Martin aussen and Christian Skau, Editors Interviews with the Abel Prize Laureates 2003–2016 Interviews with the Abel Prize Laureates 2003–2016 Martin Raussen Christian Skau Editors The Abel Prize was established in 2002 by the Norwegian Ministry of Education and Research. It has been awarded annually to mathe- maticians in recognition of pioneering scientific achievements. Interviews with the Since the first occasion in 2003, Martin aussen and Christian Skau have had the opportunity to conduct extensive interviews with the Abel Prize Laureates laureates. The interviews were broadcast by Norwegian television; moreover, they have appeared in the membership journals of several mathematical societies. 2003–2016 The interviews from the period 2003 – 2016 have now been collected in this edition. They highlight the mathematical achievements of the laureates in a historical perspective and they try to unravel the way in Martin Raussen which the world’s most famous mathematicians conceive and judge Christian Skau their results, how they collaborate with peers and students, and how they perceive the importance of mathematics for society. Editors ISBN 978-3-03719-177-4 www.ems-ph.org Raussen/Skau | Fonts: Helvetica Neue | Farben: Pantone 116, Pantone 287, Cyan | RB 15.1 mm Interviews with the Abel Prize Laureates 2003–2016 Martin Raussen Christian Skau Editors Editors: Martin Raussen Christian Skau Department of Mathematical Sciences Department of Mathematical Sciences Aalborg University Norwegian University of Science and Technology Skjernvej 4A 7491 Trondheim 9220 Aalborg Norway Denmark E-mail: [email protected] E-mail: [email protected] 2010 Mathematics Subject Classification: 01A70. 01A60, 01A61, 01A80, 00A35 Key words: Abel prize, laureates, interviews, history of mathematics, appreciation of mathematics ISBN 978-3-03719-177-4 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliogra- phy, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2017 European Mathematical Society Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum SEW A21 8092 Zürich Switzerland E-mail: [email protected] Homepage: www.ems-ph.org Typeset by Sylvia Lotrovsky, Basel, and Christoph Eyrich, Berlin Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany ∞ Printed on acid free paper 9 8 7 6 5 4 3 2 1 Table of Contents Preface ............................................................................................................................................................................................... vii Introduction ................................................................................................................................................................................ ix Abel Prize 2003: Jean-Pierre Serre ..................................................................................................................... 1 Abel Prize 2004: Sir Michael Francis Atiyah and Isadore M. Singer ............................ 11 Abel Prize 2005: Peter D. Lax .................................................................................................................................. 31 Abel Prize 2006: Lennart Carleson .................................................................................................................... 47 Abel Prize 2007: Srinivasa S. R. Varadhan ................................................................................................. 61 Abel Prize 2008: John Griggs Thompson and Jacques Tits ..................................................... 79 Abel Prize 2009: Mikhail Gromov ...................................................................................................................... 97 Abel Prize 2010: John Tate .......................................................................................................................................... 123 Abel Prize 2011: John Milnor .................................................................................................................................. 141 Abel Prize 2012: Endre Szemerédi ..................................................................................................................... 161 Abel Prize 2013: Pierre Deligne ............................................................................................................................. 183 Abel Prize 2014: Yakov G. Sinai ............................................................................................................................ 201 Abel Prize 2015: John F. Nash, Jr. and Louis Nirenberg ............................................................. 219 Abel Prize 2016: Sir Andrew J. Wiles .............................................................................................................. 245 An Imaginary Interview with Niels Henrik Abel .............................................................................. 267 v Preface The Abel Prize is an international prize established in 2002 by the Norwegian Min- istry of Education and Research and is administered through an annual grant by the Norwegian Academy of Science and Letters. It is awarded every year in recognition of pioneering scientific achievements in mathematics. The year 2002 marked the bicentennial of Nils Henrik Abel’s birth and the prize was established in honour of his exceptional mathematical heritage. The Abel Prize is also meant to promote the field of mathematics and to make the prize winners and their work known to the public. Every year from 2003 until 2016, the Abel Prize laureates have been interviewed by Martin Raussen and Christian Skau in connection with the award ceremony. These interviews have been broadcast on Norwegian national television (and of- ten repeated) and can be streamed from the Abel Prize website, www.abelprize.no. Transcripts of the interviews have been published in the EMS Newsletter and the Notices of the AMS. This book is a collection of the interviews, with a new intro- duction by the interviewers. The Abel Board and the Norwegian Academy of Science and Letters would here- by like to express our gratitude to Martin Raussen and Christian Skau for conduct- ing the Abel interviews and for preparing their transcripts for publication in this book, thus making them available to a broad audience in printed form that has proven its durability. Autobiographical pieces by the laureates and descriptions of their work by fellow mathematicians are published by Springer in volumes entitled “The Abel Prize”, ed- ited by Helge Holden and Ragni Piene. Ole M Sejersted Kristian Ranestad President Chairman Norwegian Academy of Science and Letters Abel Board vii Introduction How it all started: the first interview in 2003 The Abel Prize was established by the Norwegian government in 2002 on the occa- sion of the 200th anniversary of Niels Henrik Abel's birth. Its main aim was to recognise contributions to mathematics of extraordinary depth and influence. An Abel Committee consisting of five prominent mathematicians had the difficult task of selecting the first Abel laureate for 2003. In March of that year, its chair Erling Størmer announced the committee’s decision to award the first Abel Prize to Jean- Pierre Serre, Emeritus Professor at the Collège de France in Paris, to be honoured “for playing a key role in shaping the modern form of many parts of mathematics, including topology, algebraic geometry and number theory”. The Abel Prize, having been recently established, was not yet well known to mathematicians (and even less so to the public at large). The Abel Board tried to ad- vertise the prize by various means, including using Norwegian diplomacy. Among many other initiatives, the Norwegian embassy in Denmark approached the edi- torial board of Matilde, a small membership journal of the Danish Mathematical Society; the editors were asked whether they would be willing to cover the prize ceremony and help in making the prize more well known in Denmark. Martin Raus- sen had previously interviewed a number of well known Danish mathematicians for Matilde. After some reflection, he gathered his courage and asked whether it would be possible to have an interview with the laureate. To his surprise, arrangements were made quickly and an interview was granted by the organisers and by Professor Serre. Very shortly after this, the Norwegian Mathematical Society came up with the same idea – an interview to be conducted with the laureate. The reply from the organisers was negative as an arrangement had already been made with a mathema- tician from Denmark! Luckily, the society’s president at the time, Kristian Seip, did not take this as the end of the story; he called Martin Raussen, proposing that the interview become a joint venture with Christian Skau, a Norwegian mathematician with a keen interest in Abel and his mathematics. The two of us did not know each other at the time but it turned out that this “forced marriage” would be the begin- ning of a long and fruitful partnership. We did not have a lot of time to prepare for our