general public. In the end, the jury selected three pro- posals that satisfied both expecta- tions, being attractive as well as car- rying an important mathematical message. The recommendations by the jury were approved by the Executive Committee of the EMS at its October meeting in Zurich. The Executive Committee expressed its satisfaction with the diversity in the submissions and by the high degree of creativity shown by the pro- posers. The winners are: First prize: Stéphane Durand, Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Qc, H3C 3J7, Canada One of the prize-winning entries. Others will appear in future issues 14 EMS December 1999 EMS NEWS Puppe. Of the eleven, B. Branner, J.-M. attending the ECM, an address for accom- Deshouillers and M. Karoubi cannot be re- modation arrangements will be provided MeetingMeeting elected because they have served in this later. capacity for 8 years. The Executive Committee is responsi- Secretariat: ofof thethe ble for preparing the matters to be dis- Ms. Tuulikki Mäkeläinen cussed at Council meetings. Items for the Secretary of the EMS agenda of this meeting of the Council P.O. Box 4 EMS Council should be sent as soon as possible – and no FIN-00014 University of Helsinki EMS Council later than 10 March – to the EMS Finland 7 – 8 July 2000, Barcelona Secretariat in Helsinki. Second announcement The Council is responsible for electing Annex: 2000 timetable for the the President, Vice-Presidents, Secretary, Council Meeting Treasurer and other members of the The EMS Council meets every second year. Executive Committee. The present mem- 31 January: Deadline for nominations for The next meeting will be held in Barcelona bership of the Executive Committee, delegates of individual members. on 7-8 July 2000, before the 3rd European together with their individual terms of February: The ballots for delegates of indi- Congress of Mathematics. The exact loca- office, is as follows. vidual members are sent to individual tion will be announced later. members. Delegates to the Council will be elected President March: Candidates for delegates of indi- by the following categories of members, as Professor Rolf Jeltsch (1999–2002) vidual members are announced in the EMS per the Statutes. Vice-Presidents Newsletter. The venue and meeting times (a) Full Members: Full Members are nation- Professor Andrzej Pelczar (1997–2000) of the Council meeting are repeated. al mathematical societies, which elect 1, 2 Professor Luc Lemaire (1999–2002) April: A letter is sent to each delegate, con- or 3 delegates according to their size and Secretary taining the agenda of the Council meeting. resources. Each society is responsible for Professor David Brannan (1999–2002) June: The results of the elections for dele- the election of its delegates. Each society Treasurer gates of individual members are should notify the Secretariat of the EMS in Professor Olli Martio (1999–2002) announced in the EMS Newsletter. The Helsinki of the names and addresses of its Members venue, the meeting times, and the agenda delegate(s) no later than 10 March 2000. Professor Bodil Branner (1997–2000) of the Council meeting are given. Material As of 1 July 1999, there were 47 such soci- Professor Marta Sanz-Solé (1997–2000) for the Council meeting is sent to the del- eties – which could designate a maximum Professor Anatoly Vershik (1997–2000) egates. of 69 delegates. Professor Doina Cioranescu (b) Associate Members: There are two associ- (1999–2002) EMS Country ate members, namely the Gesellschaft für Professor Renzo Piccinini (1999–2002) Mathematische Forschung and the Representatives European Mathematical Trust. Their cur- Under Article 7 of the Statutes, members The following have become Country rep- rent common delegate is elected until of the Executive Committee shall be elect- resentatives for the EMS Newsletter. If 1999, so their delegate has to be elected in ed for a period of 4 years. Committee you would like to become a Country 2000. According to the Statutes, ‘delegates members may be re-elected, provided that Representative, please contact your representing associate members shall be consecutive service shall not exceed 8 country’s mathematical society and then elected by a ballot organised by the years. Andrzej Pelczar has served on the contact the EMS Secretariat in Finland Executive Committee from a list of candi- Executive Committee for 8 years, so he (see page 2). dates who have been nominated and sec- cannot be re-elected. onded, and have agreed to serve.’ It would be convenient if potential nom- Catalonia: (c) Institutional Members: There are three inations for office in the Executive Agusti Reventos institutional members, Institut Non- Committee, duly signed and seconded, [[email protected]] Lineare de Nice, the Moldovian Academy could reach the Secretariat by 10 March. It of Sciences and the Mathematical Institute is strongly recommended that a statement Czech Republic: of the Serbian Academy of Sciences and of intention or policy is enclosed with each Lubos Pick Arts. Their common delegate is elected till nomination. If the nomination comes [[email protected]] 1999, so their delegate has to be elected in from the floor during the Council meeting 2000. According to the Statutes, ‘delegates there must be a written declaration of the Finland: representing institutional members shall willingness of the person to serve, or Mikko Pere be elected by a ballot organised by the his/her oral statement must be secured by [[email protected]] Executive Committee from a list of candi- the Chair of the Nominating Committee (if dates who have been nominated and sec- there is such) or by the President. It is rec- Germany: onded, and have agreed to serve.’ ommended that a statement of policy of Ehrhard Behrends (d) Individual Members: A person becomes the candidates nominated from the floor [[email protected]] an individual member either through a should be available. corporate member, by paying an extra fee, The Council may, at its meeting, add to Italy: or by direct membership. On 30 June the nominations received and set up a Giuseppe Anichini 1999, there were some 1900 individual Nominations Committee, disjoint from the [[email protected]] members and, according to our statutes, Executive Committee, to consider all can- these members will be represented by didates. After hearing the report by the Luxembourg: 19–20 delegates. The final count of indi- Chair of the Nominations Committee (if Jean-Paul Pier vidual members for these elections was one has been set up), the Council will pro- [[email protected]] made on 1 November 1999. ceed to the elections to the Executive The mandates of 11 of the present 17 Committee posts. Norway: delegates ended on 31 December 1999, Delegates to the Council meeting, who Erik Bedos and so elections must be held for their are planning to attend the European [[email protected]] positions. They are: G. Anichini, G. Congress of Mathematics, are advised that Bolondi, B. Branner, J.-M. Deshouillers, K. their accommodation arrangements United Kingdom: Habetha, M. Karoubi, T. Kuusalo, A. should be made through the ECM. For Susan Oakes Lahtinen, L. Màrki, R. Piccinini, and D. delegates to the Council who are not [[email protected]] EMS December 1999 15 INTERVIEW mistakes just as we do and they do – that problems were solved with different meth- ods – that things taken for granted in some Interview with Jan van Maanen period were open questions at other peri- ods. Overall they gained a quite different (Groningen) perspective on mathematics – much better than only learning by doing problems Chair of HPM from a textbook, and often with more plea- sure too! . . . though I had them do many interviewer: John Fauvel, Open University, UK sums as well.

I think people would be interested in having Jan van Maanen graduated in mathematics There is a lot of enthusiasm in many this pinned down a bit: can you give an from the University of Utrecht in 1977, and European countries for developing histori- example? took his PhD in 1987 with a thesis on ‘Facets of cal contexts for mathematics teaching and One of my pupils, Janneke, comes to my seventeenth-century mathematics in the incorporating historical insights in a whole mind. She was not at ease with the qua- Netherlands’. For fifteen years a teacher at the range of ways, into everything from nation- dratic equation formula which she found Christelijk Gymnasium, Utrecht, he now teaches al curricula, as in Denmark and Norway, to extremely hard to remember; she felt it as at the University of Groningen and is chair of the work of individual teachers. This an alien collection of characters and other the national exam board for ‘Mathematics B’ enthusiasm is fostered and shared by the signs. One day I came back to class, full of (the pre-university school-leaving examination organisation of meetings which attract par- enthusiasm for just having read one of my in calculus and geometry). Jan van Maanen is ticipants from across Europe: I remember ancient texts, Johan Stampioen’s Algebra co-chair of an international study on the rela- especially one in Braga, Portugal, in 1996 of 1639, and got the students to read and tions between history of mathematics and the which attracted roughly equal numbers of work through the way he solved a quadrat- teaching and learning of mathematics, as well Portuguese mathematics teachers, and ic problem, with a geometric diagram (lit- as chair of HPM, the International Study mathematicians and mathematics educa- erally ‘completing a square’), then to com- Group on the Relations between History and tors from the rest of Europe and else- pare his process with our formula. Pedagogy of Mathematics, which provides the where, some 550 people in total from Stampioen described his solution rhetori- context for the opening question. around thirty countries. cally, in a ‘first do this, then do that’ kind of style. Janneke was spellbound, asked First, Jan, could you explain what ‘HPM’ What kind of people are we talking about? “why don’t we solve these equations the is? – teachers? researchers? way Stampioen did it?” We then compared You can look at HPM in two ways. I could The HPM movement is very interesting – the rhetorical solution with the quadratic reply by saying that it is an official study and important in an exemplary way, I equation formula, and found out that you group of ICMI – the International think – for its mix between teachers, acad- can also remember that formula as a series Commission on Mathematics Instruction – emics, generators and users of research: an of actions, instead of having to store a sta- which is itself a committee of the IMU environment where people who are profes- tic formula in your photographic memory. (International Mathematical Union). It sionally engaged in mathematics, in its Here the comparison with the past helped was established in the early 1970s, at the teaching and in history of mathematics to clarify the present procedures. Janneke, second ICME (International Congress on come together to learn from each other, by the way, later on went to university and Mathematics Education). From that per- exchange insights and move forward studied econometrics: I feel history helped spective it is a cog in the international together. You can see this in the annual her at a crucial stage in her mathematical machinery of mathematical and education- HIMED (‘History in Mathematics development. But maybe that is a biased al interests. But I could reply in another Education’) meetings in the UK, in the impression! way too: HPM is a collection of teachers Université d’été in history and epistemology Another example – I have read Euler and academics from around the world of mathematics which is an annual event in with my class. I like Euler very much, united in a common enthusiasm for the France, and which, since 1993, is organ- because he has a very clear and open style, role of history in mathematics teaching, ised at a European level every three years, which is such a wonderful example of how people who want to absorb the lessons of this July in Belgium. And there are numer- to write and do mathematics. When my the past in order to improve the mathe- ous sessions devoted to the topic within class came to learn logarithms the students matics education of the future. broader conferences such as ICMs, ICMEs and national mathematical conferences. How is the HPM group organised? Interestingly, it more or less works without So we’ve established that there is a lively administration or finances – which is rare and wide-ranging social structure for peo- among such international organisations! ple with common interests, but – if I may act The group runs through communications as devil’s advocate for a moment – just what between people, through conferences. It is the point? has had a newsletter for the past 20 years, The point is that mathematics teaching can thanks to the hard work of a number of be better if the teacher is aware of the individuals, both in editing it and distrib- added dimension of where the mathemat- uting it, and thanks, too, to the support of ics has come from, and has a range of institutions who have provided assistance insights and resources to share with stu- with reprographic and postage costs. To dents as is appropriate for their needs and be an HPM member has been, in effect, to difficulties at any moment. In my own be on the mailing list of a distributor; the case, I was doing research into the history world is covered with a network of distrib- of mathematics for my PhD at the same utors. But the newsletter is in a fallow peri- time as teaching mathematics at a Dutch od at the moment, I hope temporarily, so gymnasium (a six-years grammar school membership is even less formally pinned that gives direct entrance to university). I down than usual. Nonetheless a great began to find that sharing with my pupils number of activities take place. the historical insights I was gaining through my researches was a good strategy Jan van Maanen (in check shirt) discussing In Europe, for example, how does that with several benefits for the lessons. Pupils strategy with international colleagues in the work? learned that great mathematicians made HPM movement 16 EMS December 1999 INTERVIEW read Euler’s marvellous exposition as ways in which such teachers can make use University commissioned a sculpture to homework (some helping by translating it of history, from telling stories to setting commemorate Bernoulli’s association with out of Latin) then checked his reasoning projects and designing curricula. Groningen, and in particular his celebrat- and calculations. They seemed to me to ed work on the brachistochrone problem, understand logarithms, as a result, much Should history of mathematics itself be showing the curve of quickest descent to be more clearly than the way I myself was taught in schools? a cycloid. Bernoulli’s solution is represent- taught the subject thirty years ago. Also Mathematics should be taught as a living, ed in a great steel sculpture by the gener- my colleague teachers of classical lan- dynamic subject, and history can con- ating circle of the cycloid and two vast guages profited, since this Euler passage tribute to that. If history is taught as such, cycloidal arcs. It’s quite eye-catching. was the first text these students read for it is only as a means of evoking mathemat- another sake than just learning Latin. ical understanding. A teacher who monot- And has much of mathematical interest onously reads from a history book will happened in Groningen since Bernoulli’s Is history only or most useful, then, for a hardly be helping pupils! But suitably cho- day? school such as Christelijk Gymnasium sen history can be really beneficial. The Not different from many other academic whose pupils study Latin as well, and most teacher who is teaching L’Hôpital’s Rule, institutions, I guess. But let me tell you of whose students go on to university? for example, can bring a good and memo- about just one episode. In 1914 Alicia No, I do not think so. In fact, teachers rable kind of pathos into the classroom by Boole, the daughter of George Boole, was working with a range of disadvantaged or talking about Johann Bernoulli who – as a awarded an honorary degree at low attaining or unconfident students young man with advanced knowledge Groningen, which was rather revolutionary report considerable success in exploring about the new field of differential calculus at that time, for her work on polytopes (her mathematics from a historical perspective. - taught the rich nobleman L’Hôpital, who word for four-dimensional regular poly- My colleague Marjolein Kool, for example, made a contract that Bernoulli would send hedra). A few years ago Dirk Struik, the has done just this kind of thing with low- letters about his mathematical discoveries. great Dutch historian of mathematics now attaining teenagers, and found old Dutch L’Hôpital sent money in return, and could in his 105th year, asked me if there were mathematics texts an ideal source of stim- do with Bernoulli’s findings what he want- still any traces of Alicia Boole at ulation and reassurance. Part of the rea- ed. So L’Hôpital wrote, in 1696, the first Groningen; I found that indeed her own son for the success, of course, is that this textbook about differentiation, in which he wonderfully colourful drawings of poly- kind of historical material enthuses and included Bernoulli’s method for calculat- topes are still kept at our department, and motivates us, the teacher, so the teaching is ing limits, which is still known under that a set of models of three-dimensional bound to have an infectious spark, and L’Hôpital’s name – and Bernoulli could do sections of them is in the university muse- that’s so much of the battle. The difficult nothing about it (although he tried, after um. point is whether it transfers: take a school L’Hôpital’s death). For some pupils this is at random, a teacher at random – would just a rule, one of many. Pupils who know How does the presence of so much history of history also be interesting for such a the story behind the rule will not easily for- mathematics influence or benefit today’s teacher? For the pupils? How would you get it. The story gives the rule a profile, Groningen students? reach this teacher? That’s the challenge. and in this manner supports the memory. I have no firm evidence for that. The his- It’s true that other mathematics teachers tory of maths course is fairly popular, and might find they can inspire pupils through Is there any particular reason for your some of my colleagues do integrate history their involvement in something like sailing interest in Johann Bernoulli? in their lectures. The clearest thing I or sundials or football, so it’s tempting to Since you ask, he was one of the early stars notice is that students use the Bernoulli say that enthusiasm is the main quality of the University of Groningen, where I sculpture as a backdrop for taking pho- needed. But history has a whole range of teach. Bernoulli’s Groningen was the sec- tographs of each other! Maybe also busi- further benefits too, as our ICMI Study is ond university in the world (after his broth- ness administration students who have showing. er Jakob’s Basel University) to teach calcu- their own fantasy with the statue. The big lus – that was in 1698 – and we’re rather circle as a symbol for generating money So tell me about the ICMI Study. proud of that. In fact in 1996 the instead of cycloids? You could easily answer this yourself, since we are co-chairing this event, but I appre- ciate that answers are to come from me in this interview. Last year there was a con- ference at the French Mathematical Society’s retreat in Luminy, near Marseilles, at which 75 mathematics teach- ers, educators and historians from around the world came together for a week to exchange experiences and perceptions. There they made a systematic and compar- ative survey of the improvements in math- ematics teaching and learning through his- torical dimensions and resources – and also of the problems connected with this approach. The results are being written up in a book which should be published in time for the next ICME to be held in Tokyo in August 2000.

What kind of results have you got, or do you expect, from the ICMI Study? I’ve hinted at the main thing, which is the great range of students – across ages, across abilities, across subjects, across countries – whose mathematical learning and understanding is helped by having historically resourced teachers. The sec- The cycloidal lines of Henk Ovink’s Bernoulli sculpture (1996) are seen against the buildings of ond main finding is the enormous range of the University of Groningen. EMS December 1999 17 INTERVIEW the same magnitude.

Do you think that one should adapt the sub- Interview with Olavi Nevanlinna ject classification used at ICM and ECM congresses to reflect this change? President of ICIAM Well, yes, I think the classification used at interviewer: Rolf Jeltsch, EMS President ICM congresses surely has a strong sub- conscious influence on what is viewed as valuable within mathematics. And from this perspective the situation is far from Olavi, let me congratulate you on your elec- ICIAM Board at its annual meeting. Our satisfactory. It is interesting to look back tion as President of ICIAM. The applied vision of ICIAM is, I think, shared by all on the history of IMU. There have been a mathematics community always associated involved: to become a truly globally oper- number of attempts to increase connec- this name with the conferences like ating organisation in its field. I think we tions to applications. However, these have ICIAM99 in Edinburgh. Why did your will achieve this goal in an organic way, by rather been attempts to reach out to such organisation change its name from the building on the tradition of applied math- fields as theoretical mechanics or theoreti- nearly unpronounceable CICIAM? ematics where many important societies cal computer science, instead of support- CICIAM was the abbreviation of and are – and have been – multinational by ing the existing applied mathematics com- ‘Committee for International Conferences nature. munity within mathematics. on Industrial and Applied Mathematics’. It was felt that the new name describes How do you position ICIAM in the societies The acronym ICIAM comprises ‘Industrial more accurately the aims of the organisa- in the world? Some of your member soci- and Applied Mathematics’. Where do you tion as set out in its bylaws. The congress- eties are also corporate members of EMS. position this type of mathematics within the es will be advertised in the old way; for Would it still make sense for EMS to join whole of mathematics? example, the next international congress ICIAM associate member? Perhaps the customary way of thinking is on industrial and applied mathematics, ICIAM has only scientific societies as mem- to put it at the periphery, where it lives will take place in Sydney, 7–11 July 2003, bers. In Edinburgh our by-laws were closely connected with its neighbouring and will be called ICIAM2003. changed so that societies significantly – but fields within other sciences. However, if we not primarily – dedicated to applied or ask ourselves why mathematics exists in the What are the aims of ICIAM? industrial mathematics can be associate first place, in this socio-economic world, it To promote industrial and applied mathe- members of ICIAM. I am convinced that is at the very centre. matics internationally, to promote interac- EMS becoming an associate member would tions between member societies and their benefit both ICIAM and EMS. Is Industrial Mathematics not simply one goals, and to coordinate planning for reg- aspect of Applied Mathematics? ularly occurring international meetings on If I remember correctly, the ICIAM confer- Not really. To me, applied mathematics industrial and applied mathematics. ence series was started in 1987 in Paris out refers to a certain, specific area within the of protest to the ICM congresses of IMU. science of mathematics, whereas industrial What do you personally want to achieve as What is the relation nowadays between mathematics relates more to its application president of ICIAM over the next four ICIAM and IMU? in industry. For example, a smaller con- years? It is true there has been some frustration ference within some field of applied math- If one thinks of the ICIAM congresses as over the minor role accorded to applied ematics would typically take a slice of an emerging process, it has surely started mathematics at ICM congresses, but the applied mathematics following some classi- well. These congresses answer a strong main motivation was undoubtedly the need fication as in science, while a reasonable need and this positive development must for international congresses dedicated to slice of industrial mathematics might col- continue. CICIAM acted mainly as a applied mathematics. The community had lect different types of mathematical tools standing committee for these congresses. grown large and strong enough to emerge vital to one fixed industrial area. Now, however, it is time to focus also on in its own right. At present there are no other aims of the organisation. With this formal links between ICIAM and IMU, but For the newest arrival on the scene, shift of focus, we have seen that the opera- in Edinburgh a decision was reached to Computational Science and Engineering, or tional mode followed by CICIAM is no establish contacts. CSE, many centres have been created and longer sufficient. new curricula set up. Is CSE a science? In Edinburgh we changed our bylaws I’ve noticed that the applied mathematics Should it be taught? and from now on we have four elected per- community has grown in size and the num- It is true, CSE is arriving in many places manent officers: a President, a former ber of mathematicians in this area is surely now. I know you have a programme at President/President elect, a Secretary and a almost equal to the number of the mathe- ETH and we are starting a program at Treasurer. My intention is to get the offi- maticians in areas outside applied mathe- Helsinki University of Technology as well. cers to work as a team which prepares and matics. Can you confirm this? I think the name of this discipline, CSE, is executes those decisions reached by the Yes, I think we can say that their size is of very honest in that it emphasises computa-

Olavi Nevanlinna (right) and Rolf Jeltsch during a working break in Celebrating the election of Prof. Olavi Nevanlinna (right) as President of Helsinki, summer 1978. ICIAM at Rolf Jeltsch’s house in Zurich, autumn 1999. 18 EMS December 1999 INTERVIEW tion as a tool to obtain new scientific results and to propose new or develop existing engineering practices. Naturally it has to be taught. The fact that it is an interdisci- plinary subject makes teaching more diffi- Interview with Ian Frigaard cult, but no less important. Schlumberger Dowell, Paris You were elected just a few days ago and hence I feel very flattered that your first interviewer: Heinz W Engl trip, directly after the visit to your prede- cessor, Reinhard Mennicken, should be to me. Mister President. I am flattered that you are flattered. I like this city. Zurich is The EMS Committee on Applications of Schlumberger Cambridge Research after surely one of the centres of mathematics. Mathematics plans to conduct a series of inter- this and spent eighteen months there For example, it has hosted the ICM no less views with recent mathematics graduates who before starting my current job. My experi- than three times – no other venue was cho- now work in industry. These interviews with ence there was quite varied, with much sen more than once. Maybe we should tell applied mathematicians will continue in future learnt about the oil industry and oilfield- the readers that we used to work together, issues. type engineering, rather than undertaking quite a lot actually, in the late 1970s and any particular or significant mathematical early 1980s, and I am aware that we think What kind of work do you currently do in work. along similar lines: that applied mathe- your company? matics really does need a push and that The technical work involves solving practi- How do you view all this in view of your this push will eventually benefit pure math- cal engineering problems, usually involv- current work? What was especially impor- ematics. ing continuum mechanics and more specif- tant, what was missing and should have ically, fluid mechanics of non-Newtonian been emphasised more? This occasion [raising their glasses to drink fluids. The background to this is that Most of my work in the past seven or eight to their close co-operation] reminds me of Schlumberger Dowell are involved in pro- years has been in the area of an old photo of the two of us, taken in viding cementing and drilling fluid ser- industrial/applied mathematics. I think I Helsinki in 1978 where we celebrated some- vices to the oil industry. was fortunate to do the M.Sc. course, which thing, although I don’t remember what. gave me enough confidence (and a toolbox It must have been the fair number of beau- How much does it relate to mathematics? of skills) to go out and tackle some real tiful theorems we proved during the two The content of the work that I do is large- problems. After this, every experience has months on the beach at our summer place. ly mathematical. However, this does not helped to build my problem-solving abili- mean that I spend my time ‘doing mathe- ties. I’ve changed industry two or three May I ask you a more personal question? matics’. Significant proportions of my times now and each time I find the learn- You come from a very famous family of five time are spent writing reports and papers, ing curve of ‘what the problems are’ is eas- generations of mathematicians. When I presenting and explaining my work, ier to climb. Two important things from used to lecture on our joint work, people directing and helping others, program- my perspective are: always wanted to know about your family ming, training, travelling, e-mail and – in an applied mathematician’s education connection with Rolf Nevanlinna. I assume bureaucratic activity. I think this is com- ‘modelling’ and ‘problem-solving’ are that our readers would like to know this too. mon in any large multinational company. essential, but if they want to work in indus- Well, Rolf, I have been asked this question try the first thing to recognise is that the a few times too. Rolf Nevanlinna was my Tell us about your mathematical education ‘problem’ is not a mathematical one, at grandfather’s brother. When I decided to and prior experience before your current least at first. This is hard to put into a con- study mathematics I entered the Helsinki employment. ventional maths education and should not University of Technology in order to gain I have a B.Sc. in Mathematics from be at the expense of learning mathematics. distance from the function theory school University of Wales, which is a general 3- – once working in industry as a mathe- which dominated mathematics at the year UK mathematics degree. Following matician, the opportunities to stay in touch University of Helsinki at that time. I want- this I specialised in applied mathematics and work with academic mathematicians ed to pursue my own career in applied with an M.Sc. in Mathematical Modelling become very important intellectually. mathematics. and Numerical Analysis at the University Only after a dozen years as full profes- of Oxford. Finally I studied for my D.Phil. How much of your work needs numerics? sor did I allow myself to work in that area. at Oxford. Although this was within the Nearly all, but the numerical mathematics Actually, while lecturing here at ETH dur- Department of Engineering Science, it was is rarely used or useful when I don’t ing the summer term in 1992 I noticed a largely industrial mathematical modelling. already understand the problem or its link between value distribution theory of My current position is my fourth job. I solution, at least partly, through analysis or meromorphic functions and perturbation spent three years working at Alcan intuition. theory of linear operators. Bearing in International’s Banbury Research mind applications to iterative methods in Laboratory (UK), during and after my What skills in addition to mathematical large-scale computation, I wanted to be D.Phil. The work here coincided largely ones do you need most? able to estimate the growth of a resolvent with my D.Phil. thesis work and was Diplomacy, communication and presenta- in such a way that small rank perturbations involved with modelling a novel tion skills. The ability to see through busi- would be seen as small perturbations. Let Aluminium spray process. Following this I ness bullshit. me remind you that value distribution the- spent two years as an ECMI post-doctoral ory is often called Nevanlinna theory. research fellow at the Institute for Industrial Mathematics, University of Linz, Dr. Frigaard also expressed his view that in I am looking forward to an excellent coop- Austria. Here I did some feasibility type his experience, companies rarely hire eration between our two societies. research for Voest Alpine Industrean- mathematicians as such, but they are look- So am I, but should we say organisations lagenbau, on a Steel continuous casting ing for people with expertise in a specific rather than societies? process. I spent some time involved in problem area, so that mathematicians have activities with the ECMI research network usually to compete with engineers. Yes, that might be more appropriate. active at the time and some time publish- Thank you very much for this interview. ing work from my thesis. I also lectured in Heinz W. Engl is Chairman of the EMS fluid mechanics at the university. I joined Committee on Applications of Mathematics. EMS December 1999 19 ANNIVERSARIES 1999 Anniversaries

There are many mathematical anniversaries in of mathematics to quantify the world. In his earlier work and achieved many of his 2000. If you are interested in writing a column keeping with such a belief, Laplace, who most important results. These included on any of the following, please contact either of was ‘always less enamoured with the beau- his discovery of the long period inequality the column editors, June Barrow-Green and ty of mathematical speculation than he was occurring in the mutual perturbations of Jeremy Gray, in the first instance: Niccolo anxious to unfold the system of the world’ Jupiter and Saturn, and the cause of the Tartaglia (b.1500), John Napier (b.1550), [7, p.111], actively pursued methods that secular variation of the mean motion of the John Maior (b.1550), Adrian Vlacq (b.1600), could be used to yield quantitative infor- moon. These discoveries added further René Descartes (d. 1650), Daniel Bernoulli (d. mation. But by the end of the century a conviction to his belief in stability, and by 1700), Simon L’Huilier (b. 1750), Abraham significant change had taken place. Not 1788 he had become certain that stability Kaestner (d.1800), Lorenzo Mascheroni only had the subject grown well beyond the was beyond doubt. It was also the time (d.1800), Karl Feuerbach (b. 1800), Sonya scope of a single researcher, but the gener- during which he engaged in experimental Kowalewskaya (b.1850), Alfred Pringsheim al thrust of the activity had changed. No physics, most notably in the chemical (b.1850), Bernt Holmboe (d.1850), Eugenio longer dominated by a single methodolo- physics of heat, in active collaboration with Beltrami (d.1900), Joseph Bertrand (d.1900), gy, a split had emerged between the quan- Lavoisier. In the early 1790s he was also Elwin Christoffel (d.1900), Jean-Frédéric titative and the qualitative approaches. heavily involved in the preparation of the Frenet (d.1900), Mary Cartwright (b.1900), There were those, such as George Darwin, metric system. Constantin Carathéodory (d.1950), Ernst who calculated orbits using numerical By 1795 Laplace had begun to compile Hellinger (d.1950), Aleksandr Khinchin analysis [3], but the innovative theoretical material for Mécanique Céleste and in that (d.1950) and Nikolai Luzin (d.1950). development lay with the qualitative analy- year embarked on giving his first and only sis of Poincaré. In contrast to the methods lecture course at the École Normale. The of Laplace, the methods of Poincaré, which course was never completed, due to the A century of celestial relied heavily on geometric intuition and closure of the École, and for the missing reasoning, were quite unsuitable for use in lectures the students were referred to a mechanics: quantitative analysis at the time when they book that Laplace was in the process of Laplace (1799) to were conceived. writing. The book, Exposition du Système du Monde, which was published the following Poincaré (1899) Pierre-Simon Laplace (1749-1827) year, contains a non-mathematical account June Barrow-Green Laplace began his career as professor of of planetary motion, rational mechanics mathematics at the École Militaire in Paris and gravitational theory, as well as a sum- Of the myriad of subjects that feature in where he taught from 1769-76. His first mary of the history of astronomy. It 19th-century mathematical research, none published paper, on the integral calculus, proved a resounding success. Although a more completely embraces the period than was published in 1771, and he was elected work in its own right, it also acts as an out- celestial mechanics. The century both to the Académie des Sciences in 1773. line or prospectus for the Mécanique Céleste, opened and closed with seminal works of During the 1770s he established his math- and Laplace arranged for the second edi- monumental proportion. When it began, tion to be published specifically to accom- the first two volumes of Laplace’s Traité de pany the launch of the treatise. Mécanique Céleste were barely a few months Laplace was also involved in politics, old – they were published in October 1799 although not to great effect. When – and when it ended, the final volume of Napoleon seized power in 1799 Laplace Poincaré’s Les Méthodes Nouvelles de la became Minister of the Interior but after Mécanique Céleste had just appeared. There only six weeks he was replaced by was of course a substantial quantity of work Napoleon’s brother. He was later appoint- produced in between, initially prompted ed to the Senate and in 1803 became chan- by Laplace’s work which became the cellor of the Senate, a position of little springboard for research in both theoreti- power but of substantial salary. Napoleon, cal and practical astronomy. His followers having realised the limits of Laplace’s focused themselves on extending the capabilities, described him as having ‘car- results, improving the methods of investi- ried the spirit of the infinitesimal into gation, and illustrating the more obscure administration’ [5, p.176]. points of the theory. But research into celestial mechanics was not done only by Traité de Mécanique Céleste (1799-1825) those, such as Delaunay, Le Verrier, In October 1799 Laplace presented Newcomb, Hill and Tisserand, who spe- Napoleon with copies of the first two vol- cialised in the subject. Such was the sub- umes of Mécanique Céleste. Napoleon’s ject’s appeal that it frequently engaged the response is legendary. He accepted the attention of mathematicians whose reputa- Pierre-Simon Laplace gift with the promise that he would read tions resided elsewhere. Arthur Cayley, for them ‘in the first six months I have free’. example, was renowned as a pure mathe- ematical reputation, embarking on a pro- He also invited Laplace and his wife to matician, but wrote almost forty papers for gramme of research in celestial mechanics dine the following day ‘if you have nothing the Royal Astronomical Society. and in probability, the two subjects for better to do’ [5, p.176]. The third volume, Considered together, the treatises of which he would become most famous. which was dedicated to Napoleon, Laplace and Poincaré provide a remark- With regard to celestial mechanics, he was appeared in 1802, the fourth in 1805, and able example of the expansion and evolu- particularly fascinated by the problem of the final volume in 1825. Although imme- tion of mathematical thought during the the stability of the solar system. He was diately recognised as a masterpiece, its century. At the end of the eighteenth cen- convinced that stability could be proved by mathematical difficulty combined with its tury, research into celestial mechanics was Newton’s laws and his quest for a resolu- broad range of subject matter meant that sufficiently limited that it was realistic for tion of the problem was to prove a fertile only a very few were able to read it all with Laplace to aim to set down all there was to ground for his ideas, most notably in his any degree of facility [8, I, p.62]. know about the subject. Furthermore, it introduction of perturbation methods. The whole was conceived as two parts: was also a time of great faith in the ability In the 1780s Laplace pushed forward the first, consisting of Volumes I and II, 20 EMS December 1999 ANNIVERSARIES deals with the methods and formulae nec- essary to determine the different types of motion, while the second is concerned with the application of the formulae to planets, satellites and comets. As Laplace himself declared, he had dual objectives in writing the treatise. First, to provide a connected view of all the existing theories of celestial bodies which derive from the law of gravi- ty, and, second, to improve the precision of astronomical tables. Much of the work is derived from Laplace’s earlier research. In some cases he used almost complete publi- cations, while in others he made revisions to the papers so that they fitted in with his overall schema. He also included exten- sive applications of techniques he had pre- viously developed [5, Chapter 21]. The treatise opens with a mathematical exposition of the general principles of sta- tics and dynamics as applied to material points, systems of bodies and fluids. The law of gravity is deduced from observation, the differential equations of gravitational attraction are derived, and there are dis- cussions of the theory of elliptical motion and of perturbation theory, with specific techniques – such as approximating peri- odic inequalities – illustrated using partic- ular examples. Volume II covers the shape of celestial bodies, and the oscillations of the sea and the atmosphere. It begins with an exami- nation of the attraction of spheroids and includes a comparison of spheroidal attrac- tion theory with the results of geodetic sur- veys of meridional arcs. The latter, which draws on previously unanalysed data from the survey of the terrestrial meridian from Dunkirk to Barcelona (on which the metric system was based), also contains the appli- cation of error theory. Further discussions include the shape of Saturn’s rings, and the shape of the atmosphere of celestial bodies. These are followed by chapters on Jovian satellites, but it also includes short summaries. the ebb and flow of tides, the stability of chapters on the satellites of Saturn and of The early parts of Laplace’s work were equilibrium of the sea, the influence of Uranus, as well as a brief discussion of the rapidly translated into English by several local conditions, and a comparison with theory as applied to comets. The second authors, but these were supplanted by the observation. The volume concludes with part of the volume, which contains mostly masterful translation of the first four vol- an analysis of the rotation of celestial bod- new material and moves into a quite differ- umes by the American mathematician ies, with examples drawn from the earth, ent mode, examines ‘several questions rel- Nathaniel Bowditch (1773-1838). In the moon, and the rings of Saturn. ative to the system of the world’. These recognition of the difficulty of the mathe- In Volume III Laplace deals with both include astronomical and terrestrial refrac- matics, Bowditch provided an extensive planetary and lunar theory with a view to tions, barometric measurements of alti- commentary, including many diagrams, providing a tool for accurate positional tude, and the influence of the earth’s rota- which was of a similar length to the treatise astronomy. In order to obtain the neces- tion on the descent of bodies falling from a itself. He also corrected some calculating sary degree of precision he had to extend great height. errors. An estimate of the remarkably high the methods he had developed in Volume The fifth volume, originally intended to standard of Bowditch’s commentary can be I since these encompassed only those provide a history of the subject together gauged from the fact that Legendre con- inequalities independent of the eccentrici- with an account of the work of his contem- sidered it equivalent to a new edition, and ties or inclinations of the orbits, or those poraries, ended up rather differently. It that requests were made for it to be trans- dependent on the first power of these had been delayed due to Laplace’s change lated into both French and Italian. quantities. Here he carried the approxi- in priorities – probability and physics had Although Bowditch completed his transla- mations to higher powers, and applied to overtaken celestial mechanics in his inter- tion between 1814 and 1817, his insistence all the planets the method he had previ- ests – and by the time he came to publish upon publishing it at his own expense ously used on Saturn in his work on Jupiter the final volume he was in the twilight of meant that it did not appear until several and Saturn. Having derived the formulae, his career and felt unable to carry out the years later (1829-39). He wrote several he then employed the calculator Alexis task he had promised. Instead he took notes on the fifth volume but died before Bouvard to substitute in the values of the recourse in the papers on celestial he was able to complete the translation. elements according to each planet, in mechanics he had published in the early Laplace’s material was also reworked by order to get numerical expressions for 1820s (which consisted mostly of correc- other authors for different audiences, as in each radius vector and its motions in lon- tions and improvements to theory he had the edition that brought Mary Somerville gitude and latitude. previously covered in Volumes I to IV) and to fame, The Mechanism of the Heavens The first part of Volume IV is mostly reconceived Volume V as a unification of (1831). taken up with the theory applied to the these researches accompanied by historical Activity in the rest of the century strong- EMS December 1999 21 ANNIVERSARIES ly reflected the influence of Laplace and it Les Méthodes Nouvelles de la Mécanique the methods of contemporary dynamical was not until the end of the century that a Céleste (1892-99) astronomers – namely, Newcomb, Gyldén, major new development took place. The three volumes of Les Méthodes Lindstedt and Bohlin. Throughout his Nouvelles de la Mécanique Céleste were pub- researches he had become increasingly Henri Poincaré (1854-1912) lished in 1892, 1893 and 1899. When aware of the differences that had evolved Poincaré was awarded his doctorate from George Darwin presented the medal of the between the perceptions of mathemati- cians and of astronomers as to what consti- tuted a solution to a problem in celestial mechanics, and that these differences often led to what appeared to be inconsistent results. In this volume he attempted to clarify the situation and to explain the dis- crepancies. In particular, he forcefully demonstrates the importance of under- standing the nature of the convergence of the different series used in the expressions for the co-ordinates of the planets. Most of the material is completely new, apart from the discussion of the divergence of Lindstedt’s series. In the latter Poincaré reaches fundamentally the same conclu- sion with regard to divergence as he had earlier but, displaying more caution than before, he now casts doubt over the case where the frequencies are chosen in advance. (Almost seventy years later it was shown by Kolmogorov, Arnold and Moser that Poincaré had been right to be guard- Henri Poincaré, 1872 ed about his conclusions.) the University of Paris in 1879, and after a The final volume is characterised by brief appointment at the University of Royal Astronomical Society to Poincaré in Poincaré’s geometrical ideas. Here Caen, returned to the University of Paris 1900, he said, ‘It is probable that for half a Poincaré returned to the subjects of invari- where he remained for the rest of his life. century to come [Les Méthodes Nouvelles] ant integrals, stability, periodic solutions of In 1886 he became Professor of will be the mine from which humbler the second class – periodic solutions that Mathematical Physics and Probability, and investigators will excavate their materials’ make more than one orbit around the pri- in 1889 Professor of Mathematical [4]. With the benefit of hindsight it is pos- mary – and doubly asymptotic solutions. Astronomy and Celestial Mechanics. sible to say that had Darwin omitted the The volume also included a discussion of Almost from the beginning of his acad- word “half”, his prediction would still have what he now called periodic solutions of emic career, Poincaré had been concerned been fulfilled. Nevertheless, although the second species. These are solutions with the fundamental problems of celestial highly acclaimed, Les Méthodes Nouvelles which arise from a system involving two mechanics – in particular the three-body received relatively few reviews, and almost problem and the stability of the solar sys- none engaged critically with the content, tem – and many of the papers he pub- indicating the difficulty of the subject mat- lished during the 1880s relate to his inter- ter. (In recognition of the work’s general est in the subject. These include many of a inaccessibility, Poincaré produced another broad theoretical nature, such as those on three volume set, Leçons de Mécanique the qualitative theory of differential equa- Céleste, which covered similar topics but tions, as well as those in which he respond- which was aimed at a mathematically less ed to explicit questions of dynamical sophisticated audience. The Leçons, which astronomy. were based on lectures given at the In 1890 Poincaré’s celebrated Oscar Sorbonne, appeared between 1905 and prize-winning memoir on the three-body 1910 and is an altogether more practical problem was published, although the story work.) Les Méthodes Nouvelles contain the of its conception and publication had principal ideas from the 1890 memoir but begun some five years earlier [1]. Today in a more fully explained and developed the memoir is famous for providing the form. Further applications of the theory foundations for his Les Méthodes Nouvelles are included besides a substantial amount de la Mécanique Céleste, and for containing of new material, and the focus of attention the first mathematical description of chaos. is more on the general three-body problem The memoir, which is centred on the than on the restricted problem. restricted three-body problem, introduced Volume I covers the analytical part of several new ideas into the study of dynam- the theory with many of the topics dis- ical problems, including the use of varia- cussed in the 1890 memoir revisited, but tional equations and the use of invariant with a greater emphasis on the role of the integrals. But above all the memoir is Hamiltonian form of the equations. There Henri Poincaré dominated by his theory of periodic solu- is an amplified treatment of periodic solu- tions. By taking a reductionist view and tions, with a stronger affirmation of the very small bodies orbiting one large one studying the periodic solutions of a system conjecture about the denseness of the peri- and which narrowly avoid collisions at def- with two degrees of freedom, Poincaré’s odic solutions, and, as in the memoir, inite intervals, the existence of which he global qualitative perspective led him to there are chapters on characteristic expo- had conjectured at the end of the 1890 the brilliant discovery of asymptotic solu- nents, asymptotic solutions and the non- memoir. tions. His analysis of the complex nature existence of new single-valued integrals. Poincaré’s discussion of doubly asymp- of these solutions then resulted in his dis- The one completely new chapter is on the totic solutions contained essentially the covery of homoclinic points and the begin- expansion of the perturbation function. same analysis as the memoir but with one nings of the mathematical theory of chaos. In Volume II Poincaré concentrated on important addition. In the memoir 22 EMS December 1999 ANNIVERSARIES Poincaré had shown that corresponding to are techniques and results that people 5. C. G. Gillispie, Pierre-Simon Laplace 1749- each unstable periodic solution there was a wanted to use and indeed Laplace expect- 1827. A Life in Exact Science, Princeton, system of asymptotic solutions. However, ed them to use – and it was clearly a tool 1997. he had only considered the possibility of for further research. Poincaré’s work on 6. D. L. Goroff, ‘Henri Poincaré and chaos the- doubly asymptotic solutions arising from the other hand was deeply theoretical and ory: An introduction to the English transla- different families of asymptotic solutions fiercely difficult, and while it contained tion of Les Méthodes Nouvelles de la Mécanique associated with the same unstable periodic mathematical techniques of great interest Céleste’, New Methods of Celestial Mechanics solutions. These are what he called homo- to mathematicians, the inability of by Henri Poincaré, American Institute of clinic solutions. Now he proposed that a researchers to engage in a quantitative Physics, 1993. doubly asymptotic solution of a different analysis due to inadequate computing 7. R. Grant, History of Physical Astronomy, type could arise from asymptotic solutions techniques meant that it had only spe- London, 1852. associated with two different unstable peri- cialised appeal. The demand for transla- 8. P.-S. Laplace, Traité de Mécanique Céleste, 5 odic solutions, and these he called hetero- tion was generated when, with improved vols., Paris, 1799-1825; translated by N. clinic solutions. In both cases he showed computing power and the stimulus of a Bowditch, Boston, 1829-39. that the existence of one of these solutions developing space programme, Poincaré’s 9. H. Poincaré, Les Méthodes Nouvelles de la is sufficient to prove the existence of an methods could actually be applied. More Mécanique Céleste, 3 vols., Paris, 1892-99; infinite number, and, in contrast to the recently, with the advent of the modern translated by the American Institute of memoir, he is absolutely explicit about digital computer and the explosion of Physics, 1993. their bewildering complexity. research into non-linear systems resulting 10.H. Poincaré, ‘Sur le problème des trois corps in the unfolding of the mathematical theo- et les équations de la dynamique’, Acta The difference a century makes ry of chaos, interest in Poincaré’s work has Mathematica 13 (1890), 1-270. Although the aims of the two authors were intensified and in 1993 a second transla- fundamentally the same – to determine tion was published [6]. June Barrow-Green [j.e.barrow-green@open. whether Newton’s law of gravity explains Both Laplace’s Traité de Mécanique ac.uk] is a research fellow in the history of math- all astronomical phenomena – their Céleste and Poincaré’s Les Méthodes ematics at the Open University, UK. methodologies were palpably different. Nouvelles de la Mécanique Céleste opened a Laplace developed the theory and then, new era in the study of celestial mechanics. combining observation and calculation, Each work stands as a testament to the Otto Neugebauer demonstrated its usefulness, while genius of its author. Poincaré did not Poincaré, mindful of the shortcomings of supersede Laplace, he launched out in a (b. 1899) both observation and calculation, focused different direction. In the words of Gaston almost entirely on the theoretical develop- Darboux, each merits a place alongside the Jeremy Gray ment. Nevertheless there are similarities other [2]. between the two treatises. They both owe Bibliography Otto Neugebauer was one of the few great their genesis to an abiding interest in the 1. J. Barrow-Green, Poincaré and the Three Body historians of mathematics there has ever problem of the stability of the solar system. Problem, American Mathematical Society, been. Born in Innsbruck, Austria, on 26 They both rely heavily on previously pub- Providence, 1997. May 1899, he was attracted to mathematics lished work and both are showcases for 2. G. Darboux, ‘Éloge Historique d’Henri at school but joined the Austrian Army in exciting results: Laplace’s discovery of the Poincaré’ Mémoires de l’Académie des Sciences de 1917 in order to be excused the school long period inequality of Jupiter and l’Institut de France 52 (CXX-CXXI), 1914. leaving examination in Greek, which he Saturn, and Poincaré’s discovery of homo- 3. G. H. Darwin, ‘Periodic orbits’, Acta claimed he had no chance of passing. He clinic point to name but two. Both works Mathematica 21 (1897), 99-242. was taken prisoner at the armistice and are extremely mathematical and virtually 4. G. H. Darwin, ‘Presentation of the medal of spent almost a year in a prisoner of war impossible for all but the specialist to the Royal Astronomical Society to M. Henri camp; Ludwig Wittgenstein was a fellow assimilate, but in each case the author did Poincaré’, Monthly Notices of the Royal prisoner. provide a simplified counterpart: Laplace Astronomical Society 60 (1900), 406-415. By 1922 he had made his way to with the Systéme du Monde and Poincaré with the Leçons de Mécanique Céleste. Both treatises are characterised by a conspicu- ous lack of diagrams. Laplace, who did not include any, assumed his audience suffi- ciently well versed in analysis not to need them. Poincaré, who included a few, relied little on pictorial representation himself – he was renowned for his inability to draw – and was probably oblivious to the needs of others not blessed with his gift of geomet- ric visualisation. Another way in which the two works dif- fer is in the speed and type of response they received with respect to translation. Poincaré’s treatise, unlike that of Laplace, did not receive immediate attention. The first English translation of Méthodes Nouvelles, which was published in 1967 by NASA, appeared more than sixty years after the original and contained little by way of commentary. The different rates of response with respect to translation reflect the perceived utility of the two works. Laplace’s treatise is not a homogeneous whole but rather ‘a textbook, a collection of research papers, a reference book, and an almanac’ [5, p.184] rolled into one. It This Babylonian tablet, described by Neugebauer, illustrates a knowledge of Pythagorean triples has an obvious practical dimension – there 1000 years before Pythagoras. EMS December 1999 23 ANNIVERSARIES Göttingen, where he struck up life-long versities. Neugebauer published profuse- his name to Oscar Zariski, when they came friendships with Richard Courant, Harald ly, and much of our knowledge of ancient to prepare their first joint paper for publi- Bohr, and the Russian mathematician astronomy and chronology is due to him. cation. It was also in Rome that Zariski Alexandroff. His only publication in pure He received numerous honours and was met Yole Cagli. He married her on a visit mathematics is a joint paper with Bohr on elected to many learned societies, but it to his home town of Kobrin in September almost periodic functions. Bohr had may be supposed that his greatest pleasure 1924. already asked him to review T. E. Peet’s was in entirely reshaping and extending When the Fascists took power in Italy new edition of the Rhind papyrus, know- our knowledge of the history of science. life became increasingly difficult for Jews, ing that Neugebauer had embarked on a Indeed, the message that Babylonians and with Lefschetz’s help Zariski obtained serious study of Egyptian; his Göttingen knew more (and, as he impishly insisted, a postgraduate fellowship at Johns dissertation, on the vexed topic of the Egyptians knew less) than most people Hopkins University. Lefschetz’s work in Egyptian unit fractions, was conducted believe still needs amplification today. topology was just one sign that Zariski was with the approval of Courant and Hilbert. The high level of scholarship that now pre- moving beyond his Italian mentors: In 1927 he began lecturing on ancient vails in the subject gives every prospect Castelnuovo once said to him ‘You are mathematics, and it was these lectures that that received opinion will change, and that here with us but you are not one of us’, brought van der Waerden to the subject. high level is largely due to the standards referring to his algebraic inclinations and In 1927 Neugebauer began to learn he set himself, his organisational skills, and his insistence on rigour. In 1935 Zariski Akkadian, the language of Babylonian the support he was able to attract. was to write an account that satisfied him of mathematics, and embarked on his great- the algebraic theory of surfaces, which est contribution to the history of mathe- Castelnuovo and Enriques had done so matics. Whereas Egyptian sources were much to start, but, as he put it, ‘The price well known and often well studied, Oscar Zariski (b. 1899) was my own personal loss of the geometric Babylonian sources hidden away in numer- paradise in which I had so happily been ous museums were seldom read and stan- Jeremy Gray living’. dards were very low. Neugebauer was to By then Zariski had become a professor publish his 3-volume collection on mathe- Ascher Zaritsky was born in Kobrin in at Johns Hopkins, and in 1937 he became matical tablets in the mid-1930s. They White Russia on 24 April 1899, the sixth a full professor. He embarked on a pro- established the great richness of child of Bezalel and Hannah Zaritsky, and gramme of adapting and creating concepts Babylonian mathematics, far exceeding spent his first eleven years there. His in commutative ring theory to formulate anything one could have guessed from resourceful mother was able to afford a and solve problems in algebraic geometry. Greek or Egyptian sources. The ramifica- tutor for him in Russian and arithmetic He introduced the integral closure of a tions of this discovery continue to animate from the age of seven. Oscar learned these ring in 1937 and in 1939 applied it to the the study of ancient mathematics to this subjects quickly and they proved his pass- resolution of singular points on curves and day, and as Neugebauer’s own estimation port out of the Pale. The family fled the surfaces. It was also in this context that he of Babylonian mathematics and astronomy war to Chernigov in Ukraine, and Oscar introduced the topology on an algebraic continued to deepen he refused any longer returned briefly in 1918 before enrolling variety that now bears his name: the Zariski to consider them as ‘pre-Greek’; indeed he in the philosophy department at the topology. He did this in 1944 to facilitate found their level of mathematical abstrac- University of Kiev in 1921 (there was no the study of what he called at the time the tion and power exceeded Ptolemy’s. room in the mathematics faculty). Political Riemann surface associated to a field, and Neugebauer was also active in the upheaval eventually soon him to Rome, by then he was thoroughly committed to design of the new Mathematics Institute at where he enrolled under Castelnuovo and developing algebraic geometry over arbi- Göttingen, completed with money from trary fields. the Rockefeller Foundation in 1929. He In 1945 Zariski was in Sao Paolo for a was the driving force behind the creation year. His duties included giving one lec- of Zentralblatt für Mathematik und ihre ture course of three hours a week; his audi- Grenzgebiete, which came out for the first ence consisted of one student, André Weil. time in 1931. When the Nazis came to They had already met at the Institute for power students attacked him for being Advanced Study in Princeton in 1937 and politically unreliable (he was very liberal in in Harvard in 1941, and the year they his views) and he refused to sign the loyal- spent together was a stimulating one for ty oath. Bohr was able to arrange for each of them, despite, or perhaps because Neugebauer to move to Copenhagen in of, their often heated disagreements. January 1934 on a three-year appoint- In 1947 Zariski made his final move, to ment, and he was able to bring Zentralblatt Harvard, where he was to stay for the rest with him. He fought a long struggle to of his life and greatly influence the protect the journal from the Nazis and progress of algebraic geometry. Among their supporters, Blaschke in particular, his students there were Michael Artin, and eventually resigned as part of an Robin Hartshorne, Heisuke Hironaka, organised protest at the dismissal of Levi- Steven Kleiman, and David Mumford. Civita from the editorial board. Zariski’s high standards and ambition for In 1939 Neugebauer sailed to America, the subject, coupled with his urge to gen- where Brown University was offering him a eralise beyond the familiar complex case, professorship, and threw himself into the were instrumental in bringing creation of Mathematical Reviews. The first Grothendieck’s new vision of algebraic edition appeared on time in January 1940, geometry to America, a transition in which and Neugebauer is recognised as the all of his students played major roles. He founding editor (as he is of Zentralblatt, as stayed on at Harvard for five years after the revived journal proudly says). At the usual retirement age, becoming a pro- Brown he built up what became the lead- Oscar Zariski fessor emeritus in 1969, but in the late ing institution in the world for the study of 1970s his health began to fail and the history of the exact sciences, especially the more sociable Enriques. They were Alzheimer’s disease was eventually diag- of the ancient world. It was a magnet for among the great figures of algebraic geom- nosed. He died on 4 July 1986. scholars around the world, and capable of etry and this was the subject that Zariski drawing people in, despite the narrow- was to work on more than any other. It was Jeremy Gray [[email protected]] is a senior minded traditionalism of their home uni- Enriques who suggested that he Italianise lecturer at the Open University, UK. 24 EMS December 1999 NEWS Jose-Francisco Rodrigues (Lisbon) [rod [email protected]] (3 lectures (90 minutes) in English for each course) C.I.M.E.C.I.M.E. Distance function and evolution of fronts by implicit time discretisation SummerSummer CoursesCourses 20002000 Luigi Ambrosio, Pisa Numerical approximation of mean curvature flow of graphs G.Dziuk, Freiburg The Fondazione CIME will hold five cours- Course 1: Dynamical Systems, Cetraro Dynamics of patterns and interfaces in reaction- es in 2000: two courses will be held at (Cosenza), 19–26 June diffusion systems from chemical and biological Martina Franca (Taranto, Italy), two will be viewpoints. held at Cetraro (Cosenza, Italy), and one Jack Macki (Alberta) Masayasu Mimura, Hiroshima will be held at Funchal (Portugal), jointly Pietro Zecca (Florence) [pzecca@ingfi1. Evolution free boundary problem for parabolic organised by CIME and CIM (Centro ing.unifi.it] and Navier-Stokes equations Internacional de Matematica, Portugal). Stability and entropy in spatially discrete V. A. Solonnikov, St Petersburg Brief information concerning these dynamical systems (6 lectures in English) Variational and dynamic Problems for the courses is presented below. Further infor- Shui-Nee Chow, Singapore Ginzburg-Land Functional. mation can be found on the Web server of Planar dynamical systems (3 lectures in H. M. Soner, Princeton the CIME, English) http: //www.math.unifi.it/CIME Roberto Conti, Florence Course 4: Mathematical Methods for If you are interested, please contact: Non-autonomous dynamical systems (6 lectures Protein Structures Analysis and Design, Fondazione C.I.M.E. c/o Dipartimento di in English) Martina Franca (Taranto), 9 – 15 July Matematica ‘U. Dini’, Viale Morgagni, 67, Russell Johnson, Florence Scientific Direction: A-50134 Firenze, Italy Waves in spatially discrete dynamical systems (6 Concettina Guerra (Padua) [guerra@dei. tel: (+39)-55-434975 / (+39)-55-4237123 lectures in English) unipd.it] fax: (+39)-55-434975 / (+39)-55-4222695 John Mallet Paret, Providence Sorin Istrail (Sandia) [[email protected]. e-mail: [email protected] Recent trends in the theory of non-linear delay sandia.gov] Director: Prof. Arrigo Cellina equations (6 lectures in English) (4 lectures in English for each course) [[email protected]] Roger Nussbaum, Rutgers Mathematical protein Structure Analysis. Secretary: Prof. Vincenzo Vespri Arthur Lesk, Cambridge [[email protected]] Course 2: Diophantine Approximation, (Title to be announced) If you wish to attend, you should send Cetraro (Cosenza), 28 June – 6 July Michael Levitt, Stanford an application to the C.I.M.E Foundation Scientific Direction: High Speed Computations for the Design of at the address above, one month before the Francesco Amoroso (Caen) [amoroso@ Proteins. beginning of each course (not later than 20 math.unicaen.fr] John Moult, Maryland July for courses starting in September). In Umberto Zannier (Venice) [zannier@brez Geometric Computing in Structural Molecular the application your field of current za.iuav.unive.it] Biology. research must be specified. (6 lectures in English for each course) Haim Wolfson, Tel Aviv An important consideration in the Diophantine Approximation on Commutative acceptance of applications is the scientific Groups Varieties Course 5: Noncommutative Geometry, relevance of the Session to the field of David Masser, Basel Martina Franca (Taranto), 3–10 interest of the applicant. Participation will The Absolute Subspace Theorem September be allowed only to persons who have Hans Peter Schlikewei, Marpurg Scientific Direction: applied in due time and have had their Zeros of linear recurrence sequences Sergio Doplicher (Rome) [dopliche@mat. application accepted. CIME will be able Wolfgang Schmidt, Colorado uniroma1.it] partially to support some of the youngest Linear Independence measures for Logarithms Roberto Longo (Rome) [[email protected] participants. Those who plan to apply for of algebraic numbers roma2.it] support must mention this explicitly in the Michel Waldschmidt, Paris (6 lectures in English for each course) application form. Noncommutative Geometry Course 3: Mathematical Aspects of Alain Connes, Paris Sites and Lodging Evolving Interfaces, Funchal (Portugal), K-Theory and Cyclic Cohomology Martina Franca is a charming, beautifully 3 – 9 July Joachim Cuntz, Munster preserved ancient city on the hills of Puglia Organised by CIME and CIM (Centro Group C*-algebras and K-Theory (South Italy), an architectural jewel. Internacional de Matematica, Portugal) Nigel Higson, Pennsylvania Participants are lodged at the Park Hotel Scientific Direction: The Algebraic Approach to Quantum Field S. Michele, a nice hotel with a well-kept Pierluigi Colli (Pavia)[[email protected]. Theory. garden and a large swimming pool. The pv.cnr.it] John E. Roberts, Rome Lectures will be at the Palazzo Ducale (City Hall), within short walking distance, at the Sala Arcadia. Cetraro is a beatiful location on the Tirrenian coast of Calabria (South Italy). The nearest train station is Paola on Journal of the European Mathematical Society (JEMS) the line Roma-Salerno-Reggio-Calabria, easily reached even by fast trains (Eurostar The contents list of the fourth issue of the JEMS is as follows: trains stop in Paola). CIME activities are made possible Volume 1, Number 4 thanks to the generous support received Edson de Faria and Welington de Melo, Rigidity of critical circle from The European Commission, Division mappings I XII, TMR Programme ‘Summer Schools’; Consiglio Nazionale delle Ricerche; Stefan Müller and Vladimir Sverák, Convex integration with con- Ministero dell’ Università e della Ricerca straints and applications to phase transitions and partial differential Scientifica e Tecnologica; UNESCO- equations ROSTE, Venice Office. EMS December 1999 25 SOCIETIES Societies Corner

Societies corner is a column concerning the mention: ‘Mathematics and Reality’ Fichera, I. Gelfand, M. Guillaume, W. K. mathematical societies in European countries. (1974), ‘Mathematical Language and Hayman, C. Houzel, A. Lichnerowicz, L. The articles in this column could describe the Mathematical Thought’ (1976), and Nirenberg and W. Schwarz (see picture); history of a particular society or discuss some ‘Poincaré’s Philosophy of Science’ (1986). – ‘Developments in mathematics at the event connected with the society. If you feel that The speakers have included J. Dieudonné eve of 2000’, at Centre universitaire de your society would interest others, please contact and R. Thom. Luxembourg in 1998; foreign speakers the column editor, Krzysztof Ciesielski (e-mail: A regular congress of GMEL were J. P. Bourguignon, C. Houzel, V. [email protected]) in the first instance. (Groupement des Mathématiciens Kac, J.-P. Kahane, J. Mawhin, N. Nikolskii, d’Expression Latine) was held in R. Penrose and R. Remmert. Luxembourg in 1981. It involved mainly At the end of 1997 UNESCO unani- Luxembourg mathematicians from neo-Latin speaking mously adopted a motion introduced by countries (French, Spanish, Italian, Luxembourg, declaring its sponsorship for Mathematical Portuguese and Romanian). The SML is WMY2000 (draft resolution 29C/DR126). much concerned with cooperation in the A new motion has recently been proposed Society ‘Grande Région’ centred in Luxembourg, by Luxembourg, asking UNESCO to Jean-Paul Pier and regional meetings have included increase its support for mathematical pro- Université de Liège, Centre universitaire jects during WMY2000. In Luxembourg organised mathematical de Luxembourg, Université de Metz, Jean-Paul Pier is President of the Société activities, other than pedagogical ones, FUNDP Namur, Université Henri Mathématique de Luxembourg. started around 1970, under the name of Poincaré Nancy, Universität des ‘Séminaire de Mathématique de Saarlandes and Universität Trier. Luxembourg’. In 1988, the members of Specialised symposia have also taken Kharkov that group created the Société place, such as ‘Harmonic Analysis’ (1987), Mathématique du Luxembourg (SML), with the participation of G. Mackey Mathematical which became a founding member of the (Springer Lecture Notes 1359). Besides European Mathematical Society. the publication of symposia proceedings, Society Currently the Luxembourg Mathematical the SML has for ten years edited a yearly I. V. Ostrovskii Society has 35 members, of whom 21 issue of ‘Travaux mathématiques’, which belong to the EMS. The regular activities should now be expanded further. In this note, we give a short history and of the SML consist of weekly seminars. In the context of World Mathematical some general information on the Kharkov The topics vary, but usually relate to har- Year 2000 (WMY2000), the SML has given Mathematical Society (KMS) and the math- monic analysis or differential geometry. much consideration to understanding the ematicians who have played an important The SML endeavours to popularise evolution of mathematical ideas during the role in its activities. mathematics in a small country, and from now-ending century. Two symposia have The KMS was founded in 1879 on the time to time organises conferences for the already been organised: initiative of V. G. Imshenetskii (1832-92). general public. Among the symposia on – ‘The Development of mathematics He was a professor at Kharkov University general mathematical subjects, each 1900-1950’, at Bourglinster Castle in 1992; and worked in partial differential equa- attended by about one hundred people, we foreign speakers were J. L. Doob, G. tions. According to the Charter of the

26 EMS December 1999 SOCIETIES KMS, ‘the goal of the mathematical society From 1908 to 1933, S. N. Bernstein Levin (1906-93), B. M. Levitan (b. 1914), is support of development of pure scientif- (1880-1968), one of the leading mathe- M. S. Livshic (b. 1917), V. A. Marchenko ic and pedagogical questions in the field of maticians of the 20th century, worked in (b. 1922), A. D. Myshkis (b. 1920), A. Ya. mathematics’. Meetings with scientific Kharkov. Scientific activity, and all other Povzner (b. 1915), A. V. Pogorelov (b. reports were held monthly, as a rule. kinds of KMS activity, were under his 1919), A. K. Sushkevich (1889-1961) and Starting from 1880, the KMS has pub- strong influence during these years. Many E. M. Zhmud’ (b. 1918). lished Communications of KMS, first as a of his famous results were first reported at In 1950, the Institute of Mathematics in supplement to the Transactions of KMS meetings and then published in the Kharkov was closed by a decision of the Kharkov University, and then as a separate Communications of KMS. Among his stu- Soviet Government. Conditions for scien- journal. dents were V. L. Goncharov (1896-1955) tific work started to deteriorate. In this In 1885, A. M. Lyapunov (1857-1918), a and Ya. L. Geronimus (1898-1984), both of connection, an important event was the former student of P. L. Chebyshev, moved whom became well-known mathemati- foundation in Kharkov, in 1960, of the from St Petersburg to Kharkov and played cians. After 1917, S. N. Bernstein used his Institute for Low Temperature Physics and a leading role in the KMS. During his years great international reputation to maintain Engineering (ILTPE). The founder and in Kharkov (1885-1902) Lyapunov carried and promote further development of first Director of the Institute was the physi- out research in stability theory, potential mathematics in Kharkov. In 1929, he cist B. I. Verkin (1919-91). A broad-mind- theory and probability theory, gaining him organised the Institute of Mathematics at ed person with great respect for pure a world-wide reputation. He gave 27 Kharkov which provided an opportunity mathematics, he invited the leading reports on this work at the meetings of the for scientific research for many mathemati- Kharkov mathematicians, Akhiezer, KMS. Because of Lyapunov, mathematical cians. Due to Bernstein’s world-wide repu- Glazman, Levin, Marchenko, Myshkis and research and reports at KMS meetings tation, the First All-Union Mathematical reached a much deeper level. In the next Congress took place in 1930 at Kharkov period (1902-06), the chairman of KMS (rather than in the capital of the USSR, as was V. A. Steklov (1863-1926), a former one would expect according to the tradi- student of Lyapunov. Steklov is well tions of that time). A number of mathe- known for his work in mathematical maticians from the West participated in A Russian postage physics and analysis, and also as one of the this Congress, among them being stamp featuring organisers of scientific research in the Hadamard, Denjoy and Montel. A. M. Lyapunov. Soviet Union. In particular, he founded Soon, after a conflict with the Kharkov the Institute of Mathematics in Moscow Communist party leaders, Bernstein had named after him. to leave Kharkov. But before doing so, he During the forty-year period 1906-46, invited N. I. Akhiezer (1901-80) to move to the chairman of KMS was D. M. Sintsov Kharkov. In 1933, Akhiezer became the (1876-1946), who worked in geometry and Director of the Institute of Mathematics, Pogorelov, to join the Institute with a in the geometrical theory of Pfaff and and in 1947, the chairman of the KMS. group of their former students and to con- Monge equations. Sintsov was an active Akhiezer’s work on approximation theory, tinue their mathematical research in the participant of the movement for the the moment problem and operator theory Institute. The scientific activity of Levin, reform of school education in mathemat- are well known today. His books on these Marchenko, Myshkis and Pogorelov led to ics, and worked on the international com- and other topics are outstanding pieces of the further flourishing of mathematical mittee for the promotion of these reforms, mathematical literature. Akhiezer man- studies in Kharkov which lasted till the headed by F. Klein. Through Sintsov’s ini- aged to create a strong mathematical com- beginning of the 1990s. An important tiative, the KMS was deeply involved in the munity in Kharkov. We mention here a few honour for the KMS was when V. G. improvement of mathematical education names that should be of interest today to Drinfeld (b. 1954), a member of the in the schools of the Kharkov region. specialists in related fields: Ya. P. Blank Mathematical Division of ILTPE, was Sintsov also put considerable effort into (1903-87), A. M. Danilevskii (1906-41), G. awarded a Fields Medal in 1990. maintaining the KMS mathematical library I. Drinfeld (b. 1908), A. M. Efros (1906- Until 1992, the KMS usually held which is still one of the most complete 41), I. M. Glazman (1916-68), M. I. Kadets monthly scientific meetings with talks by mathematical libraries in the Ukraine. (b. 1923), N. S. Landkof (b. 1915), B. Ya. Kharkov mathematicians and others from all over the Soviet Union. Publication of Communications of KMS was stopped in the 1960s by officials, in spite of the energetic protests of N. I. Akhiezer. However, he succeeded in starting a new journal, Function theory, functional analysis and their applications, which was published till 1992. From 1994 to 1999, the KMS participated in the publication of the journal Mathematical Physics, Analysis and Geometry, and in 2000 a new journal, Mathematical Analysis and Geometry, will be published. After the break-up of the Soviet Union and the cut-off of finance for scientific research, many Kharkov mathematicians have found positions abroad. Certainly, this has caused serious damage to the work of the KMS. Nevertheless, the KMS con- tinues to hold scientific meetings and to supplement its mathematical library with new mathematical literature. The KMS also participates in the distribution of urgent support that comes from other mathematical societies to the Kharkov mathematicians. I. V. Ostrovskii is Chairman of the Kharkov The four Fields Medalists in 1990, V. G. Drinfield is on the right. Mathematical Society. EMS December 1999 27 NEWS EMS-EMS-WWiRiR SummerSummer SchoolSchool Numerical Simulation of Flows 6 - 21 September 1999 Rolf Jeltsch

Sixty mathematicians, computer scientists, lations is so great that a realistic descrip- methods were presented by Prof. physicists and engineers from twelve coun- tion requires sophisticated mathematical Rannacher and Prof. Kroener. tries took part in the EMS-WiR Summer methods and models. In particular, the Further topics were interface flows, low School, Numerical Simulation of Flows, held modelling and simulation of turbulent mach number flows, conjugate gradient in September 1999 at the chair of flows, as well as nearly incompressible and other Lanczos-type methods for large Technical Simulation, IWR, of the flows, are challenging problems for mathe- linear systems, multi-grid methods, and University of Heidelberg, Germany. The matical models and numerical methods. algebraic multi-level methods. Dr. Bastian summer school was organised in coopera- The numerical simulation of flows requires gave an overview on software concepts and tion with the European Mathematical the co-operation of several mathematical tools suited to the solution of flow prob- Society (EMS), the research association disciplines such as analysis, numerics, lems. Further lectures on grid generation WiR Ba-Wu (Wissenschaftliches Rechnen mathematical physics, and computational and methods for the visualisation of flows Baden-Wurttemberg), ESF-AMIF (Euro- science. were presented. An evening reception at pean Science Foundation – Applied The programme comprised a theoreti- the chair of Technical Simulation, IWR, Mathematics for Industrial Flow cal and a practical part. The first week (in and an excursion to Heidelberg Castle and Problems), and SFB 359 (Reactive Flow, Heidelberg) consisted of basic instruction. the Königstuhl in bright seasonable weath- Diffusion and Transport) of Heidelberg During this week mathematical models er completed the first week. University. The members of the EMS-WiR and methods were presented in lectures by During the second week the partici- Summer School Scientific Committee were specialists. In particular, Prof. Yserentant pants worked on different flow problems Dr. P. Bastian (Heidelberg), Prof. G. Dziuk presented a survey of the mathematical formulated by the lecturers in different (Freiburg), Prof. W. Hackbusch (Leipzig), description of flows and Prof. Jeltsch gave places (Heidelberg, Freiburg, Stuttgart Prof. R. Jeltsch (Zurich), Prof. D. Kroener a talk on the modelling of compressible and Zurich). Finally the results of the (Freiburg), Prof. C.-D. Munz (Stuttgart), flows and the method of transport for sim- practical work were presented in a plenary Prof. R. Rannacher (Heidelberg), Prof. W. ulation. The lectures by Prof. Kinzelbach meeting in Heidelberg. The summer Rodi (Karlsruhe), Prof. S. Sauter (Zurich), and Prof. Helmig, focused on the model- school ended with a dinner in a restaurant Prof. S. Wagner (Stuttgart), Prof. G. ling of groundwater flows and transport, in Heidelberg. The financial support of Wittum (Heidelberg) and Prof. H. and the theoretical basis of multi-phase European Mathematical Society (EMS), Yserentant (Tubingen). flows in porous media. Prof. Wagner pre- ESF-AMIF (European Science Foundation The numerical simulation of flows is sented a survey on turbulent flows. Prof. – Applied Mathematics for Industrial Flow one of the central problems in scientific Quarteroni spoke on flows in biosystems. Problems) and SFB 359 of Heidelberg computing. The complexity of flow simu- Surveys of finite element and finite volume University is gratefully acknowledged.

European Mathematical Society European Mathematical Society Summer School Summer School 24 July – 2 August 2000 17 August – 3 September 2000 Edinburgh, Scotland St Flour, Cantal, France Probability Theory New Analytic and Geometric Methods in inverse problems LECTURERS and TOPICS LECTURERS and TOPICS Sergio Albeverio – Dirichlet forms and infinite Dima Burago – Topics in Riemannian geometry Gilles Lebeau – Carleman estimates and boundary control of dimensional processes differential equations Walter Schachermayer – Mathematical Finance Vladimir Sharafutinov – Topics in intergral geometry Michel Talagrand – Spin Glasses Gunter Uhlmann – Anisotropic inverse geometry Anders Melin – Intertwining operator methods and inverse scatterring REGISTRATION Alexander Katchalov & Matti Lassas – Boundary control Deadline – 15 April 2000 methods for Gel’fand inverse problem Contact – Danièlle Courageot, St Flour Summer Lassi Päiärinta – Analytic techniques in inverse scattering School on “Probability Theory”, Laboratoire de REGISTRATION Mathématiques Appliquées, Les Cézeaux, Deadline – 15 May 2000 F–63177 Aubiere Contact – Erkki Somersalo, Summer School Edinburgh 2000, Helsinki University of Technology. Fax: +33-4 73 40 70 64 Fax: +358-94 51 30 16 www.math.hut.fi/projects/inverse wwwlma.univ-bpclermont.fr/stflour

28 EMS December 1999 EDUCATION Education Section Reference levels in school education in mathematics A project of the EMS

Antoine Bodin (Besancon) and Vinicio Villani (Pisa)

Presentation – those who plan to enrol in a scientific fac- define one reference level, relative to the The differing structure of school systems in ulty. appropriate field. various European countries presents A possible structure of the study, includ- Until now, priority has been given to remarkable heterogeneity, but also note- ing its main goals is illustrated in the figure aspect 1, since aspect 2 should be seen in worthy similarities, concerning the overall below. the light of the outcomes of aspect 1. The goals for the education of young genera- working team plans to consider aspect 2 tions. What is it about? during the second year of the project. With the increasing mobility of students A first task of the working team has been to To help gathering, selecting, dissemi- and workers at all levels throughout specify and delimit the meaning of ‘refer- nating (and where appropriate, translat- Europe, it is urgent to identify common ence levels’. ing) relevant background information, a reference levels concerning general abili- Two main aspects have been identified: resource centre devoted to Mathematics ties, as well as knowledge of specific topics 1. References concerning the general mathemat- Curriculum and Evaluation (both exami- related to specific age groups. ical curriculum nations and large-scale assessments) in Regarding mathematics, more than a As a starting point the working team is col- Europe, as well as in other places (U.S.A., year ago the European Mathematical lecting ‘national references’, general infor- Japan), is currently being developed at the Society promoted an international study mation about mathematics education in all Institute of Mathematical Research and involving all E.C. countries and some countries involved, along with specific Education (IREM) in the Mathematics selected non-E.C. countries. The questions to be asked at country level. The Department of the University of Franche- Education Committee of the EMS has ‘European reference’ will be a synthesis Compté in France. For the moment, the agreed to take responsibility in the study. from these national references. Centre focuses mainly on ages 14-16, to A first two-year project, concerning the 16- 2. References concerning students’ abilities and keep with the reference levels project, but year-old age group has been submitted to knowledge it is planned to extend its scope up to the the E.C., under the Socrates programme. These ‘references’ will consist of state- first university years. It has been accepted and was funded for ments concerning the students’ mathemat- 1999. Besides the E.C. countries, the fol- ical behaviour and in samples of tasks that What is peculiar about this project? lowing non-E.C. countries are involved: can be submitted to 16-year-old students. Several international large-scale studies the Czech Republic, Hungary, Poland, Some of these statements and tasks may have been already performed in the past Russia and Switzerland. concern students’ achievement, either (IEA, TIMSS). They provide us with useful In future, other age groups may also be observed or expected. They will obviously information about curricula and achieve- considered. The choice to start with the vary across countries, and according to the ment, although not specifically mirrored at 16-year age group is because this age coin- different aims of mathematics education, age 16. Meanwhile, it is well acknowl- cides, at least de facto, with the end of full- as highlighted in the national curriculum edged that those studies were largely dri- time compulsory education in most E.C. reference levels. ven by governments and psychometricians, Countries. We do not claim that the whole set of and that their influence on the mathemat- However, already at age 16, three dis- statements and tasks can (or should) be ical community has been dramatically low. tinct sub-populations must be considered: ranked in order. It seems more meaning- In addition, those studies have not ade- – those who are going to quit school ful to organise specific subsets, giving rise quately taken into account the specific – those who will use mathematics mainly as to several distinct ‘reference scales’; each needs and sensitivities of European coun- a tool statement from a reference scale will tries. Moreover, any information concerning educational systems rapidly becomes obso- lescent. Part of the information released today already belong to history! Our project will have to cope with the same problem. We are thus already plan- ning to put on track a continuous updating of the outcomes of our study, via an inter- active involvement of the mathematical community at large, through the EMS web- site. We plan to present a preliminary report on the project at the EMS Congress in Barcelona in July. Antoine Bodin is at the Institute of Mathematical Research and Education (IREM) at the Université de Franche-Compté in Besancon, France. Vinicio Villani is in the Department of Mathematics at the Università di Pisa, Italy.

Position of the study Editor’s note: We regret that the Problem Width of the arrows relate to the relative importance as seen at 16. Corner, due for publication in this issue, This relative importance would not be the same if the age were 14, 18 or 20. has had to be held over to the March issue. EMS December 1999 29 CONFERENCES 11-12: School Mathematics 2000, Helsinki, Finland Information: FForthcomingorthcoming conferconferencesences e-mail: [email protected]

13-16: Geometry and Applications, compiled by Novosibirsk, Russia Kathleen Quinn [on the 70th anniversary of the birthday of Victor Andreevich Toponogov] Topics: geometry, geometrical questions of Please e-mail announcements of European conferences, on Hyperbolic Problems, Magdeburg, Germany analysis (including differential equations), topol- workshops and mathematical meetings of interest to Information: contact HYP-2000 c/o Institut für ogy, applications (mathematical methods of EMS members, to [email protected]. Announce- Analysis und Numerik, Otto-von-Guericke- chemistry in particular) ments should be written in a style similar to those below, Universität, Magdeburg, PSF 4120, D-39016 Organisers: The Sobolev Institute of and sent as Microsoft Word files or as text files (but not Magdeburg, Germany; fax: HYP-2000 at +49- Mathematics of the Siberian Branch of the as TeX input files). Space permitting, each announce- 391-67-18073 Russian Academy of Sciences, Novosibirsk State ment will appear in detail in the next issue of the e-mail: [email protected] University Newsletter to go to press, and thereafter will be briefly Web site: http://rubens.math.uni-magdeburg. Programme committee: Yu. G. Rushetnyak noted in each new issue until the meeting takes place, de/~hyp2000 (chair) (Novosibirsk), A. A. Borisenko (Kharkov), with a reference to the issue in which the detailed [For details, see EMS Newsletter 33] Yu. D. Burago (St Petersburg), V. M. Goldshtein announcement appeared. March 2000 (Beer-Sheva), M. L. Gromov (Paris), I. G. January 2000 Nikolaev (Urbana-Champaign), S. P. Novikov 6-10: International Conference on Differential (Maryland) 5-8: Non-Fermi Liquid Effects in Metallic Geometry and Quantum Physics, Berlin, Information: Systems with Strong Electronic Correlation, Germany e-mail: [email protected] Cambridge, UK Scope: this will reflect a good part of the Information: research activities of SFB 288 (see below). The 27-31: ICMS Instructional Course: Quantum Web site: http://www.newton.cam.ac.uk/programs/ conference is centred around the interests of Computing, Edinburgh, UK scew01.html Dirk Ferus, Ruedi Seiler and Robert Schrader, to Theme: in the past five years the new subject of honour their contribution to the SFB and to sci- quantum computing has emerged; this offers the 7-9: 2nd Mediterranean Conference on ence in general, on the occasion of their sixtieth potential of immense practical computing power Mathematics Education, Nicosia, Cyprus birthdays and also suggests deep links between the well- Information: Topics: differential geometry and geometric established disciplines of quantum theory and Web site: http://www.kutzler.com/medconf2000- analysis: submanifolds, integrable systems, spec- information theory and computer science. A mathedu/ tral geometry; partial differential equations in notable feature of the subject is its interdiscipli- mathematical physics: Dirac and Schrödinger nary nature with contributions from physicists, 17-22: Workshop on Computational Stochastics, equations, transport equations, soliton equations, mathematicians and computer scientists Aarhus, Denmark microlocal analysis, spectral theory; quantum Aim: to provide a comprehensive introduction to Information: contact Eva B. Vedel Jensen, mechanics and quantum field theory: semiclassi- current developments in quantum Department of Mathematical Sciences, University cal, adiabatic, perturbative and Born- computation/quantum information theory of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Oppenheimer approximations, n-body and Lecturers: Charles Bennett (tbc), quantum com- Denmark many-body quantum theory, algebraic quantum munication; Harry Buhrman, complexity/com- e-mail: [email protected] field theory munication complexity; Chris Fuchs, quantum Web site: http://www.maphysto.dk/events/Comp Speakers: J. Avron, W. Ballmann, communication; David DiVincenzo, implementa- Stoc2000/ J. Bourguignon, J. Cheeger, J.-M. Combes, tions; Richard Jozsa, algorithms and complexity; [For details, see EMS Newsletter 32] L. Faddeev, J. Froehlich, E. Lieb, W. Mueller, Noah Linden, introduction to quantum mechan- S. Novikov, B. Simon, C.-L. Terng ics and entanglement; Hoi-Kwong Lo, cryptogra- 27-29: Congreso RSME2000 de la Real Programme: plenary talks and special sessions phy; Sandu Popescu, quantum information; Sociedad Matemàtica Española, Madrid, Spain on the above mentioned topics Andrew Steane, error correction/fault Speakers: Fernando Chamizo (Madrid), Oscar Organisers and sponsors: tolerance/decoherence Garcìa-Prada (Madrid), Juan Josè Lòpez Sonderforschungsbereich (SFB) 288 ‘Differential Scientific organising committee: Richard Jozsa Velàzquez (Madrid), Rafael de la Llave (Texas), Geometry and Quantum Physics’ of Deutsche (Bristol), Noah Linden (Bristol), Angus Mark Melnikov (Barcelona), Sebastiàn Montiel Forschungsgemeinschaft, which links the Macintyre (Edinburgh), Andrew M. Pitts (Granada), Marta Sanz-Solé (Barcelona), Luis Mathematics Departments of Humboldt (Cambridge) Caffarelli (Texas), John H. Conway (Princeton) Universität zu Berlin, Technische Universität Audience: accessible to computer scientists as Organisers: Carlos Andradas (Univ. Berlin, the Universität Potsdam, and the Physics well as graduate students and post-Docs from Complutense), Emilio Bujalance (UNED), Department of Freie Universität Berlin other relevant disciplines Antonio Còrdoba (Madrid), Ildefonso Dìaz (Univ. Applications: titles and abstracts for special ses- Sponsor: the course is an activity of UK Complutense), Alberto Ibort (Univ. Carlos III), sions should be sent (preferably by e-mail) to one Quantum Computing Network, funded by the Manuel de Leòn (CSIC), Juan Llovet (Univ. de of the organisers, Volker Bach and Jochen EPSRC Alcalà), Francisco Martìn (Fed. Española Soc. Bruening (for addresses, see below) Information: Profs. Matemàticas, FESPM), David Rìos (Univ. Site: Technische Universität (TU) Berlin Web site: http://www.ma.hw.ac.uk/icms/current Rey Juan Carlos), Josè Manuel Vega (Madrid) Deadlines: for submission of titles and abstracts, Site: Universidad Complutense de Madrid 31 December 1999; for registration, 31 January 31-1 April: LMS Two-Day Meeting: Modelling Information: 2000; for payment of the fee, 6 March 2000 Spatiotemporal Dynamics in Interacting Web site: http://www.mat.ucm.es/rsme2000 Information: contact Volker Bach, FB Systems, Oxford, UK February 2000 Mathematik (17), Universität Mainz, D-55099 April 2000 Mainz, Germany, or Jochen Bruening, Institut 3-5: Mathematics Today, Trondheim, Norway für Mathematik, Humboldt-Universität zu Berlin, 5-14: ICMS Instructional Conference: Operator Note: primarily intended for a Scandinavian Unter den Linden 6, D-10117 Berlin, Germany Algebras and Operator Spaces, Edinburgh, audience e-mail: [email protected], vbach@mathe- Scotland Information: matik.uni-mainz.de, [email protected] Scientific organising committee: V. Jones (UC Web site: http://www.math.ntnu.no/talltiltusen/ berlin.de Berkeley), C. Lance (Leeds), G. Pedersen Web site: http://www.math.TU-Berlin.DE/~bach/ (Copenhagen), G. Pisier (Paris), S. Popa (UCLA), 28-3 March: Eighth International Conference FSS.html A. Sinclair (local organiser, Edinburgh),

30 EMS December 1999 CONFERENCES G. Skandalis (Paris) Sokolovskà 83, 186 75 Praha 8, Czech Republic, Web site: http://www.maphysto.dk/events/S-and- Aim: to introduce this active field of mathematics tel./fax: +420 - 2 - 232 3390 GT2000/ to younger scientists and to provide an opportu- e-mail: [email protected] nity for specialists to exchange ideas Web site: http://www.karlin.mff.cuni.cz/katedry/ 28-3 June: Spring School on Analysis: Some Topics: operator spaces, free probability, exact kma/ss/ Recent Techniques in Harmonic Analysis, C*-algebras, subfactors and related areas of oper- Paseky nad Jizerou, Czech Republic ator algebras 26-28: Mathematical Education of Engineers, Aim: to bring together adepts with an interest in Programme: several series of lectures (each series Loughborough, UK the field consisting of 2 or 3 one-hour lectures) designed Information: Speakers: Sergei Treil (Michigan), title to be to introduce and elaborate upon a particular Web site: http://www.ima.org.uk/mathematics/ announced; Igor Verbitsky (Missouri), Best con- field. These series will be complemented by more conferences.htm stant inequalities for some classical Fourier multi- specialised talks examining current trends. In [For details, see EMS Newsletter 33] plier operators; Alexander Volberg (Michigan), addition to the formal lectures, there will be Bellman function and some sharp estimates in ample opportunity for informal tutorials and dis- 25-6 May: NATO Advanced Study Institute, harmonic analysis cussions Nonlinear Dynamics in Life and Social Programme: a series of lectures on the above Speakers: include C. Anantharamam-de la Roche Sciences, Moscow, Russia topic (Orleans), D. Bisch (Santa Barbara), K. Dykema Information: Organizer: Faculty of Mathematics and Physics, (Texas), U. Haagerup (Odense), V. Jones Web site: Charles University (Berkeley), E. Kirchberg (Berlin), V. Paulsen http://www.cas.mcmaster.ca/~sulisw/asi.html Notes: there will be opportunities for informal (Houston, Texas), G. Pisier (Paris), S. Popa May 2000 discussions. Graduate students and others begin- (UCLA), M. Rieffel (Berkeley), D. Voiculsecu ning their mathematical careers are encouraged (Berkeley) 20-25: MaPhySto and StocLab Summer School to participate Sponsor: supported by the European on Stereology and Geometric Tomography, Site: Paseky nad Jizerou, in a chalet in the Commission Sandbjerg Manor, Denmark Krkonose Mountains Information: contact Allan M. Sinclair, Aim: to give an overview of modern stereology Information: contact Katedra matematickè Department of Maths and Statistics, JCMB, KB, and its relation to geometric tomography, includ- analýzy, Matematicko-fyzikàln fakulta UK, Edinburgh EH9 2DE, Scotland ing both the mathematical and statistical theory Sokolovskà 83, 186 75 Praha 8, Czech Republic, e-mail: [email protected] and the practical applications tel/fax: +420-2-232 3390 Web site: http://www.ma.hw.ac.uk/icms/current Scope: stereology is the area of stochastics deal- e-mail: [email protected] ing with statistical inference about spatial struc- Web site: http://www.karlin.mff.cuni.cz/katedry/ 10-20: NATO Advanced Study Institute/EC tures from geometric samples of the structure kma/ Summer School, New Theoretical Approaches such as two-dimensional sections and one-dimen- to Strongly Correlated Systems, Cambridge, UK sional probes. The development of stereological 29-2 June: Deuxième Rencontre Internationale Information: methods involve the use of advanced mathemati- sur les Polynomes à valeurs entières CIRM, Web site: http://www.newton.cam.ac.uk/programs/ cal tools, especially from geometric measure the- Luminy, France scew.html ory and integral geometry. Stereology is now in Main themes: integer-valued polynomials, multi- world-wide use in many areas of biology and plicative ideal theory, dimension theory, factori- 11-14: Workshop on Harmonic Maps and medicine, most importantly in neuroscience and sation properties, commutative monoids Curvature Properties of Submanifolds 2, Leeds, cancer grading. Other areas of application are Organisers: P. J. Cahen (Aix-Marseille III), J. L. UK geology, metallography and mineralogy. Chabert (Picardie) Information: contact J. C. Wood, School of Geometric tomography is closely related to stere- Information: Mathematics, University of Leeds, Leeds LS2 ology, as is apparent from its definition: ‘geomet- e-mail: [email protected] 9JT, UK ric tomography is the area of mathematics deal- e-mail: [email protected] ing with the retrieval of information about a geo- 29-9 June: Foliations: Geometry and Dynamics Web site: http://www.amsta.leeds.ac.uk/pure/geom metric object from data about its sections, or pro- Revisited, Banach Centre, Warsaw, Poland etry/leeds2000.html jections, or both’. Geometric tomography has Information: [For details, see EMS Newsletter 33] connections with convex geometry, geometric Web site: http://fol2000.math.uni.lodz.pl/ probing in robotics, computerized tomography, June 2000 17-20: 52nd British Mathematical Colloquium, and other areas Leeds, UK Teaching team: includes Adrian Baddeley 5-9: Sixth International Conference on Information: (Australia), Richard Gardner (Washington), Hans Probability, Poraj (near Czestochowa), Poland e-mail: [email protected] Jørgen G. Gundersen (Aarhus), Eva B. Vedel [dedicated to Professor Kazimierz Urbanik] Web site: http://www.amsta.leeds.ac.uk/bmc/ Jensen (Aarhus), Kiên Kiêu (Versailles) Topics: the latest scientific output of people [For details, see EMS Newsletter 33] Programme: lectures by invited researchers in working creatively in the field of probability related fields such as convex geometry, stochastic theory 23-29: Spring School on Functional Analysis: geometry and spatial statistics are also planned, Organisers: the Institute of Mathematics of (Non)smooth Analysis in Banach Spaces, as well as lectures by the participants of the sum- Polish Academy of Sciences, the Faculty of Paseky nad Jizerou, Czech Republic mer school Mathematics and Information Science of Warsaw Aim: to bring together adepts with an interest in Organisers: StocLab (Laboratory for University of Technology, the Institute of the field Computational Stochastics) and MaPhySto Mathematics of Wroclaw University and the Speakers: Alexander Ioffe (Haifa), Terry (Centre for Mathematical Physics and University of Commerce in Kielce Rockafellar (Seattle), Philip Loewen (Vancouver), Stochastics), both Department of Mathematical Programme committee: Dobieslaw Bobrowski, Robert Deville (Bordeaux) Sciences, University of Aarhus Krzysztof Burdzy, Zbigniew Ciesielski, Wieslaw Programme: a series of lectures on the above Audience: PhDs, post-Docs and other Dziubdziela, Ryszard Jajte, Michal Karonski, topic researchers in mathematics. Scientists from the Boleslaw Kopocinski, Stanislaw Kwapien, Organiser: Faculty of Mathematics and Physics natural sciences with a strong background and Zbigniew Morawiecki, Agnieszka Plucinska, of Charles University interest in mathematics are also welcome. The Tomasz Rolski, Jan Rosinski, Zdzislaw Rychlik, Notes: there will be opportunities for informal number of participants is limited to 50 Lukasz Stettner, Jan Suwala, Dominik Szynal, discussions. Graduate students and others begin- Site: Sandbjerg Manor, a conference centre Kazimierz Urbanik, Jan Waluszewski, Aleksander ning their mathematical careers are encouraged owned by University of Aarhus, situated in the Weron, Wojbor A. Woyczynski, Jerzy Zabczyk, to participate southern part of Jutland, Denmark Ryszard Zielinski Site: Paseky nad Jizerou, in a chalet in the Grants: a limited number available for students Information: Krkonose Mountains Deadline: for application, 1 March 2000 e-mail: [email protected] Information: contact Katedra matematickè Information: analýzy, Matematicko-fyzikàln fakulta UK, e-mail: [email protected] 7-11: PhD Euroconference on Complex

EMS December 1999 31 CONFERENCES Analysis and Holomorphic Dynamics, quantum field theory, but there will be talks on fer in manufacturing, cooling of electric and elec- Catalonia, Spain other subjects in mathematical physics trical equipment, gas turbine heat transfer, heat Focus: complex analysis and holomorphic Invited speakers: include J. Boeckenhauer, D. transfer enhancement, modelling and experi- dynamics are classical domains of the mathemati- Buchholz, A. Connes, K. Fredenhagen, G. ments in heat transfer cal sciences which are now going through an Gallavotti, U. Haagerup, M. Izumi, A. Jaffe, V. Organizer: Wessex Institute of Technology, exciting phase of fruitful interplay Jones, Y. Kawahigashi, M. Mueger, G. Pedersen, Southampton, UK Aim: to bring together young researchers in S. Popa, H.-K. Rehren, M. Rieffel, I. Singer, R. Sponsor: Developments in Heat Transfer Book order to expose and discuss work in progress and Stora, E. Stoermer, M. Takesaki, D. Voiculescu, Series recent advances on these fields R. Verch, S. Woronowicz Conference proceedings: will be published to a Main speakers: Xavier Buff (Toulouse), Gregery Social event: dinner on 22 June high standard by WIT Press Buzzard (Cornell), Mattias Jonsson (Michigan), Site: the Certosa di Pontignano, a splendid 15th- Information: contact Conference Secretariat, Ricardo Perez Marco (UCLA & Paris), Stephen century building in the countryside near Siena Heat Transfer 2000, Wessex Institute of Rohde (Seattle) (pictures at Technology, Ashurst Lodge, Ashurst, Programme: lectures given by the main speakers, http://www.unisi.it/servizi/certosa/Certosa.html) Southampton SO40 7AA,UK tel: 44-(0)-23-80- shorter talks and one session of exposition and Deadline: for registration, 15 April 2000 293223, fax: 44-(0)-23-80-292853 discussion of open problems Information : contact Roberto Longo e-mail: [email protected] Organising committee: Nuria Fagella Dipartimento di Matematica, Università di Roma web site: http://www.wessex.ac.uk/conferences/2000 (Barcelona), Xavier Jarque (Barcelona), Xavier ‘Tor Vergata’, I-00133 Roma, Italy, fax: +39- Massaneda (Barcelona), Joaquim Ortega Cerda 0672594699 26-30: Formal Power Series and Algebraic (Barcelona) e-mail: [email protected] Combinatorics (FPSAC ‘00), Moscow, Russia Organising institution: Centre de Recerca web site: http://mat.uniroma2.it/~mp/siena2000. Topics: algebraic and bijective combinatorics Matematica (CRM) html and their relations with other parts of mathemat- Site: Platja d’Aro (Costa Brava), Catalonia, Spain ics, combinatorial and computer algebra, com- Note: the conference is restricted to young 25-28: IMACS-ACA’2000 6th International puter science and physics researchers (normally those aged up to 35) Conference on Applications of Computer Programme: invited lectures, contributed pre- Information: Algebra, St Petersburg, Russia sentations, poster sessions, problem sessions and e-mail: [email protected] Scope: actual or possible applications of nontriv- software demonstrations Web site: http://crm.es/cad2000 (from 1 January ial computer algebra techniques to other fields Chairmen, program committee: Daniel Krob 2000) and substantial interactions of computer algebra (LIAFA), Alexander A. Mikhalev (MSU, Russia with other fields and Hong Kong) 13-16: First AMS-Scandinavian International General chair: Nikolay Vassiliev, Chairman, organizing committee: Alexander V. Mathematics Meeting, XXIII Scandinavian [email protected] Mikhalev (MSU, Russia) Congress of Mathematicians, Odense, Denmark Programme chairs: Victor Edneral, Site: Moscow State University Information: contact Hans J. Munkholm, [email protected], Richard Liska, Information: Odense University, Campusvej 55, DK 5230 [email protected], Michael Wester, west- web site: http://www.liafa.jussieu.fr/~fpsac00/ Odense M, Denmark, tel: +45-65572309/+45- [email protected] 65932691 Meeting format: standard IMACS format; indi- 26-30: POISSON 2000, France e-mail: [email protected] viduals are invited to organise a special session. Information: Web site: http://www.imada.ou.dk/~hjm/AMS. Individuals can propose a special session by con- e-mail: [email protected] Scand.2000.html tacting the program chairs. All paper submis- [For details, see EMS Newsletter 33] sions must be directed to an organiser of an 28-1 July: First World Congress of the appropriate special session Bachelier Finance Society, Paris, France 14-17: International Workshop for Operator Sponsors: Steklov Institute of Mathematics at St Information: Theory and Applications (IWOTA), Bordeaux, Petersburg, Euler International Mathematical e-mail: [email protected] France Institute, St Petersburg Mathematical Society, St Information: Petersburg State University 29-3 July: International Workshop on e-mail: [email protected] Information: Nonlinear Spectral Theory, Würzburg, Web site: http://www.math.u-bordeaux.fr/~iwota/ web site: http://www.pdmi.ras.ru/EIMI/2000/imacs/ Germany [For details, see EMS Newsletter 33] Information: contact Jurgen Appell, Department 26-28: Sixth International Conference on of Mathematics, University of Würzburg, Am 18-21: International Conference on Monte Advanced Computational Methods in Heat Hubland, D-97074 Würzburg, Germany; tel: Carlo Simulation, Monte Carlo, Monaco Transfer, Madrid, Spain +49-931-8885017; fax: +49-931-8885599 Information: Aim: to provide a forum for the presentation of e-mail: [email protected] Web site: http://www.uibk.ac.at/c/c8/c810/conf/mcs_ new approaches to the numerical solutions of web site: www.mathematik.uni-wuerzburg.de/ 2000.html heat transfer problems. Methods of interest ~appell/nlst.html [For details, see EMS Newsletter 33] include all well-established and efficient numeri- [For details, see EMS Newsletter 33] cal techniques such as finite differences, finite July 2000 18-24: Perspectives of Mathematics, Goslar, volume, finite elements and boundary elements. Germany Special attention will be paid to complex thermal 2-7: Sixth International Conference on p-Adic Information: contact K. Hulek, Institut für problems from engineering practice. Heat Analysis, Ioannina, Greece Mathematik, Universität Hannover, Postfach Transfer 2000 is of importance to all scientists Scope: analysis over valued fields other than the 6009, D-30060 Hannover, Germany and engineers who are actively involved in devel- fields of real or complex numbers (such as the e-mail: [email protected] oping innovative approaches, as well as in solving field of p-adic numbers) Web site: http://www-ifm.math.uni-hannover.de/ a variety of industrial problems Topics: Banach spaces, Hilbert spaces, locally info/perspectives.html Topics: conduction including non-linear prob- convex spaces and modules, operators, spaces of [For details, see EMS Newsletter 33] lems, diffusion-convection, natural and forced continuous functions, distributions and measures, convection, thermal radiation, fire and combus- function theory, classical and harmonic analysis, 20-25: Mathematical Physics in Mathematics tion simulation, phase change, thermal problems applications in mathematical physics and in Physics: Quantum and Operator in porous media fibres and composites, metal Speakers: (preliminary list) Shavgat Ayupov Algebraic Aspects, Siena, Italy casting, welding, forging and other processes, (Uzbekistan), Jesus Araujo (Spain), Jose Manuel [dedicated to Sergio Doplicher and John E. energy power systems, inverse problems and Bayod (Spain), Kamal Boussaf (France), Roberts on the occasion of their 60th birthdays] other ill-posed problems, combined heat and Abdelbaki Boutabaa (France), Gilles Christol Scope: the conference is centred around the mass transfer, advances in heat transfer software, (France), N. De Grande-De Kimpe (Belgium), interplay between mathematics and physics, coupling different numerical methods, hot spots Bertin Diarra (France), B. Dragovich mainly with reference to operator algebras and and thermal shocks, heat exchangers, heat trans- (Yugoslavia), Alain Escassut (France), Jose

32 EMS December 1999 CONFERENCES Aguayo Garrido (Chile), Thomas Gilsdorf (USA), Information: web site: http://www.unifr.ch/math/catop2000/ L. Van Hamme (Belgium), Jerzy Kakol (Poland), e-mail: [email protected] A. K. Katsaras (Greece), Hans A. Keller web site: http://www.math.leidenuniv.nl/ants4/ 4-7: Second International Conference on (Switzerland), Andrei Khrenikov (Sweden), Mathematical Methods in Reliability, Anatoly Kochubei (Ukraine), Sara Krantz 3-7: Functional Analysis Valencia 2000, Spain Bordeaux, France (Sweden), Nicolas Mainetti ( France), M. S. Information: contact: K. D. Bierstedt or J. Bonet, Aims: to serve as a forum for discussing funda- Moslehian (Iran), L. Narici (USA), P. N. Univ. Paderborn, FB 17, Math., D-33095 mental issues of reliability mathematical methods Natarajan (India), S. Navarro (Chile), Robert Paderborn, Germany or Universidad Politècnica with respect to its applications; to assemble Nyqvist (Sweden), H. Ochsenius (Chile), C. de Valencia, Departamento de Matemática researchers in probability, statistics and applied Perez-Garcia (Spain), C. G. Petalas (Greece), Aplicada, E-46071 Valencia, Spain mathematics, working in the field of reliability, Marie-Claude Sarmant (France), W. H. Schikhof e-mail: [email protected] from university laboratories and research institu- (The Netherlands), Stany De Smedt (Belgium), web site: http://math-www.uni-paderborn.de/ tions in Europe and elsewhere V. K. Srinivasan (USA), Susana Vega (Spain), Ann VLC2000 Scope: common methods and models used in Verdoodt (Belgium), T. Vidalis (Greece) [For details, see EMS Newsletter 32] survival analysis and reliability will be considered Scientific committee: A. K. Katsaras (Ioannina), from a general point of view. Theoretical, mod- W. H. Schikhof (Nijmegen), L. Van Hamme 3-9: Euro-Summer School on Mathematical elling, computational and case study contribu- (Brussels) Aspects of Evolving Interfaces, Madeira, tions will be presented, ranging from academic Organising committee: A. K. Katsaras Portugal considerations to industrial approaches (Ioannina), C. G. Petalas (Ioannina), T. Vidalis [Joint school of CIM (Centro Internacional de Programme: invited talks, plenary sessions, par- (Ioannina) Matematica, Portugal) and CIME (Centro allel sessions and posters Site: University of Ioannina Internazionale Matematico Estivo, Italy), Satellite Information: contact Dr Valentina Nikoulina, Information: contact A. K. Katsaras, Dept. of Activity of the Third European Congress of Université Victor Segalen, Bordeaux 2, Math., Univ. of Ioannina, 45110, Ioannina, Mathematics in Barcelona, Spain, 10-14 July] Statistique Mathematique, UFR MI2S, B.P. 69 Greece, tel: +30-651-98289, fax: +30-651-46361 Aims: interfaces are geometrical objects model- 33076 Bordeaux Cedex, France; tel: +33-(0)-5- e-mail: [email protected] ling free or moving boundaries which arise in a 57-57-10-70/(0)-5-57-57-14-25; fax: +33-(0)-5- web site: http://www.uoi.gr/conf_sem/p-adic wide range of phase change problems in continu- 56-98-57-36/+33-(0)-5-57-57-12-63 um physics, in particular in material sciences. e-mail: [email protected], 2-15: NATO Advanced Study Institute 20th Recent mathematical advances in the theory of [email protected] Century Harmonic Analysis-a Celebration, geometric evolution problems will be presented web site: http://www.mass.u-bordeaux2.fr/MI2S/ Tuscany, Italy in a set of lectures with an interdisplinary per- MMR2000/ Information: spective, covering several aspects from theory to web site: http://www.cs.umb.edu/~asi/analysis2000 applications 5-7: Scandinavian Workshop on Algorithm Programme: a series of five complementary Theory, Bergen, Norway 3-7: ALHAMBRA 2000, Granada, Spain courses each consisting of three 90-minute lec- Information: [joint European-Arabic conference] tures plus tutorials; a limited number of selected e-mail: [email protected] Scope: (morning sessions) historical perspectives talks of 20-30 minutes each by young researchers web site: http://www.ii.uib.no/swat2000 on contributions of both cultures to the present or post-Docs mathematical knowledge, the state of the more Speakers and course titles: Luigi Ambrosio 6-8: 6th Barcelona Logic Meeting, Barcelona, relevant mathematical concepts over the cen- (Pisa), Distance function and evolution of fronts Spain turies and the way they have evolved; (afternoon by implicit time discretization; Gerhard Dziuk Invited speakers: Jose Luis Balcazar (Catalunya), sessions) current mathematical subjects from the (Freiburg), Numerical approximation of mean Pilar Dellunde (Barcelona), Peter Koepke list below curvature flow of graphs; Masayasu Mimura (Bonn), Anand Pillay (Urbana-Champaign), Yde Topics: computational mathematics, geometry of (Hiroshima), Dynamics of patterns and interfaces Venema (Amsterdam), Michael Zakharyaschev submanifolds, mathematical demography, non- in reaction-diffusion systems from chemical and (Moscow) linear problems, orthogonal polynomials, public biological viewpoints; Vsvolod A. Solonnikov (St Scientific and organising committee: Joan mathematics, representation theory of algebras, Petersburg), Evolution free boundary problems Bagaria (Barcelona), Enrique Casanovas symmetry for parabolic and Navier-Stokes equations; Halil (Barcelona), Rafel Farre (Catalunya), Josep Maria Programme: plenary lectures on the above sub- M. Soner (Princeton), Variational and Dynamic Font (Barcelona), Juan Carlos Martinez jects, short communications Problems for the Ginzburg-Landau Functional (Barcelona), Hiroakira Ono (Japan), Margarita Information: contact ALHAMBRA 2000 Organisers: Pierluigi Colli, Jose-Francisco Otero (Madrid), Stevo Todorcevic (Paris) Conference eurocongres Avda. Constitución, 18 - Rodrigues Information: Blq.4 E-18012 - Granada, Spain, tel: +34-958- Audience: the school is mainly intended for e-mail: [email protected] 209-361, fax: +34-958-209-400 European postgraduate students, including web site: http://www.mat.ub.es/~logica/news.html e-mail: [email protected], recent PhDs, but selected participants from out- or http://www.crm.es/ [email protected] side Europe and senior scientists wishing to learn web site: http://www.ugr.es/local/alhambra2000 about the subject are not excluded 10-14: IUTAM Symposium on Free Surface Lecture notes: expected to be published Flows, Birmingham, UK 3-7: ANTS IV Algorithmic Number Theory Financial support: some grants for younger Information: Symposium, Leiden, The Netherlands researchers are available. Applications should be web site: http://www.mat.bham.ac.uk/research/ Invited speakers: include Frits Beukers, Peter made to the organising committee iutam.htm Borwein, Jin-Yi Cai, Noam Elkies, Victor Flynn, Site: University of Madeira, Funchal, Portugal [For details, see EMS Newsletter 33] Jacques Stern Information: Topics: algorithmic aspects of number theory, e-mail: [email protected] 10-14: Third European Congress of including elementary number theory, algebraic web site: http://maei.lmc.fc.ul.pt Mathematics, Barcelona, Spain number theory, analytic number theory, geome- Information: contact Societat Catalana de try of numbers, algebraic geometry, finite fields, 4-6: Catop 2000, Fribourg, Switzerland Matemátiques, Carrer del Carme, 47, E-08001 cryptography and computational complexity Scope: categorical topological methods Barcelona; Deadline: for submission of contributed papers, Aim: to discuss categorical topological methods tel: (34 3) 270 16 26; fax (34 3) 270 11 80 1 January 2000 that are likely to be mathematically important in e-mail: [email protected] Proceedings: to appear in the series of Lecture the next century. Furthermore, on Thursday, we web site: http://www.iec.es/3ecm/ Notes in Computer Science of Springer-Verlag celebrate the 70th birthday of Prof. Heinrich [For details, see page 13] Organising committee: Bart de Smit (Leiden), Kleisli (Fribourg) Herman te Riele (CWI), Jaap Top (Gronigen), Programme committee: Hans-Peter A. Kuenzi 13-14: Computational Challenges for the Peter Stevenhagen (chair, Amsterdam); Wieb (Bern), Ernst A. Ruh (Fribourg) Millenium, Cambridge, UK Bosma (Nijmegen) Information: Information:

EMS December 1999 33 CONFERENCES web site: http://www.ima.org.uk web site: http://www.math.helsinki.fi/~analysis/ NevanlinnaColloquium/ 5-7: Quantitative Modelling in the Management 17-20: IUTAM Symposium 2000/10 Diffraction [For details, see EMS Newsletter 33] of Health Care, Salford, UK and Scattering in Fluid Mechanics and Participants: conference delegates will include Elasticity, Manchester, UK 17-3 September: EMS Summer School in those involved in quantitative policy, evaluation Information: contact Professor David Abrahams, Probability Theory, Saint-Flour, Cantal, France and decision making in health care relating to Department of Mathematics, University of Programme: short courses of 10 lectures each, the British National Health Service, private sec- Manchester, Oxford Road, Manchester M13 9PL, on the topics below tor, and overseas experience. The first confer- UK, tel: +44-(0)-161-275-5901, fax: +44-(0)- Speakers: Sergio Albeverio (Germany), Dirichlet ence in 1994 attracted medical practitioners 161-275-5819 forms and infinite-dimensional theory; Walter working in hospitals and general practice; health e-mail: [email protected] Schachermayer (Vienna), Mathematics and service managers; and operational research spe- web site: http://www.keele.ac.uk/depts/ma/iutam/ finance; Michel Talagrand (France), Spin glasses cialists, economists, statisticians and mathemati- [For details, see EMS Newsletter 33] Organiser: Prof. Pierre Bernard cians employed in health care and universities Programme committee: Martin Barlow, Gerard Themes: the conference will focus on practical 17-21: Ninth International Conference on Benarous, Pierre Bernard, Lucien Birge, Michel methodologies in budgeting, financing, setting of Fibonacci Numbers and their Applications, Emery, Hans Follmer, Jean-Francois Le Gall, priorities, and allocation of resources for the pro- Luxembourg-City, Luxembourg Michel Ledoux, David Nualart, Etienne Pardoux, vision of services, and the formulation and mea- Information: Jean Picard, Alain-Sol Sznitman, Liming Wu surement of performance indicators. Papers cov- e-mail: [email protected] Information: contact: P. Bernard, Laboratoire de ering experience with established methodologies 17-22: Colloquium on Lie Theory and Mathématiques Appliquées, Univ. Blaise Pascal, and issues relating to their implementation are Applications, Vigo, Spain F-63177 Aubière, tel/fax: +33-4 73-40-70-64 welcome together with those describing new Information: contact I Colloquium on Lie e-mail: [email protected] methodologies Theory and Applications, E. T. S. I. Programme: keynote speeches, contributed Telecomunicación, Universidad de Vigo, 36280 21-25: IMACS 2000, Lausanne, Switzerland papers and an exhibition of software Vigo, Spain; tel: +86-81-21-52/+86-81-24-45; [International Association for Mathematics and Invited speakers: (confirmed) Sandy Macara fax: +86-81-21-16/+86-81-2- 01 Computers World Congress] (BMA), Peter Millard (St George’s Hospital e-mail: [email protected] Information: contact Prof. Robert Owens, Medical School, London), Jonathan Rosenhead web site: http://www.dma.uvigo.es/~clieta/ IMACS Congress 2000, DGM-IMHEF-LMF, (London), Tom Treasure (St George’s Hospital [For details, see EMS Newsletter 33] Swiss Federal Institute of Technology, CH-1015 Medical School, London) Lausanne, Switzerland; tel: +41-21-693-35-89; Organising committee: Rose Baker (Salford, 17-22: International Congress of Mathematical fax: +41-21-693-36-46 chair), Sally Brailsford (Southampton), Peter Physics, London, UK e-mail: [email protected] Millard (St George’s Hospital Medical School), Information: web site: http://imacs2000.epfl.ch Patrick Rivett (Cumbria), Alison Round (North & web site: http://icmp2000.ma.ic.ac.uk/ [For details, see EMS Newsletter 32] East Devon Health Authority) 19-26: Third World Congress of Non-linear Proceedings: selected papers to be published Analysts (WCNA-2000), Catania, Italy 30-2 September: Innovations in Higher Site: University of Salford 23-31: ASL European Summer Meeting (Logic Education 2000, Helsinki, Finland Call for papers: abstracts of 300-500 words Colloquium 2000), Paris, France Information: should be sent to Pamela Bye, Institute of Information: e-mail: [email protected] Mathematics and its Applications, Catherine e-mail: [email protected] web site: http://www.helsinki.fi/inno2000 Richards House, 16 Nelson Street, Southend-on- web site: http://lc2000.logique.jussieu.fr September 2000 Sea, Essex SS1 1EF, UK, by 1 May 2000 [For details, see EMS Newsletter 33] Information: 4-6: Mathematics of Surfaces, Cambridge, UK web site: http://www.ima.org.uk/mathematics/ 24-3 August: EMS Summer School, New analyt- Information: conferences.htm ic and geometric methods in inverse problems, web site: http://www.ima.org.uk Edinburgh, Scotland 5-16: Advanced Course on Algebraic Quantum Organisers: Prof. Erkki Somersalo, Prof. 4-8: FGI2000 French-German-Italian Groups, Bellaterra, Spain Yaroslav V. Kurylev, Prof. Brian Sleeman Conference on Optimisation, Montpellier, Speakers: Kenneth Brown (Glasgow), Kenneth Note: in collaboration with the International France Goodearl (Santa Barbara) Centre for Mathematical Sciences (ICMS; Aim: to enable the exchange of results and ideas Site: Centre de Recerca Matemàtica, Campus of www.ma.hw.ac.uk/icms/) about the state of the art in mathematical optimi- the Universitat Autònoma de Barcelona, Information: contact Erkki Somersalo, Helsinki sation in a broad sense Bellaterra, Spain University of Technology, Finland Topics: continuous and discrete (scalar and vec- Information: e-mail: [email protected] tor) optimisation, calculus of variations, optimal e-mail: [email protected] control, games, non-smooth analysis, critical web site: http://crm.es/quantum 31-3 August: Third Conference of Balkan point theory, equilibria. Analytical as well as Society of Geometers, Bucharest, Romania numerical aspects are of interest, along with 10-17: Summer School on Geometry of Quiver- Information: contact V. Balan, University applications Representations and Preprojective Algebras, Politehnica of Bucharest, Department Scientific committee: H. Attouch (Montpellier), Isle of Thorn, UK Mathematics I, Splaiul Independentei 313, RO- G. Buttazzo (Pisa), G. Di Pillo (Rome), F. Topics: degenerations of modules, theorem of 77206, Bucharest, Romania; fax: (401) 411.53.65 Giannessi (Pisa), C. Lemaréchal (Grenoble), W. Kac, moduli spaces, preprojective algebras, semi- e-mail: [email protected] Oettli (Mannheim), J.-J. Strodiot (Namur), M. invariants of quivers, Young tableaux and [For details, see EMS Newsletter 33] Théra (Limoges), R. Tichatschke (Trier), J. Zowe Schubert calculus August 2000 (Erlangen-Nuernberg) Programme: the meeting is in two parts: in the Organising committee Laboratoire d’Analyse, de first part the participants will lecture on intro- 2-9: Summer School on Mathematical Physics Calcul Scientifique et Industriel et ductory topics; the second part is a workshop (emphasis on Quantum Field Theory), d’Optimisation de Montpellier (ACSIOM) where specialists in the area will lecture on recent Sandbjerg Manor, Denmark Programme: invited lectures and contributed results Information: talks Organisers: W. W. Crawley-Boevey (Leeds), K. web site: http://www.maphysto.dk/events/ Information: contact: Bernard Lemaire, Erdmann (Oxford), Ch. Geiss (at present UNAM, Mathématiques, Université de Montpellier II, Mexico) 8-12: XVIII Nevanlinna Colloquium, Helsinki, Place Eugène Bataillon, 34095 Montpellier cedex Support: provided by the TMR scheme of the EC Finland 05 Information: contact Karin Erdmann, Information: e-mail: [email protected] Mathematical Institute, University of Oxford, e-mail: [email protected] web site: http://www.math.univ-montp2.fr/ Oxford OX1 3LB, UK

34 EMS December 1999 CONFERENCES e-mail: [email protected] Proceedings: to be published applications to modelling and analysing complex web site: http://www.mathematik.uni-bielefeld.de/ Information: processes and patterns ~sek/summerseries.html web site: http://www.ima.org.uk/mathematics/ Themes: measure theory and fractal measures, conferences.htm multi-fractal measures, novel iteration function 11-15: Boundary Integral Methods: Theory and sequences, statistically self-affine functions and Applications, Bath, UK 12-15: IWOTA-Portugal 2000 International Lévy statistics, fractional dynamics, stochastic Aim: to provide a forum for the exchange of Workshop on Operator Theory and modelling with fractals, inverse problems in frac- ideas between academic and industrial Applications, Faro, Portugal tal geometry, efficient algorithms for computing researchers in different disciplines whose com- Main topics: factorisation theory, factorisation fractals, applications to time-series modelling mon interest is boundary integral methods and integrable systems, operator theoretical (e.g. financial forecasting), applications to com- Scope: as well as discussing recent developments methods in diffraction theory, algebraic tech- puter graphics (e.g. fractal surfaces), applications in the theory and numerical analysis of boundary niques in operator theory, related topics and to simulation (e.g. L-systems), applications to integral equations, the conference will strive to applications to mathematical physics data compression, applications to chaotic dynam- encompass applications of contemporary rele- Steering committee: T. Ando, H. Bart, H. ical systems analysis vance such as direct and inverse (medium and Berovici, R. Dijksma, H. Dym, C. Foias, I. Invited speakers: presentations on state of the high frequency) scattering, electromagnetics and Gohberg, J. W. Helton, M. A. Kaashoek, H. art research will be given by a number of invited moving boundary problems in hydrodynamics. Langer, R. Mennicken, L. Rodman, J. G. speakers who are internationally recognised for Continuing progress in key computational tech- Stampfli their contribution to the field niques such as multipole, wavelets and panel Registration: use IWOTA web-page or e-mail to Organising committee: Prof. J. M. Blackledge clustering, together with innovative algorithm receive second announcement (Leicester, chairman), Prof. K. Cevik design will be an additional theme Information: contact N.Manojlovic, U. C. E. H., (Fachhochschule Bielefeld), Dr. A. Evans Speakers: W. C. Chew (Illinois), C. Constanda Universidade do Algarve, Campus de Gambelas, (Leicester), Prof. M. Goman (Moscow), Dr. K. (Strathclyde), T. Hou (California), A. Kirsch 8000 Faro, Portugal, tel: +351-89-800914 ext Hopcraft (Nottingham), Dr. S. Mikhailov (Karlsruhe), A. Rathsfeld (Berlin), S. A. Sauter 7637, fax: +351-89-818560 (Moscow), Dr. M. Turner (Leicester) (Leipzig), I. H. Sloan (Sydney), W. L. Wendland e-mail: [email protected], Proceedings: to be published (Stuttgart), L. Wrobel (London) web site: http://www.ualg.pt/cma/iwota/ Short course: a one-day short course, Organising committee: Ivan Graham (Chair) Introduction to Fractal Geometry and its (Bath), Sia Amini (Salford), Simon Chandler- 18-22: International Data Analysis Conference, Applications, will precede the conference on 19 Wilde (Brunel), Ke Chen (Liverpool), Penny Innsbruck, Austria September Davies (Strathclyde) Scope: all aspects of data-analysis will be consid- Site: De Montfort University, Leicester Site: University of Bath ered, ranging from applied aspects to fundamen- Call for papers: abstracts of 300-500 words Information: tal questions on the description and analysis of should be sent to Pamela Bye, Institute of web site: http://www.ima.org.uk/mathematics/ real data Mathematics and its Applications, Catherine conferences.htm Topics: exploratory, fuzzy, statistical data analy- Richards House, 16 Nelson Street, Southend-on- sis Sea, Essex SS1 1EF, UK, by 31 January 2000. 12-15: Imaging and Digital Image Processing: Organizer: Prof. Reinhard Viertl Notification to authors will be mid-March 2000. Mathematical Methods, Algorithms and Information: Final papers should be submitted by late- Applications, Leicester, UK e-mail: [email protected] December 2000 for inclusion in the conference Aim: to provide a forum for discussing the math- web site: http://www.statistik.tuwien.ac.at/ida2000/ proceedings ematical modelling of imaging systems, the Information: design and implementation of specialised image 18-23: International Congress on Differential web site: http://www.ima.org.uk/mathematics/ processing algorithms and novel applications of Geometry, in Memory of Alfred Gray, Bilbao, confractalgeometry.htm image processing software in industry and com- Spain December 2000 merce Programme committee: Th. Banchoff, J. P. Topics: inverse problems in imaging, statistical Bourguignon, E. Calabi, S. Donaldson, J. Eells, S. 18-20: Fifth International Conference on methods in image processing, image compres- Gindikin, M. Gromov, O. Kowalski, M. Mezzino, Mathematics in Signal Processing, Coventry, sion techniques, fuzzy systems theory, artificial S. Novikov, M. Pinsky, A. Ros, S. Salamon, L. UK neural networks, multi-fractals and wavelets, Vanhecke, J. Wolf Scope: signal processing constitutes an important colour image processing, 3D imaging and image Organisers: M. Fernandez (chairman), L. C. de area for the application of mathematical concepts processing, real-time image processing and sys- Andres, L. A. Cordero, A. Ferrandez, R. Iba-ez, and techniques fuelled, for example, by recent tems modelling M. de Leon, M. Macho-Stadler, A. Martinez developments in mobile communications, multi- Invited speakers: presentations on state of the Naveira, L. Ugarte media systems and digital TV. The last IMA con- art research will be given by a number of invited Information: ference on this subject was held in December speakers who are internationally recognised for e-mail: [email protected] or 1996 and the intervening years have witnessed their contribution to the field [email protected] significant developments in many topics such as Organising committee: J. M. Blackledge web site: http://www.ehu.es/Gray non-linear/non-Gaussian signal processing, (Leicester, chair), P. Andrews (Leicester), B. multi-rate signal processing, blind deconvolu- Carroll (GEC Marconi), M. McCormick 18-27: 8th Workshop on Stochastic and Related tion/signal separation and broadband systems (Leicester), N. Phillips (Leicester), M. Rycroft Fields, G. Magusa, Famagusta, North Cyprus Aim: the aim of this conference is to bring (Cambridge), P. Smith (Loughborough), Dr. H. Speakers: include P. Malliavin, D. W. Stroock together mathematicians and engineers with a Tassignon (Belgium), M. Turner (Leicester) Programme committee: U. Capar, L. view to exploring recent developments and iden- Short course: a one-day short course, Decreusefond, A. S. Ustunel, M. Zakai tifying fruitful avenues for further research. It is Introduction to Imaging and Digital Image Organisers: U. Capar, A. S. Ustunel hoped that the meeting will also help to attract Processing, will precede the conference on 12 Information: contact A. S. Ustunel, ENST, 46, more mathematicians into this important and September rue Barrault, 75634 Paris Cedex 13, France, challenging field Site: De Montfort University, Leicester tel/fax: +33-1-45-81-31-19 Programme committee: Prof. J. G. McWhirter Call for papers: abstracts of 300-500 words e-mail: [email protected] (chairman) (DERA, Malvern), Prof. O. R. Hinton should be sent to Pamela Bye, Institute of web site: http://mozart.emu.edu.tr/workshop (Newcastle) Mathematics and its Applications, Catherine Site: University of Warwick Richards House, 16 Nelson Street, Southend-on- 19-22: Fractal Geometry: Mathematical Information: contact Mrs. Pamela Bye, Institute Sea, Essex SS1 1EF, UK, by 31 January 2000. Techniques, Algorithms and Applications, of Mathematics and its Applications, Catherine Notification to authors will be mid-March 2000. Leicester, UK Richards House, 16 Nelson Street, Southend-on- Final papers should be submitted by late- Aim: to provide a forum for discussing the math- Sea, Essex SS1 1EF, UK, fax: +44-(0)-1702- December 2000 for inclusion in the conference ematical basis of fractal geometry, the computer 354111, e-mail: [email protected] proceedings implementation of fractal algorithms and their

EMS December 1999 35 RECENT BOOKS al categorical constructions. In principle, one might consider it possible to read only the second part, but practically this is impossible, and in fact would make no RecentRecent booksbooks sense. It seems that it is quite profitable to edited by Ivan Netuka and Vladimír Sou³ek read both parts more or less simultaneous- ly. The book is not directly designed for beginners in topology, but nevertheless Books submitted for review should be sent to the Riemannian geometry and non-linear they can understand and learn from it. following address: Ivan Netuka, MÚUK, PDE’s on manifolds. (jbu) They can find here even the definition of Sokolovská 83, 186 75 Praha 8, Czech homotopy groups – of course, in a more Republic. K. M. Ball and V. Milman, Convex abstract setting, but I think that it is natur- Geometric Analysis, Mathematical Sciences al for young mathematicians to start on a D. Alpay, Algorithme de Schur, espaces à Research Institute Publications 34, Cambridge higher level of abstraction than their noyau reproduisant et théorie des systèmes, University Press, Cambridge, 1999, 236 pp., teachers started. For specialists in topology Panoramas et Synthèses 6, Société £30, ISBN 0-521-64259-0 the book presents a higher viewpoint and a Mathématique de France, Paris, 1998, 189 This book collects articles on convex more profound understanding of homolo- pp., ISBN 2-85629-067-1 geometry reflecting the research presented gy and homotopy theories and opens new The aim of the book is to describe applica- in lectures or completed at the perspectives. It can be strongly recom- tions of the theory of spaces with repro- Mathematical Sciences Research Institute mended. (jiva) ducing kernels in various fields of mathe- within the framework of the programme matics. Principal examples of such spaces ‘Convex Geometry and Geometric J. A. Beachy, Introductory Lectures on are spaces of analytic functions of L. de Analysis’ in 1996. Rings and Modules, London Mathematical Branges and J. Rovnyak. An important An incomplete list of topics and authors Society Student Texts 47, Cambridge University property of reproducing kernels used in follows. J. Bourgain and G. Zhang give a Press, Cambridge, 1999, 238 pp., £15.95, the book is their positivity. The main part negative answer to the generalised ISBN 0-521-64340-6 and 0-521-64407-0 of the book contains a discussion of the Busemann-Petty problem. V. Milman and The first three chapters of this text cover Schur algorithm, the mathematical scatter- G. Schechtman prove an extension of the basic results on (non-commutative) associa- ing theory, function models in the theory Dvoretzky theorem. New results on poly- tive rings and modules over them. The of operators and interpolation problems tope approximations are presented by W. final chapter consists of an introduction to for holomorphic functions. Similar meth- T. Gowers and C. Schütt. A. Pajor esti- the representation theory of finite groups. ods are used in the last several chapters in mates the metric entropy of the All results are presented with full proofs, more general cases (e.g., for non-positive Grassmann manifold and M. and are illustrated by a great variety of metrics and non-stationary systems). The Schmückenschlager defines curvature for examples and exercises. book contains an extended and detailed graphs. The inverse Brunn-Minkowski Among other things, the Gauss theorem bibliography of the field (360 items). (vs) inequality is improved by A. E. Litvak. on UFDs is presented in Section 1.4, Further new results on geometric function- Maschke’s theorem in Section 2.3, the T. Aubin, Some Nonlinear Problems in al analysis are achieved by S. Alekser, A. E. Krull-Schmidt theorem for indecompos- Riemannian Geometry, Springer Litvak and B. Maurey. Advanced probabil- able finite length modules in Section 2.5, Monographs in Mathematics, Springer, Berlin, ity techniques with application in option the Wedderburn-Artin and Hopkins’ theo- 1998, 395 pp., DM168, ISBN 3-540-60752- pricing are developed by C. Borell. The rems in Section 3.3, and the orthogonality 8 whole collection provides a useful source of relations for irreducible characters in This is an extended and updated version inspiration for mathematicians working in Section 4.3. Moreover, each chapter ends of the author’s earlier book ‘Non-linear convex geometry and functional analysis. with a section on more advanced related Analysis on Manifolds, Monge-Ampère (jrat) material, such as Weyl algebras and Goldie Equations, Grundlehren 252, Springer, theorems. 1982’. Many important geometrical prob- H.-J. Baues, Combinatorial Foundation of The text is aimed at advanced under- lems are explained there, together with Homology and Homotopy, Springer graduate or beginning graduate students, their history, up-to-date results and recent Monographs in Mathematics, Springer, Berlin, as a complement to Sharp’s book on com- methods of proofs. All presented prob- 1999, 362 pp., DM 159, ISBN 3-540-64984- mutative algebra (Volume 19 in the LMS lems are related to non-linear partial dif- 0 student text series). Thus it was possible to ferential equations arising in geometry and This book is devoted to a new categorical skip over some of the basic notions of mod- physics. formulation of homology and homotopy ule theory that appear more frequently in The first part of the book is a nice intro- theories. Quite naturally, such an a commutative setting, such as flat modules duction to Riemannian geometry, the the- approach leads to a general view of these and pure submodules. The text provides ory of Sobolev spaces and the theory of theories, unifies many notions, presents a an excellent introduction to the Goodearl- partial differential equations on deeper understanding of the subject, and Warfield text on non-commutative noe- Riemannian manifolds. One interesting reveals new fields of investigation and therian rings (Volume 16 in the series). topic treated in the book is the famous applications. In this book a theory is a cat- (jtrl) Yamabe problem, which is described here egory with an initial object and with finite in detail. Several proofs are presented sums, and a theory of coactions is a theory in N. L. Biggs, E. K. Lloyd and R. J. Wilson, using several different methods (variation- which each object X is endowed with a Graph Theory 1736-1936, Clarendon Press, al, topological, etc.). Another topic dis- cogroup object X´ and a coaction Oxford, 1998, 239 pp., ISBN 0-19-853916-9 cussed extensively in the book is the prob- X → X ∨ X´. The notion of a theory of This is a new edition of the successful book lem of prescribed scalar curvature (both coactions is of fundamental importance for originally written in 1976. As the authors cases of positive and negative functions on the constructions performed in the book. claim (and as the reviewer can certify), this compact and non-compact manifolds are This is because each homotopy theory con- is a corrected and complemented (but for- treated). There is a nice overview of results tains theories of coactions. tunately not expanded) edition which pre- and methods for the solution of the prob- The book is divided into two parts, sents the vivid origins of a popular field. lem. Solutions of the existence problems chapters A, B, C, D, and chapters I-VIII. One cannot overlook that again the ref- for a Kaehler-Einstein metric or a metric The first part describes ‘classical’ examples erences are incomplete. For example, the with prescribed Ricci curvature can also be of homology and homotopy theories, pre- first paper initiating a study of the Steiner found in the book. sented in such a way that their common Tree Problem (V. Jarník and M. Kössler, This book can be strongly recommend- and fundamental features come to light. About minimal graphs containing n given ed to all those interested in contemporary The second part is then devoted to gener- points, Èas. Pì st. Mat. 63 (1934), 223-235) 36 EMS December 1999 RECENT BOOKS is omitted. Representations, Cambridge Studies in ence organised in Birmingham in July This is a useful and general purpose Advanced Mathematics 55, Cambridge 1995, to mark the tenth anniversary of the book. (jnes) University Press, Cambridge, 1998, 574 pp., Atlas of Finite Groups. It contains twenty £24.95, ISBN 0-521-65818-7 articles by leading experts in the field. N. Bouleau, Philosophies des mathéma- This is a paperback edition of the book Besides research papers we note a histori- tiques et de la modélisation, L’Harmattan, published in 1997; for a review, see EMS cal article on the development of the Atlas Paris, 1999, 363 pp., ISBN 2-7384-8125-6 Newsletter 29, September 1998, p.39) (vs) project since 1970 by three of its authors, The author, an active mathematician in the J. H. Conway, R. T. Curtis and R. A. field of probability and mathematical J. H. Conway and N. J. A. Sloane, Sphere Wilson. Of particular interest are also sur- analysis, and the head of an institute of Packings, Lattices and Groups, A Series of vey papers on applications of character applied mathematics, discusses a large Comprehensive Studies in Mathematics 290, theory to surfaces by G. A. Jones, on recent spectrum of topics: philosophy of science Springer, New York, 1999, 703 pp., DM139, advances in the representation theory by and contemporary mathematics, the ISBN 0-387-98585-9 G. Hiss, and on Zassenhaus conjectures on impact of computer science and modelling The third edition of this famous book con- integral group rings by W. Kimmerle. (jtu) to philosophy of mathematics, comparison tinues to pursue the question of determin- of the work of a computer with that of a ing the most efficient way to pack a large S. Donkin, The q-Schur Algebra, London creative mathematician, pure and applied number of equal spheres into n-dimen- Mathematical Society, Lecture Note Series 253, mathematics, teaching of mathematics, the sional Euclidean space. Related problems, Cambridge University Press, Cambridge, 1998, role of abstraction in education, etc. such as the classification of lattices and 179 pp., £24.95, ISBN 0-521-64558-1 The introductory chapter brings a con- quadratic forms, the covering and kissing These notes relate the representation the- temporary view to a philosophical charac- numbers and quantising problems, are ory of quantum linear groups Gq(n), of the terisation of mathematics and its face also examined, and connections with cod- q-Schur algebras Sq(n, r) and of the Hecke under the influence of the computer age ing theory, digital communication, group algebras H(r) defined by the symmetric and the extensive use of modelling. theory, data compression, n-dimensional group Sym(r). This generalizes the classi- The first part of the book summarises the crystallography and number theory are cal theory which is recovered as the case most important moments and ideas in the studied. A supplementary biography since q = 1. There are two main tools employed. development of philosophy of mathemat- 1988 containing over 800 items is of spe- First, the Schur functor F from Sq(n, r)- ics (crises in foundation of mathematics, cial interest. (jtu) mod to H(r)-mod: for r ≤ n, one has failure of Hilbert’s programme, mathemat- H(r) ≈ eSq(n, r)e for an idempotent e, and F ics from a logical point of view, impact of K. R. Coombes, B. R. Hunt, R. L. is defined simply as the ‘descent’, the work of (among others) Bachelardi, Lipsman, J. E. Osborn, and G. J. Stuck, F(V)=eV. Second, the identification of Bourbaki, Carnap, Desanti, Feyerabend, The Mathematica Primer, Cambridge Sq(n, r)-mod with a full subcategory of Gödel, Heyting, Husserl, Lakatos, University Press, Cambridge, 1998, 214 pp., Gq(n)-mod consisting of modules that are Lautman, Mill, Popper, Quine, Russell, hardback £50, paperback £16.95, ISBN 0- polynomial of degree r. etc.). 521-63130-0 and 0-521-63715-5 Donkin’s approach is homological The second part deals with mathemat- This book provides an introductory course rather than combinatorial. Among other ics: the nature of research, universality of for Mathematica, version 3, but even users things, the character formula for irre- mathematical language, a role of simplifi- of an earlier version may learn a lot. It ducible Sq(n, r)-modules at q = 0 is proved cations. The notion of ‘polysémie et dic- covers the most important parts of the sys- in 2.2, and the Steinberg’s tensor product tionnaire’ in mathematics is explained by tem, the front end, numerical and symbol- theorem in 3.2. There is an explicit com- means of several examples: geometrical ic calculations, graphics, and Web. The putation of tilting modules for the quan- transformations, non-Euclidean geometry, book consists of eight chapters: tum GL2 in 3.4, and an explicit description intuitionistic logic, symbolic calculus, vari- 1. Getting started (how to work with of the graded Grothendieck ring ous aspects of potential theory, non-stan- Mathematica on different platforms), ⊕d≥0 Grot(H(d)) in 4.4. In 4.8, the global dard analysis, etc. Creative processes, 2. Mathematica basics, dimension of Sq(n, r) for r ≤ n is deter- rigour and abstraction in mathematics are 3. Mathematica notebooks, mined. analysed and pedagogical aspects are also 4. Beyond basics, The main part of the notes is written in discussed. 5. Mathematica graphics, article style. This is compensated for by a The third part deals with the use of 6. Applications (illuminating a room, long expository Chapter 0, and by an mathematics – the author does not speak mortgage payments, cryptography, appendix on quasi-hereditary algebras. of applied mathematics, but coins the term Fibonacci numbers, Monte Carlo simu- The book is an important addition to the ‘les mathématiques mixtes’: representation lation, population dynamics, chemical literature on the highly topical quantum and communication by means of semi-arti- reactions, the 360° pendulum), version of the classical representation the- ficial ways of description. Various exam- 7. Mathematica and the Web, ory. (jtrl) ples of modelling are offered: car traffic, 8. Trouble-shooting (common problems, environment, finance, change of climate, common mistakes). H. M. Enzensberger, Zugbrücke ausser symbolic description of dancing, etc. The At the end there are two appendices: Betrieb, Drawbridge Up, A. K. Peters, Ltd., central notion here is that of a model and Solutions to the practice sets and Glossary Natick, 1999, 47 pp., £4, ISBN 1-56881- modelling, which enables engineers to use of commands, options, built-in functions 099-7 mathematics directly, not necessarily in the and selected standard packages. The style This booklet is written by the distinguished framework of traditional disciplines. The of explanation is learning by carefully cho- German poet and essayist Hans Magnus author also expresses his opinion on what sen examples. Chapter 6, in particular, Enzensberger. His first book for children mathematics should be taught future engi- demonstrates the power of Mathematica in (and for other thinking beings) called neers. The concluding chapter deals with various fields. The book is strongly recom- ‘The Number Devil’ (Metropolitan Books, modernity and post-modernity in mathe- mended for beginners and also for inter- N.Y. 1998 – translation from the German matics. mediate or experienced users who may dis- ‘Der Zahlenteufel: Ein Kopfkissenbuch für This book can be recommended to any- cover new features of Mathematica. (jh) alle, die Angst vor der Mathematik haben’, body who is interested in general and Carl Hanser Verlag, München 1997) is philosophical aspects of mathematics. R. Curtis and R. A. Wilson (eds.), The quite well known. Professional mathemati- Mathematicians surely appreciate that var- Atlas of Finite Groups: Ten Years On, cians are accustomed to live surrounded by ious philosophical concepts are document- London Mathematical Society Lecture Note people who declare with an odd sort of ed and explained by means of well-chosen Series 249, Cambridge University Press, pride that they are mathematically illiter- examples from mathematics. (in) Cambridge, 1998, 293 pp., £27.95, ISBN 0- ate. Enzensberger wishes to build a draw- 521-57587-7 bridge between these two groups and D. Bump, Automorphic Forms and This book is the proceedings of a confer- believes that progress in teaching is possi- EMS December 1999 37 RECENT BOOKS ble and that mathematics can be made Cambridge, 1999, 798 pp., £70, ISBN 0-521- Young measures here, except the last sec- exciting to young minds. Public attitudes 45125-6 tion where unbounded Rk-valued controls toward mathematics can be improved as This extensive monograph is a fundamen- are admitted, too. Finally, Chapter 14 mathematics is a part of the cultural tal contribution to optimal control theory develops a relaxation theory both for sphere. Drawbridge up is a ‘beautiful essay of evolution of finite- or infinite-dimen- abstract infinite dimensional systems and and a great delight for a mathematician to sional systems, and summarises and for concrete semi-linear parabolic or read’ says David Mumford in the preface. extends the author’s many decades of last- hyperbolic partial differential equations, (lbo) ing intensive research in this area. where often the controls range naturally a The first part (Chapters 1-4) deals with non-compact set, so that the generalised G. Farin, NURBS: From Projective ‘finite-dimensional control problems’, (i.e., finitely-additive) Young measures Geometry to Practical Use, A. K. Peters, Ltd., optimisation problems governed by initial- appear. Natick, 1999, 267 pp., £30, ISBN 1-56881- value problems for systems of (possibly Bibliographical comments accompany 084-9 non-linear) ordinary differential equa- each part. This outstanding monograph Today’s design technologies use sophisti- tions. Chapter 1 ‘Calculus of variations will be a great source both for experts and cated mathematical methods. Modelling and control theory’ contains motivating for graduate students interested in calculus complex objects such as ships, car bodies, examples. Chapter 2 deals with ‘Optimal of variations, non-linear programming, or airplane fuselages has given rise to tech- control problems without target condi- optimisation theory, optimal control, and niques known as Bézier curves and Coons tions’, starting from measure and integra- relaxation theory. (trou) methods. If we want to deal with the prob- tion theory and functional analysis, and lem of how we see things, the Euclidean then continuing with (non-)existence in D. Fowler, The Mathematics of Plato’s viewpoint is no more advantageous. A new classical optimal control problems, spike Academy, Clarendon Press, Oxford, 1999, tool called NURBS (non-uniform rational variations, minimum principle, 441 pp., £60, ISBN 0-19-850258-3 B-splines) appeared in 1975. A natural Hamiltonian formalism, and linear-qua- ‘The Mathematics of Plato’s Academy’ is an setting for it is projective geometry. dratic problems, including the feedback updated second edition of a well-known The book starts with a general outline of Riccati equation. Then Chapters 3 and 4 book devoted to early Greek mathematics. projective geometry. Conics are intro- deal with (time-)optimal control problems, The book is divided into three parts: duced through the classical projective def- both on an abstract level and on the level Interpretation, Evidence and Later develop- inition, first as line conics and then as of concrete examples. Here Ekeland’s ments. point conics. After Pascal’s and variational principle and the Kuhn-Tucker The first part (Chapters 1-5) presents a Brianchon’s theorems, the author presents theorem are the main tools used on the new interpretation of some mathematical conics in parametric form, conic splines abstract level. ideas and topics found in the works of and rational Bézier curves. Further chap- The second part (Chapters 5-11) is Plato, Aristotle, Euclid, Archimedes, etc. ters are devoted (e.g.) to rational cubics, devoted to ‘Infinite dimensional control The author shows that the methods, algo- NURBS curves and surfaces, rectangular problems’. Chapter 5, ‘Differential equa- rithms and procedures derived from their patches and Gregory patches. A chapter tions in Banach spaces and semigroup the- works had a great influence on the devel- on Pythagorean curves is incorporated in ory’ includes elements of functional analy- opment of early Greek mathematics. this second edition. The reader is assumed sis, the theory of the Lebesgue-Bochner Chapter 5 has been rewritten, while other to know linear algebra, calculus and basic integral, and (semi-)linear parabolic and chapters have many smaller additions, computer graphics. A significant feature hyperbolic partial differential equations as modifications and corrections. of the book is a large collection of exercis- abstract Cauchy problems using the semi- The second part (Chapters 6-7) es, both practical and theoretical, at the group approach. Chapters 6 and 7 treat describes the evidence forour knowledge end of each chapter. (lbo) abstract minimisation problems in Hilbert of Plato’s Academy, describing the trans- and Banach spaces, with various applica- mission of Greek texts to our time and G. Farin and D. Hansford, The Geometry tions to linear or semi-linear hyperbolic looking at the treatment of numbers and Toolbox for Graphics and Modeling, A. K. and parabolic control problems, respec- fractions. Peters, Ltd., Natick, 1998, 288 pp., £34, tively, deriving always the minimum prin- The third part (Chapters 8-11) ISBN 1-56881-074-1 ciple of Pontryagin’s type. Chapter 8 deals describes the development of continued The subject of this book is an investigation with interpolations and domains of frac- fractions since the seventeenth century. of basic concepts of analytic geometry in tional power with application to Sobolev- Chapter 10 (Appendix) introduces new the plane and three-dimensional space. It Slobodeckii spaces and parabolic equa- material that can be considered as a mod- approaches linear algebra from a geomet- tions, including Navier-Stokes equations. ern interpretation of Greek mathematics ric viewpoint. Many figures and hand- ‘Linear control systems’ forms Chapter 9, and the mathematical topics of Plato’s drawn sketches help to explain linear ana- including such special topics as bang-bang Academy. The new brief autobiographical lytic geometry (dot and cross product, theorems and controllability. Chapters 10 Epilogue, the new significantly expanded barycentric coordinates, affine maps, and 11 address ‘Optimal control problems Bibliography, the Index of cited passages, eigenvectors, etc.). Only the last chapter is with state constraints’, admitting (possibly the Index of names and the General index devoted to non-linear geometry, namely as only finitely additive) vector-valued mea- have been added to this second edition. an introduction to the theory of curves sures as the respective Lagrange multipli- (mbec) (parametric curves, Bézier curves, curva- ers. Suboptimal controls and their conver- ture and the Frenet frame). As an applica- gence are studied in detail. J. Glynn and T. Gray, The Beginner’s tion, the authors mention curves used to The third part (Chapters 12-14) deals Guide to Mathematica® Version 3, design cars (computer-aided geometric with ‘Relaxed controls’ which come into Cambridge University Press, Cambridge, 1997, design). The theoretical level is kept to a consideration if an original optimal con- 347 pp., ISBN 0-521-62202-6 and 0-521- minimum, and the emphasis of the book is trol problem lacks solutions. A unique the- 62734-6 not on abstract proofs but rather on exam- ory of ‘Spaces of relaxed controls’ forms This book serves both as a tutorial and as a ples and algorithms. The book can be rec- Chapter 12. Classical Young measures reference book. It is written as seventy ommended to students, and can serve also (i.e., parametrised probability Radon mea- short chapters in Question and Answer as a general introduction to geometry and sures) are only a particular case arising if form. It covers a variety of problems like to applications of linear algebra (e.g. controls range a metrisable compact. In the front end, symbolic and numerical cal- matrix theory) in geometry. (lbo) non-compact cases, a generalisation to cer- culation, typesetting, packages, graphics, tain finitely-additive probability measures Internet environment, and programming. H. O. Fattorini, Infinite Dimensional is made. Chapter 13 applies relaxed con- A lot of information contained in the book Optimization and Control Theory, trols to finite-dimensional evolution sys- may be found in the Mathematica help Encyclopedia of Mathematics and its tems. Original controls range a compact topics, and the style of presentation Applications 62, Cambridge University Press, set so that the relaxed controls are classical enables the Mathematica user (both the 38 EMS December 1999 RECENT BOOKS beginner and the advanced user) to get ties. There is also an interesting chapter will appeal to specialists in set theory, important pieces of information very containing a description of Witten’s con- mathematical analysis, measure theory and quickly. The book is strongly recommend- jectures and the Kontsevich theorem. general topology. It is also recommended ed not only to all Mathematica users but Deformation theory, stable reduction and as a textbook for postgraduate students. also to those who would like to learn how the Grothendieck-Riemann-Roch are (pp) to use the full capability of Mathematica. described in the second part of the book. (jh) The rest of the book contains a selection of Y. Kitaoka, Arithmetic of Quadratic Forms, contemporary results on the geometry of Cambridge Tracts in Mathematics 106, W. M. Goldman, Complex Hyperbolic moduli spaces. Cambridge University Press, Cambridge, 1999, Geometry, Oxford Mathematical Monographs, These theories are presented here in a 270 pp., £18.95, ISBN 0-521-40475-4 and Clarendon Press, Oxford, 1999, 316 pp., £65, very nice form, with examples and many 0-521-64996-X ISBN 0-19-853793-X exercises. The authors’ preference has The aim of this book is to provide an intro- This book is a very good introduction to been to focus on examples and applica- duction to the arithmetic theory of qua- the geometry of a complex hyperbolic tions rather than on theoretical founda- dratic forms. The book starts from the space and its boundary. It is accessible tions. This method seems to be very basics and proceeds to many recent results. even for undergraduate students. The appropriate for this topic. The book ends It covers several aspects of the subject author’s motivation was the need to have a with a rich bibliography. (jbu) including lattice theory, Siegel’s formula, well and systematically organised introduc- and tensor products of positively definite tory text on this subject - namely, it was A. B. Kharazishvili, Applications of Point quadratic forms. Quadratic forms are desirable to unify and ‘normalise’ exposi- Set Theory in Real Analysis, Mathematics mainly considered over the rationals or the tions which appeared mostly in various and Its Applications 429, Kluwer Academic ring of rational integers and their comple- journals. Anyhow, this book seems to be Publishers, Dordrecht, 1998, 236 pp., £66, tions. the first one that presents such a systemat- ISBN 0-7923-4979-2 The reader is required to have only an ic treatment. The author himself considers The main goal of this book is to demon- elementary knowledge of algebraic num- his book as a ‘user’s guide’ to complex strate the usefulness of set-theoretical ber fields. This makes the book ideal for hyperbolic geometry. His exposition uses methods in various questions of real analy- graduate students and researchers from minimal possible technical tools. He tries sis and classical measure theory. The book other fields interested in quadratic forms. to avoid references to general theorems is devoted to some results from classical (jtu) exceeding the framework of the complex point-set theory and their applications to hyperbolic geometry, and prefers to derive certain problems in mathematical analysis P. Koosis, Introduction to Hp spaces, results by concrete considerations and of the real line. Second Edition. Cambridge Tracts in computations; this is exactly the point that The author concentrates on the follow- Mathematics 115, Cambridge University Press, will surely be appreciated by an under- ing topics: Cambridge, 1998, 287 pp., £45, ISBN 0-521- graduate reader. His idea is to introduce (a) similarities and differences between 45521-9 the reader into geometry via concrete measure and category: many non-trivial The first edition of this book was published examples, and complex hyperbolic geome- examples and facts are presented in the in 1980. There is a Russian translation try suits this purpose well. book; that is accompanied by two appendices on In order to motivate the reader, the (b) set-theoretic, topological and algebraic Jones interpolation formula and weak author starts with a chapter that reviews aspects of the measure extension problem: completness of the factor L1/H1(0), written the complex 1-dimensional geometries. in particular, there are applications of by V. P. Havin; these appendices are They are presented in such a manner that Ershov’s measure extension theorem to the reproduced in the new edition. There are they suggest generalisations to higher classical property of Luzin and to the also some other changes, but they do not dimensions. The next chapter deals with uniqueness property of invariant mea- alter the spirit of the first edition. the relevant linear algebra and necessary sures; The contents of the book can be divided notions from differential geometry. Then (c) various constructions of Lebesgue non- into two parts. The first part, consisting of we come to the main parts of the book. measurable sets and of sets without the Chapters I-VI is devoted to basic informa- The author presents the complex n-dimen- Baire property: some connections between tion on the Hilbert transform and the sional hyperbolic space first in the form of these constructions and infinite combina- Hardy spaces Hp for the disk and the the unit ball model (in Cn) and then in the torics (namely, the Ulam matrix) and the upper half-plane. Here the author uses form of the paraboloid (or Siegel domain) general theory of commutative groups are the so-called ‘complex function methods’, model. We remark explicitly that the indicated; but some key results (such as the Riesz author also devotes systematic attention to (d) various singular objects in mathemati- brothers’ theorem on analytic measures the geometry of the boundary of the com- cal analysis from the point of view of the and the M. Riesz theorem on Lp bounded- plex hyperbolic space. It is here where the Kuratowski-Ulam theorem: in particular, it ness of the Hilbert transform) have several Heisenberg geometry appears. He pre- is established that the classical principle of proofs. sents old results (usually in more modern condensation of singularities follows The second part contains deeper and elegant way) as well as quite recent directly from the above-mentioned theo- results. The duals of Hp and Hp-best ones. There are many interesting exercis- rem; approximation of Lp-functions are investi- es that substantially enrich the main text, (e) geometrical properties of certain sub- gated in Chapter VII. The characterisa- and many nice pictures. The bibliography sets of an abstract space E, equipped with a tion of ReH1 based on the Hardy- contains 175 items and goes up to 1998. group G of its transformations: first, the Littlewood maximal functions is discussed (jiva) so-called G-thick sets, G-scattered sets, G- in Chapter VIII. Interpolation results for thin sets, G-negligible sets and absolutely Hp-functions (Carleson and Shapiro- J. Harris and I. Morrison, Moduli of G-negligible sets, and several relationships Shields theorems) and for bounded har- curves, Graduate Texts in Mathematics 187, between these properties, the theory of monic functions (Garnett theorem) are Springer, New York, 1998, 366 pp., DM118, invariant (quasi-invariant) measures and proved in Chapter IX. Chapter X is devot- ISBN 0-387-98438-0 and 0-387-98429-1 the general theory of G-equidecomposabil- ed to functions of bounded mean oscilla- The main topic of this book is a descrip- ity of sets are thoroughly considered; tion (two proofs of the Fefferman repre- tion of the properties of moduli spaces of (f) some set-theoretical aspects of the theo- sentation of the dual of ReH1(0) are pre- algebraic curves. This subject has grown ry of differential equations, concerning the sented); the main changes with respect to rapidly in the last few years. In the first existence and uniqueness of solutions of the first edition are in this chapter. The part, there is a short summary of basic facts such equations. Wolff’s proof of the Carleson corona theo- concerning moduli and parameter spaces The material presented in this book is rem is given in the last chapter. of curves, Hilbert schemas, the space Mg essentially self-contained and is accessible This book is written chiefly for graduate and its geometric and topological proper- to a wide audience of mathematicians. It students with a working knowledge of real EMS December 1999 39 RECENT BOOKS and complex function theory, and contains The fifth chapter consists of some com- hyperbolic plane geometry and hyperbolic many valuable comments on ideas and ments beyond the Mandelbrot 1963 surfaces. But for the reader’s convenience, techniques of proofs. The use of different model. and also as motivation, the authors include typographical forms also helps to clarify This book is recommended to any Chapter 0, a summary about hyperbolic complicated proofs. (jmil) mathematician and/or financial analyst surfaces and Fuchsian groups. Then, from who wishes to learn more about the variety Chapter 1, the reader is presented with all M. Kracht, M. de Rijke, H. Wansing and of alternative models and to avoid using the necessary details. This means that M. Zakharyaschev (eds.), Advances in just the classical methods. (jh) even 3-dimensional hyperbolic space is Modal Logic 1, CSLI Publications, Stanford, introduced and three of its models are 1998, 392 pp., £15.95, ISBN 1-575-86102- P. Marage and G. Wallenborn (eds), The carefully studied. Then hyperbolic 3-man- X and 1-575-86103-8 Solvay Councils and the Birth of Modern ifolds are defined and the Kleinian groups The first conference in the Advances in Physics, Historical Studies, Science Networks appear as the universal covering transfor- Modal Logic (AiML) conference series was 22, Birkhäuser, Basel, 1999, 224 pp., mation groups of their universal covering, held at the Free University of Berlin in DM118, ISBN 3-7643-5705-3 and 0-8176- 3-dimensional hyperbolic space. Chapters October 1996. AiML is also a forum, 5705-3 2, 3 and 4 deal directly with the Kleinian established in 1995, for scientists working The Solvay Councils, held in Brussels since groups. Special attention is devoted to in various areas of modal logic and its 1911 following an initiative of the Belgian geometrically finite and finitely generated applications. The book contains 21 papers industrialist E. Solvay, played an essential Kleinian groups. But even Chapter 5, ‘The in the field. The book covers a large spec- role in forming the paradigm of modern sphere at infinity’, studies the actions of trum of topics, offering results on the physics. Organised as a series of meetings Kleinian groups on this sphere and mathematics of modal logic, proof-theoret- of the most distinguished physicists of that describes how the hyperbolic geometry is ical properties, theoretical and applied time, the Councils provided ground for the mirrored by this sphere. Chapter 6 is computer science, applications in knowl- constitution of new physics beyond ‘classi- about the ends of hyperbolic manifolds edge representation, philosophy and lin- cal’ mechanics and field theory, of the and the final chapter studies algebraic and guistics. We find here contributions on quantum theory of matter and radiation. geometric convergence of Kleinian groups. terminological modal logic, hybrid lan- Reports of the Councils, at least of those A short appendix is devoted to the guages, topological next-time logic, mini- before the Second World War, can be read Thurston uniformisation theorem. mal knowledge states in non-monotonic as a detective story on how the contempo- The presentation of the whole theory is modal logics and relations between models rary knowledge of atoms, atomic nuclei, very nice; we find here many concrete and parallel computations. The papers and subatomic particles came into being examples and interesting remarks. Simply, motivate the field and review basic notions through a brilliant stroke of experiments the book reads well, and will be interesting and facts. A subject index is included. The and seemingly bizarre hypotheses, often and accessible for mathematicians from book can be seen as a good and represen- inspired by vivid discussions at the several branches of mathematics. The lit- tative source of information concerning Councils. The book ‘tells the story’ of the erature has 108 items and goes up to 1997. research in the subject. It is accessible to Councils, together with short explanations (jiva) advanced students in non-classical logic. of the necessary physical background, so (jmlc) that it is useful not only for physicists (who G. Navarro, Characters and Blocks of will find here historical facts that are often Finite Groups, London Mathematical Society K. Leichtweiss, Affine Geometry of oversimplified in physics textbooks), but Lecture Note Series 250, Cambridge University Convex Bodies, Johann Ambrosius Barth also for scientists of non-physical areas and Press, Cambridge, 1998, 287 pp., £24.95, Verlag, Heidelberg, 1998, 310 pp., DM148, the broad public seeking reliable informa- ISBN 0-521-59513-4 ISBN 3-335-00514-7 tion on the birth of quantum mechanics. This book presents an account of the theo- The author presents a systematic The text is based on the Brussels 1995 ry of Brauer (alias modular) characters and equiaffine theory of convex bodies, and exhibition and conference devoted to the blocks for finite groups. The motivating stresses connections and differences from Solvay Councils, and contains (besides a result for the first part of the book is the the convex geometry in Euclidean spaces. description of the most important Councils Z*-theorem of G. Glauberman which is one Special attention is paid to the definition before the Second World War) contribu- of the main applications of modular repre- of the affine surface area and to a compar- tions dealing with the role of some person- sentation theory to finite groups. The first ison of the author’s definition with other alities in the science of that period and the chapters develop the theory and include ones. Some generalisations of classical historical and sociological background. It the main theorems of R. Brauer. After inequalities from convex geometry (such as is worth mentioning that the book contains proving the Z*-theorem, the author con- the isoperimetric inequality) to the affine excellent and not commonly known pho- centrates on p-solvable groups and, finally, case are also presented. (jrat) tographs of the most influential Council on the groups with Sylow p-group of order participants. The book is recommended to p and description of their p-blocks. B. R. Mandelbrot, Fractals and Scaling in all who are interested in the fascinating This book can be used by both graduate Finance, Springer-Verlag, New York, 1997, development of physics in the 20th centu- students and researchers interested in 551 pp., ISBN 0-387-98363-5 ry. (pc) modular representation theory of finite This book presents an alternative groups. Its style is accessible and includes approach to the analysis of financial data, K. Matsuzaki and M. Taniguchi, some recent results. At the end of each or more generally, to any data set possess- Hyperbolic Manifolds and Kleinian chapter is a set of open problems. (rb) ing features like financial time series. Groups, Oxford Mathematical Monographs, Approximately half of the book consists of Clarendon Press, Oxford, 1998, 253 pp., £60, J. A. Nohel and D. H. Sattinger (eds.), the author’s contributions to various prob- ISBN 0-198-50062-9 Selected Papers of Norman Levinson, 2 lems from the last 40 years in the form of This book is a revised and enlarged trans- vols., Contemporary Mathematicians, preprints from journals (together with con- lation of a book by the same authors which Birkhäuser, Boston, 1998, 1152 pp., DM976, tributions of other authors related to the appeared in 1993 in Japanese. It is devot- ISBN 3-764-33862-8 and 3-764-33979-9 topic), while the remaining half is com- ed to the study of hyperbolic 3-manifolds This selection reflects Levinson’s contribu- pletely new. The key concept in the book and Kleinian groups, which since 1980 tion to complex, harmonic and stochastic is scaling. have attracted much attention. The book analysis, to differential and integral equa- The first two chapters are devoted both starts from the very beginning of hyperbol- tions, and to analytic number theory. His to non-mathematical and mathematical ic geometry and leads the reader up to list of publications contains 124 items, of presentations. The third chapter deals contemporary research. Its prerequisites which 76 are reproduced in this collection. with personal incomes and firm sizes. The are rather modest. Practically, it requires Each section contains a complete list of fourth chapter describes and illustrates the only basic knowledge of geometry, algebra papers covering the topic of the section Mandelbrot 1963 model of price variation. and analysis, and some familiarity with and commentaries written by B. Conrey, B. 40 EMS December 1999 RECENT BOOKS Levitan, J. Moser, J. Nohel, M. Pinsky, A. approximation theory are used. equations. The authors use a practical Radakrishnan, R. Redheffer, D. Sattinger, Consequently, important results are approach based upon solving model ellip- H. Sussman and E. Zeidler. Photos from obtained for the geometry of (infinite- tic, parabolic, hyperbolic and convection- various periods of his life can be found in dimensional) Banach spaces. The presen- diffusion problems, and all ideas are intro- both volumes. Finally, personal tributes by tation is self-contained and, due to its duced from this viewpoint. The text con- H. McKean, W. T. Martin, B. Konstant and interdisciplinary character, should attract tains solved exercises as a bridge from the his wife Zipporah (Fagi) complete the pic- the attention of a wide group of mathe- theory to the applications. (jfel) ture about his life and personality, helping maticians. (jrat) those of us who never had an opportunity Y. B. Rudyak, On Thom Spectra, to meet him. B. Polster, A Geometrical Picture Book, Orientability, and Cobordism, Springer The first volume is devoted to the fol- Universitext, Springer, New York, 1998, 291 Monographs in Mathematics, Springer-Verlag, lowing topics: stability and asymptotic pp., DM98, ISBN 0-387-98437-2 Berlin, 1998, 587 pp., DM198, ISBN 3-540- behaviour of solutions of ordinary differ- Pictures are what this book is all about. 62043-5 ential equations, non-linear oscillations They illustrate various kinds of geometry, This is a fundamental monograph on the and dynamical systems, inverse problems such as incidence structures, affine and topics in the title, written by an author who for Sturm-Liouville and Schrödinger oper- projective planes and spaces, linear spaces, has substantially contributed to the subject. ators, eigenfunction expansions and spec- designs, circle planes, generalised poly- It contains a relatively large amount of tral theory for ordinary differential equa- gons, etc. material, even in comparison with older tions, singular perturbations of ordinary The book is divided into two parts. The books on these subjects. (This can be and partial differential equations, elliptic first part presents pictures of finite geome- already seen from the number of pages.) A partial differential equations and integral tries with small numbers of points, the sec- great deal of material cannot be found in equations. ond part contains pictures of topological any other monograph. The main topics The second volume treats harmonic and geometries, mainly those that live on sur- here are spectra and (co)homology theo- complex analysis, stochastic analysis, ele- faces. Each chapter contains definitions, a ries, with special emphasis on the (co)bor- mentary number theory and the prime minimum of theory, and references to text- dism theories. We note that two chapters number theorem, the Riemann zeta-func- books and survey articles. The book is are devoted to the (co)bordism with singu- tion and miscellaneous topics. (špor) addressed at advanced undergraduates larities, and that there is a chapter about and graduate students. (lbo) the phantom maps and a chapter about B. Novák (ed.), Life and Work of Vojtì ch orientability with respect to cohomology Jarník, Society of Czech Mathematicians and A. D. Polyanin and A. V. Manzhirov, theories. Physicists, Prometheus, Praha, 1999, 197 pp., Handbook of Integral Equations, CRC The book is indispensable for research ISBN 80-7196-156-6 Press, Boca Raton, 1998, 787 pp., DM228, workers in algebraic topology. The pre- Vojtì ch Jarník (1897-1970) was one of ISBN 0-8493-2876-4 sentation of the material is very nice and leading personalities of Czechoslovak In this book, more than 2100 integral thorough, and this makes the book conve- mathematics of the 20th century. His pre- equations with solutions are given. New nient for students with preliminary knowl- cise style of writing, both in his famous exact solutions to many linear and non-lin- edge of algebraic topology. The book is series of books on analysis and in his own ear equations are included. Special atten- not self-contained, because this would research work, heavily influenced many tion is paid to equations of general form enlarge its size still further. But whenever generations of mathematicians in that depend on arbitrary functions. Other the author decides not to introduce a Czechoslovakia. equations contain one or more free para- notion or present a proof, he gives an ade- Besides biographical articles, personal metrs. The number of equations described quate reference. The beginner will espe- recollections and articles on his pedagogi- in the book is of an order of magnitude cially appreciate the author’s historical cal activities, the book contains a descrip- greater than in other available books. remarks that help one understand the ori- tion of Jarník’s research contribution to Equations considered here appear in vari- gins and spirit of the theory. But even diophantine approximations (by M. ous fields of mechanics and theoretical from a formal point of view the author tries Dodson), geometry of numbers (by P. physics (elasticity, plasticity, hydrodynam- to make the reading as easy as possible. Gruber), combinatorial optimisation (by B. ics, heat and mass transfer, electrodynam- The list of notations is carefully arranged Korte and J. Nešetøil), real analysis (by D. ics, etc.). The second part contains exact into several groups, which enables quick Preiss) and lattice theory (by B. Novák). and approximate analytical and numerical orientation. The references extend to 18 These contributions show the continuing methods for solving linear and non-linear pages. (jiva) impact of Jarník’s ideas in number theory integral equations. and real analysis up to the present time. The handbook has no analogue in the G. Sambin and J. Smith, Twenty-Five The last 85 pages contain 7 selected papers literature and is intended for a wide audi- Years of Constructive Type Theory, Oxford of Jarník, including his pioneering paper ence of researchers, college and university Logic Guides 36, Clarendon Press, Oxford, on Hausdorff measure and diophantine teachers, engineers, and students in the 1998, 283 pp., ISBN 0-19-850127-7 approximations and his bibliography. (vs) various fields of mathematics, mechanics, Beginning in 1970, Per Martin-Løf has physics, chemistry, and queueing theory. developed a constructive foundation of G. Pisier, The Volume of Convex Bodies (mbr) mathematics which he called intuitionistic and Banach Space Geometry, Cambridge type theory. On the occasion of the 25th Tracts in Mathematics 94, Cambridge J. Rappaz and M. Picasso, Introduction à anniversary, a special conference on the University Press, Cambridge, 1999, 250 pp., l’analyse numérique, Presses Polytechniques et subject took place and it was decided to £17.95, ISBN 0-521-36465-5 and 0-521- Universitaires Romandes, Lausanne, 1998, publish the proceedings without restricting 66635-X 256 pp., sFr62, ISBN 2-880-74363-X contributions to participants of the confer- The classical Dvoretzky’s Theorem relates This book is aimed at undergraduate engi- ence. Thus, among others, it contains one the analytic properties of Banach spaces to neering and science students who need a of the first preprints of Martin-Løf (1971) the geometry of its finite dimensional sub- readable textbook on numerical mathe- on the subject. It is published here for the spaces. This book presents some recent matics. It presents a comprehensive first time. results of a similar nature. The basic tools description of the fundamental tools for Type theory has increasing applications are various (classical and recent) inequali- numerical solutions of ordinary and partial to a variety of fields like constructive math- ties for volumes of convex bodies in finite- differential equations. The text is centred ematics, logic, computer science, linguis- dimensional Euclidean spaces, such as the around those topics that form the essen- tics etc. Fourteen remaining papers in the (inverse) Brunn-Minkowski inequality or tials of the finite-difference and finite-ele- proceedings cover many of these applica- the (inverse) Santaló inequality. Besides ment method: polynomial interpolation, tions. The book presents a good survey of the classical methods of convex geometry, numerical differentiation and integration, the current state of the subject. (ak) the techniques of Gaussian processes and solution of linear and non-linear algebraic EMS December 1999 41 RECENT BOOKS

A. Scott, Nonlinear Science: Emergence bility theory, its role in the theory of quasi- EMS Newsletter Index for 1999 and Dynamics of Coherent Structures, conformal mappings, and special classes of Oxford Applied and Engineering Mathematics solutions of first-order elliptic systems. 1, Oxford University Press, Oxford, 1999, 474 The reader is expected to have a good Editorials pp., £39.95, ISBN 0-19-850107-2 knowledge of basic functional analysis, dis- Rolf Jeltsch (EMS President) 31-3 Originally prepared as notes for courses tribution theory, function theory and par- Luc Lemaire (EMS Vice-President) 32-3 presented to advanced undergraduates at tial differential equations (pseudo-differ- Andrzej Pelczar (EMS Vice-President) 33-3 the Technical University of Denmark, this ential operators). This comprehensive text David Brannan (EMS Secretary) 34-3 book is designed as an introduction to the (479 pp.) provides rich material that may Introducing . . . study of non-linear partial and difference- be used in specialised seminars. (jokr) the Committee 31-5, 32-5 differential equations. the Editorial team 33-5, 34-7 It starts with a description of the histor- M. Yamaguti, M. Hata and J. Kigami, EMS News ical development of non-linear models. Mathematics of Fractals, Translations of Executive Committee Meetings (Barcelona The reader is supposed to have a basic Mathematical Monographs 167, American and Zurich) 32-6, 34-8 knowledge of physical notions and of the Mathematical Society, Providence, Rhode 3rd European Congress of Mathematics 31-7, linear theory (Fourier transform, stability, Island, 1997, 78 pp., £19.50, ISBN 0-821- 34-12 scattering theory), although the latter is 80537-1 World Mathematical Year 31-15, 34-11 briefly reviewed in an introductory chap- The translation of the Japanese original EMS Summer Schools: Call for proposals ter. In the main part of the book are pre- starts with the basic concepts concerning 32-11 sented classical soliton equations fractals (dimension, Hausdorff measures Fourth Diderot Mathematical Forum: (Korteveg-de Vries, sine-Gordon, non-lin- and dimension, etc.). The self-similarity is Mathematics and Music 33-4 ear Schrödinger), non-linear diffusion described with many nice examples and Felix Klein Prize 34-10 equations (Fisher, Hodgkin-Huxley, Fitz- relations to nowhere-differentiable func- Feature articles Hugh-Nagumo), non-linear lattices (here tions and the Takagi function are present- John Fauvel: Caring for the mathematical the spatial variable takes its values in a lat- ed. Some problems concerning wavelets past 31-10 tice of points), and their exact solutions are also treated. The final chapter is con- Ian Stewart: Making the magical maze 32-7 (travelling waves, solitons) are discussed. cerned with some equations of mathemati- Short articles The Bäcklund transform and the inverse cal physics (Laplace’s equation, Gauss- Mathematics in Eastern Europe (Peter scattering method are explained by means Green formula, Poisson equation, Michor) 31.16 of examples, as well as being generally for- Dirichlet problem, etc.) on sets having a Obituary of André Weil (Jeremy Gray) 31-22 mulated. A discussion of perturbations fractal character. The book is a good Oxford Doctorate for Andrew Wiles 33-7 and quantum lattice solitons is also includ- introduction to the topic. Interesting A Universal Mathematical Resource Locator? ed. The final chapter is a personal view on applications are presented. (ss) (Alain Damlamian) 33-12 future directions of research in applied sci- ence. The presentation in the book is Interviews based on concrete equations and the for- Robert M. Mattheij 31-13 mulas are often derived from physical intu- Helmut Neunzert 32-10 ition. There are no definitions and theo- List of reviewers for 1999 Tim Gowers 33-8 rems. Much attention is paid to the physi- The Editor would like to thank the follow- Jan van Maanen 34-16 cal, biological or chemical context. (efa) ing for their reviews this year: Olaus Nevanlinna 34-18 J. Andì l, R. Bashir, J. Beèváø, L. Beran, Ian Frigaard 34-19 N. N. Tarkhanov, The Analysis of L. Bican, L. Boèek, M. Brzezina, J. Bureš, Societies Solutions of Elliptic Equations, Mathematics M. Èadek, P. Èejnar, K. Cuda, A. Drápal, The Union of Bulgarian Mathematicians and its Applications 406, Kluwer Academic E. Fašangová, M. Feistauer, J. Felcman, 31-20 Publishers, Dordrecht, 1997, 479 pp., £146, D. Hlubinka, P. Holický, J. Hurt, London Mathematical Society: De Morgan ISBN 0-7932-4531-1 M. Hušek, J. Jelínek, O. John, House 31-21 This book includes a broad analysis of gen- J. Jureèková, T. Kepka, M. Klazar, Finnish Mathematical Society 32-16 eral elliptic systems of differential equa- O. Kowalski, A. Kuèera, J. Král, M. Lichá, Polish Mathematical Society 32-17 tions. It starts with singularities of solu- M. Loebl, J. Lukeš, J. Malý, J. Milota, Swiss Mathematical Society 33-18 tions and their removability. Several J. Mlèek, K. Najzar, M. Nì mcová- Edinburgh Mathematical Society 33-20 results illustrate the role of adequate Beèváøová, J. Nešetøil, I. Netuka, Luxembourg Mathematical Society 34-26 capacities, as well as the Hausdorff mea- S. Porubský, P. Pyrih, J. Rataj, M. Rokyta, Kharkov Mathematical Society 34-26 sures and Minkowski’s content, in estimat- T. Roubíèek, Š. Schwabik, J. Slovák, 1999 anniversaries ing the size of singular sets. Parallels with J. Souèek, V. Souèek, J. Štì pán, J. Trlifaj, Maria Agnesi (June Barrow-Green) 31-18 the development of the theory of functions V. Trnková, J. Troják, J. Tùma, P. Valtr, Hilbert’s Grundlagen der Geometrie (Jeremy of complex variables are underlined. The J. Vanžura, J. Veselý, M. Zahradník, Gray) 31-19 Laurent series for solutions of homoge- L. Zajíèek, J. Zichová, V. Zizler, J. Žemliè- Felix Klein & Sophus Lie (Jeremy Gray) 32-12 neous elliptic systems and an investigation ka. Wolfgang Krull (Jeremy Gray) 32-13 of appropriate expansions of solutions may All of the above are on the staff of the Caspar Wessel (Bodil Branner) 33-13 serve as an example; another such topic is Charles University, Faculty of Mathematics E. C. Titchmarsh (Robin Wilson) 33-16 the theory of uniform approximation by and Physics, Prague, except: Laplace’s & Poincare’s Mécanique céleste holomorphic functions, which stimulated M. Èadek and J. Slovák (Masaryk (June Barrow-Green) 34-20 the study of questions concerning uniform University, Faculty of Natural Sciences, Otto Neugebauer (Jeremy Gray) 34-22 approximation by solutions of general sys- Brno), J. Král, Š. Schwabik and J. Vanžura Oscar Zariski (Jeremy Gray) 34-23 tems of differential equations. While the (Mathematical Institute, Czech Academy of Conferences problem of uniform approximation has a Sciences), Š. Porubský (Technical Oberwolfach programme 2000 31-23 long history, investigation of the mean University, Prague). Forthcoming conferences (Kathleen Quinn) approximation has begun comparatively 31-25, 32-23, 33-22, 34-29 recently. There is also a chapter that ICIAM in Edinburgh (Rolf Jeltsch) 33-10 includes a discussion of how approxima- SIAM/EMS Joint Conference on tion within BMO may be seen as interme- Computational Science (Gil Strang) 33-11 diate between the approximation theories Book reviews in uniform and in Sobolev norms. Other Editor’s note: We regret that the Problem Recent books (Ivan Netuka & Vladimír themes treated in the book include solv- Corner, due for publication in this issue, Soucek) 31-31, 32-29, 33-26, 34-35 ability of the Cauchy problem and the sta- has had to be held over to the March issue. Book review by Sir Michael Atiyah 32-28 42 EMS December 1999 PERSONAL COLUMN PPersonalersonal ColumnColumn

This is a new venture. We list below informa- Robin Wilson has been appointed a an Honorary Fellow of the Institute of tion about some appointments, awards and Fellow by Special Election at Keble Mathematics and its Applications. deaths that have occurred during 1999. Since College, Oxford University. this list is inevitably incomplete (containing Helge Kristian Jenssen (Trondheim) has mainly UK items) we invite you to send appro- Awards been awarded the Esso Young Researcher priate information from other countries to the Prize for the best NTNU (Trondheim ) Editor [[email protected]] or to your Ph.D. thesis. Country representative (see page 15) for inclu- Sir Michael Atiyah has been awarded an sion in the next issue. Please also send items for Honorary Doctorate at Heriot-Watt Christine Keltel-Kreidt (Berlin) has been inclusion in the 2000 Personal Columns. University, Edinburgh. awarded an Honorary Doctorate at the University of Chichester. Appointments Alan Baker (Cambridge) has been award- ed an Honorary Doctorate in Strasbourg. Adam McBride (Strathclyde) received the Order of the British Empire for services to Sir Michael Atiyah and Ioan James have John Ball (Oxford) has been awarded a mathematics in schools. been elected to Honorary Fellowships at Theodore von Kármán Prize by the Society New College, Oxford University. for Industrial and Applied Mathematics Sir Roger Penrose (Oxford) has been (SIAM). awarded an Emeritus fellowship by the David Brannan has been re-elected Dean Leverhulme Trust. of Mathematics at the Open University, Arrigo Bonisoli (Potenza) and Marco UK. Buratti (Penigia) have been awarded the Mike Powell (Cambridge) has been award- Hall Medal by the Institute of ed the Senior Whitehead Prize by the Terry Griggs and Mike Grannell have Combinatorics and its Applications. London Mathematical Society. been appointed Research Fellows. Barbara Maenhaut (Queensland), Toby O’Neil Martin Bridson (Oxford), Gero Friesecke John Rognes (Oslo) has been awarded the (Edinburgh), Kathleen Quinn and Steven (Oxford), Nicholas Higham (Manchester) 1999 Dals Research Prize for research in Vickers (London) have been appointed and Imre Leader (London) have been K-theory. Lecturers in Mathematics. awarded Senior Whitehead Prizes by the London Mathematical Society. Tomás Roubí³ek (Prague) has been Christopher Campbell, Sarah Rees and awarded the prize of the Minister of Anvar Shukurov have been promoted to David Burns (London) has been awarded Education of the Czech Republic. Readerships at Newcastle University, and the Junior Berwick Prize by the London A.M. Constantin, M.A. Dritschel and Mathematical Society. Caroline Series (Warwick) has been award- G. Sarson have been appointed to lecture- ed an EPSRC Senior Research Fellowship. ships. David Crighton (Cambridge) has been awarded an Honorary Doctorate at Jaromír Šimša (Prague) has been awarded Philip Candelas (Texas) has been appoint- UMIST, Manchester. the Prize of the Czech Academy of Sciences ed Rouse Ball Professor of Mathematics, for the popularisation of mathematics. Oxford University, succeeding Roger Simon Donaldson (London) has been Penrose. awarded the 1999 Polya Prize by the John Tate (Austin, Texas) has been elected London Mathematical Society. an Honorary Member of the London S. J. Chapman has been appointed to the Mathematical Society. Chair of Mathematics and its Applications, George A. Elliott (Copenhagen and Oxford University, from 1 July 1999. Toronto) has received the John L. Synge Andrew Wiles has been awarded an Award for applied mathematics. Honorary Doctorate at Oxford University. Boris Zilber (Kemerovo) has been appointed to the Chair of Mathematical Ali Fröhlich (Cambridge) has been award- Deaths Logic, Oxford University, from 1 October ed an Honorary Doctorate at the 1999. University of Bristol. We regret to announce the deaths of: David Draper has been promoted to Tim Gowers (Cambridge), John Ernest Albasiny (18 July) Professor of Statistics at the University of Ockendon (Oxford), William Stirling Jiøi Be³vár (25 January) Bath. (Durham) and John Toland (Bath) have Roland Clark (28 July) been elected Fellows of the Royal Society Sir Wilfred Cockcroft (27 September) Noel Lloyd, Professor of Mathematics at of London. Walter Deuber (16 July) the University of Wales (Aberystwyth) has Albert Green (12 August) been appointed Registrar and secretary of Stephen Hawking (Cambridge) has Jack Howlett (5 May) the University. received the Albert Medal from the Royal Johann Leicht (14 May) Society of Arts. Sir William McCrea (25 April) Terence Lyons (London) has been Josef Novák (20 August) appointed to the Wallis Chair of Anthony Hilton (Reading) has been Vlastimil Pták (9 May) Mathematics, Oxford University, from 2 awarded the 1999 Euler Medal by the Werner Raffke (11 May) April 2000, succeeding Simon Donaldson. Institute of Combinatorics and its Gian-Carlo Rota (19 April) Applications for distinguished research in Zbyñek Sidák (12 November) Roger Penrose has been appointed combinatorics. Christine Shiu (16 October) Gresham Professor of Geometry, in Helmut Titze (30 March) London, succeeding Ian Stewart. Robert Hiorns (Oxford) has been elected Jürgen Weishaupt (29 July) EMS December 1999 43