ARNOLD: Real Analysis A Comprehensive Course in Analysis, Part 1
Barry Simon
Boris A. Khesin Serge L. Tabachnikov Editors http://dx.doi.org/10.1090/mbk/086
ARNOLD:
AMERICAN MATHEMATICAL SOCIETY Photograph courtesy of Svetlana Tretyakova Photograph courtesy of Svetlana Vladimir Igorevich Arnold June 12, 1937–June 3, 2010 ARNOLD:
Boris A. Khesin Serge L. Tabachnikov Editors
AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island Translation of Chapter 7 “About Vladimir Abramovich Rokhlin” and Chapter 21 “Several Thoughts About Arnold” provided by Valentina Altman.
2010 Mathematics Subject Classification. Primary 01A65; Secondary 01A70, 01A75.
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Library of Congress Cataloging-in-Publication Data Arnold: swimming against the tide / Boris Khesin, Serge Tabachnikov, editors. pages cm. ISBN 978-1-4704-1699-7 (alk. paper) 1. Arnold, V. I. (Vladimir Igorevich), 1937–2010. 2. Mathematicians–Russia–Biography. 3. Mathematicians–Soviet Union–Biography. 4. Mathematical analysis. 5. Differential equations. I. Khesin, Boris A. II. Tabachnikov, Serge.
QA8.6.A76 2014 510.92–dc23 2014021165 [B]
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Development of mathematics resembles a fast revolution of a wheel: sprinkles of water are flying in all directions. Fashion – it is the stream that leaves the main trajectory in the tan- gential direction. These streams of epigone works attract most attention, and they constitute the main mass, but they inevitably disappear after a while because they parted with the wheel. To remain on the wheel, one must apply the effort in the direction perpendicular to the main stream.
—V. I. Arnold, translated from “Arnold in His Own Words,” an interview with the mathematician originally published in Kvant Magazine, 1990 and republished in the Notices of the American Mathematical Society, 2012.
v
Contents
Epigraph v
Preface ix
Permissions and Acknowledgments xiii
Part 1. By Arnold
Chapter 1. Arnold in His Own Words V. I. Arnold 3
Chapter 2. From Hilbert’s Superposition Problem to Dynamical Systems V. I. Arnold 11
Chapter 3. Recollections Jurgen¨ Moser 31
Chapter 4. Polymathematics: Is Mathematics a Single Science or aSetofArts? V. I. Arnold 35
Chapter 5. A Mathematical Trivium V. I. Arnold 47
Chapter 6. Comments on “A Mathematical Trivium” Boris Khesin and Serge Tabachnikov 57
Chapter 7. About Vladimir Abramovich Rokhlin V. I. Arnold 67
Photographs of V. I. Arnold
1940s–1970s 79
1980s–1990s 87
The 2000s 99
Part 2. About Arnold
Chapter 8. To Whom It May Concern Alexander Givental 113
vii viii CONTENTS
Chapter 9. Remembering Vladimir Arnold: Early Years Yakov Sinai 123
Chapter 10. Vladimir I. Arnold Steve Smale 127
Chapter 11. Memories of Vladimir Arnold Michael Berry 129
Chapter 12. Dima Arnold in My Life Dmitry Fuchs 133
Chapter 13. V. I. Arnold, As I Have Seen Him Yulij Ilyashenko 141 Chapter 14. My Encounters with Vladimir Igorevich Arnold Yakov Eliashberg 147 Chapter 15. On V. I. Arnold and Hydrodynamics Boris Khesin 151 Chapter 16. Arnold’s Seminar, First Years Askold Khovanskii and Alexander Varchenko 157 Chapter 17. Topology in Arnold’s Work Victor Vassiliev 165 Chapter 18. Arnold and Symplectic Geometry Helmut Hofer 173 Chapter 19. Some Recollections of Vladimir Igorevich Mikhail Sevryuk 179 Chapter 20. Remembering V. I. Arnold Leonid Polterovich 183 Chapter 21. Several Thoughts about Arnold A. Vershik 187 Chapter 22. Vladimir Igorevich Arnold: A View from the Rear Bench Sergei Yakovenko 197 Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that “Mathematics is a part of physics where experiments are cheap” is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.
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