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View This Volume's Front and Back Matter Michael Atiyah Assaf Naor Béla Bollobás Sarah Jones Nelson Enrico Bombieri -DURVODY1HŕHWŒLO Edward Frenkel AnnMarie Perl Timothy Gowers 0LURVODY3HWŒķËHN Andrew Granville Klaus Friedrich Roth Jennifer Granville Michael Spencer ,]DEHOODDED Balázs Szegedy Peter David Lax Cédric Villani Yuri Manin Vladimir Voevodsky Matilde Marcolli ART IN THE LIFE OF MATHEMATICIANS AMERICAN MATHEMATICAL SOCIETY http://dx.doi.org/10.1090/mbk/091 ART IN THE LIFE OF MATHEMATICIANS Anna Kepes Szemerédi Editor AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island 2010 . Primary 00A99. For additional information and updates on this book, visit www.ams.org/bookpages/mbk-91 Front and back cover photographs courtesy of Izabella aba. Library of Congress Cataloging-in-Publication Data Art in the life of mathematicians / Anna Kepes Szemerédi, editor ; Michael Atiyah [and 20 others]. pages cm ISBN 978-1-4704-1956-1 (alk. paper) 1. Mathematics. 2. Art–Mathematics. 3. Music–Philosophy and aesthetics. I. Szemerédi, Anna Kepes, 1945- editor. II. Atiyah, Michael Francis, 1929- QA8.4.A75 2015 510–dc23 2015000061 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink® service. For more information, please visit: http://www.ams.org/rightslink. Send requests for licensed reprints to [email protected]. Excluded from these provisions is material for which the author holds copyright. In such cases, requests for permission to reuse or reprint material should be addressed directly to the author(s). Copyright ownership is indicated on the copyright page, or on the lower right-hand corner of the first page of each article within proceedings volumes. © 2015 by Anna Kepes Szemerédi. All rights reserved. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/. 10 9 8 7 6 5 4 3 2 1 20 19 18 17 16 15 v CONT ENT S Preface vii Acknowledgments ix Introduction 1 Assaf Naor and AnnMarie Perl The Art of Mathematics 8 Michael Atiyah Opera and Music—A Mathematician’s View 12 Béla Bollobás The Fragility of Beauty in Mathematics and in Art 54 Enrico Bombieri and Sarah Jones Nelson Mathematics, Love, and Tattoos 68 Edward Frenkel Music—A Life Not Chosen 80 Timothy Gowers Writing and Performing Mathematics as Metaphor 112 Andrew Granville, Jennifer Granville, and Michael Spencer Photography 138 Izabella aba Painting and Mathematics 164 Peter Lax Mathematics, Art, Civilization 168 Yuri I. Manin vi CONT ENT S De Novo Artistic Activity, Origins of Logograms, and Mathematical Intuition 187 Yuri I. Manin A Drifter of Dadaist Persuasion 210 Matilde Marcolli Inside Out, Outside In (Mathematics on a Single Snapshot) 232 aroslav eetil and iroslav Petek Conversation with Klaus Roth 248 Anna Kepes Szemerédi Salsa and Mathematics 254 Balázs Szegedy Thoughts on Art and Mathematics 258 Balázs Szegedy Mathematics and Art 262 Cédric Villani Into the Woods 272 Vladimir Voevodsky vii PREFACE The mathematician’s best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another. —Gosta ittag-Leffl er The idea for this collection was born in 2, when I organized an exhibition, entitled Art in the orld of athematicians, for the th birthday of my husband, Endre Szemerdi. The exhibition’s theme of mathematics and art generated such great public interest, from mathematicians and non-mathematicians alike, that I decided to create a book gathering the writings of mathematicians on art. It occurred to me: hy not let mathematicians speak for themselves and express their thoughts on art I was interested to hear what art means to them. The color palette is vast. athematicians range from being devout opera fans and art enthusiasts to being playwrights, musicians, painters, photographers, actors, and dancers themselves, often at a professional level. I asked world-class mathematicians to contribute to this book and many have graciously consented. orking with them has been a thrilling experience. aturally, many other mathematicians could have contributed to this book but did not due to various reasons such as time constraints or simply the fact that I did not know of their artistic interests and therefore did not contact them. I hope that some of them will be inspired by this book and will share their per- spective in a future edition. Acknowledgements. I cannot thank enough all of the brilliant mathemati- cians who have been eager to share their priceless thoughts in writing. I am viii PREFACE immensely grateful for their time, patience, and the enthusiasm with which they have contributed to this project. I would like to express special thanks to Sergei Gelfand for having faith in my idea for this book and his help in bringing it to publication. I greatly thank my husband, Endre Szemerdi, for his support and comments. I am grateful too for the opportunity to meet all his great colleagues and friends, many of whom have contributed to this book. Finally, I would like to thank my daughters for their patience, time, and some- times unvarnished critical comments while I was working on this collection. I dedicate this book to my grandchildren hoping to teach them that mathemat- ics is everywhere. Anna epes Szemerdi ix ACKNOWLEDGMENT S Front and ack over Photographs courtesy of Izabella aba. p. Photograph of Assaf aor. ourtesy of Annearie Perl. p. Photograph of Annearie Perl. ourtesy of ossi asa. p. Photograph of Sir ichael Atiyah. ourtesy of Sir ichael Francis Atiyah. p. Poem by Sir ichael Francis Atiyah. epublished with permission of Taylor and Francis Group LL ooks, reams, The Unravelers: Mathemat- ical Snapshots, copyright 2; permission conveyed through opy right learance enter, Inc. p. Photograph of Sir ichael Atiyah. ourtesy of Sir ichael Francis Atiyah. p. 2 Photograph of la ollobs. ourtesy of Gabriella ollobs. p. Photograph of La Clemenza di Tito in the et, th ecember, 22. ourtesy of la ollobs. p. 2 Photograph of Gabriella with Endre and Panni Szemerdi at Rodelinda in the et, rd ecember, 2. ourtesy of la ollobs. p. 2 Image of ichard agner (). Public domain. p. 2 Photograph of the ast of Der Fliegende Holländer taking a bow, udapest, th anuary, 2. ourtesy of la ollobs. p. 2 Photograph of Gabriella by the grand staircase of the opera house, udapest, th anuary, 2. ourtesy of la ollobs. p. Image of Salome, poster by Ludwig ohlwein. Public domain. p. Photograph of the cast from War with the Newts, Prague th anuary, 2. ourtesy of la ollobs. p. Photograph of la ollobs with arik eetil at the premier of War with the Newts. ourtesy of Gabriella ollobs. p. Photograph of la ollobs outside the et, th ecember, 22. ourtesy of Gabriella ollobs. p. Photograph of la ollobs on the upper level of the atrium at ovent Garden, 2th anuary, 2. ourtesy of Gabriella ollobs. p. Photograph of the cast of The Minotaur, 2th anuary, 2. ourtesy of la ollobs. p. Photograph of Ponchielli’s La Gioconda at the Estates Theater, Prague, th anuary, 2. ourtesy of la ollobs. p. 2 Photograph of the olshoi theater on 2th uly, 2, before the start of Der Rosenkavalier. ourtesy of la ollobs. p. 2 Photograph of la ollobs at the olshoi theater on 2th uly, 2, before the start of Der Rosenkavalier. ourtesy of Gabriella ollobs. p. Photograph of Boris Godunov, with ladimir atorin in the title role, olshoi Theater, th arch, 2. ourtesy of la ollobs. p. Photograph of la ollobs. ourtesy of Gabriella ollobs. x ACKNOWLEDGMENT S p. Photograph courtesy of Anna epes Szemerdi. p. Image of rer’s Melencolia I. Public domain. p. Photograph of Enrico ombieri in art studio. ourtesy of Anna epes Szemerdi. p. Photograph of Sarah ones elson. opyright is owned by Taylor Photographics, Inc. p. Photograph of Edward Frenkel. ourtesy of Edward Frenkel. p. Photograph from Rites of Love and Math. ourtesy of Edward Frenkel. p. Photograph from Rites of Love and Math. ourtesy of Edward Frenkel. p. Photograph from Rites of Love and Math. ourtesy of Edward Frenkel. p. Photograph of Edward Frenkel. ourtesy of Edward Frenkel. Photo by Elizabeth Lippman. p. Photograph of Timothy Gowers. ourtesy of . arrau. p. Photograph of Timothy Gowers. Public domain. p. 2 Photograph of Andrew Granville. Photo courtesy of the Simons Foundation. p. 2 and drawn fi gures courtesy of ichael Spencer. p. and drawn fi gure courtesy of ichael Spencer. p. and drawn fi gures courtesy of ichael Spencer. p. 2 and drawn fi gure courtesy of ichael Spencer. p. Top left photograph from a play at Princeton by ennifer and Andrew Granville. ourtesy of the Simons Foundation. p. ottom left photograph from a play at Princeton by ennifer and Andrew Granville. ourtesy of the Simons Foundation. p. Top right photograph from a play at erkeley by ennifer and Andrew Granville. ourtesy of avid Eisenbud, SI. p. ottom right photograph from a play at erkeley by ennifer and Andrew Granville. ourtesy of avid Eisenbud, SI. p. Photograph of Andrew Granville. Photo courtesy of the Simons Foundation. p. Photograph of ennifer Granville. Photo courtesy of avid Eisenbud, SI.
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