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 ,]DEHOOD‘DED 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.

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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

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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. p. Photograph of ichael Spencer. ourtesy of hristine isatt. p. Photograph of Izabella aba. ourtesy of Izabella aba. p. 2 Photograph of the oman aqueduct. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of a street in Seoul. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of ount aker. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of a store window in Padua. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of a rainforest, ancouver Island. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of a leaf macro, ancouver. From Photography by Izabella aba: all photographs by Izabella aba, 222. ART IN T HE LIFE OF MAT HEMAT ICIANS xi p. Photograph of a street view, enice. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of a leaf macro, ancouver. From Photography by Izabella aba: all photographs by Izabella aba, 222. p. Photograph of tree trunks. From Photography by Izabella aba: all photo- graphs by Izabella aba, 222. p. Photograph of leaves. From Photography by Izabella aba: all photo- graphs by Izabella aba, 222. p. 2 Photograph of a sunset. From Photography by Izabella aba: all photo- graphs by Izabella aba, 222. p. Photograph of Izabella aba. ourtesy of Izabella aba. p. Photograph of Peter avid Lax in Toledo, Spain, 2. ourtesy of Author: amn Escobedo p. Photograph of Peter Lax. Photo courtesy of the Simons Foundation. p. Article athematics, Art, ivilization by uri I anin. u. anin. This article also appears in I, Mathematician, Peter asazza, Steven G. rantz and andi . uden, Editors, athematical Association of America, 2. p. Photograph of uri I. anin. Photo courtesy of Tatiana Plotnikova. p. 2 Figure . Image of Margarita Philosophica, Strasburg, . Public domain. p. Figure 2. Image of apier’s tables of logarithms. Public domain. p. Figure . Pappus’s theorem. ourtesy of uri anin. p. Figure . athematical ubism. ourtesy of uri anin. p. Figure . (Top) Archimedes Tomb. Photo by G. . Gingerelli. p. Figure . (ottom) Photo of sphere. Public domain. p. Figure . ommutative 2-diagram. ourtesy of uri anin. p. Figure . ommutative square. ourtesy of uri anin. p. Figure . One and negative one. ourtesy of uri anin. p. 2 Figure . anuscript of Sonata for Violin Solo, by . S. ach. Public domain. p. Figure . Photo of rer. ands on a book. Public domain. p. Figure . rawings after unilateral ET (ND) vs. development of two logo- grams. . . ikolayenko, . L. eglin . Semiotics of space and functional asymmetry of the brain. Sign Systems Studies (Trudy po zna- kovym sistemam) ; . p. 2 Figure 2. Table taken from aratteri inesi’’ by Edoardo Fazzioli and Eileen han ei Ling, originally published in by Arnoldo ondadori Editore SpA, ilano. All rights reserved. p. Figure . Lascaux cave painting: bison and man. Public domain. p. Figure . (Top) Owl and Sun (oil on canvas), . ourtesy of uri anin. p. Figure . (ottom) A view in Mussomeli (ink, paper), . ourtesy of uri anin. xii ACKNOWLEDGMENT S p. 2 Photograph of uri I. anin. Photo courtesy of Tatiana Plotnikova p. 2 Photograph of atilde arcolli. ourtesy of atilde arcolli. p. 22 Figure . Image by Annarosa otta, Segni, . p. 2 Figure 2. Image by Attilio arcolli, Struttura Segni, . p. 2 Figure . Triptych, left panel, . ourtesy of atilde arcolli. p. 2 Figure . Triptych, right panel, . ourtesy of atilde arcolli. p. 2 Figure . Triptych, center panel, . ourtesy of atilde arcolli. p. 22 Figure . Bioscosmism N.1, 2. ourtesy of atilde arcolli. p. 22 Figure . Bioscosmism N.2, 2. ourtesy of atilde arcolli. p. 22 Figure . Et in Arcadia Ego, . ourtesy of atilde arcolli. p. 22 Figure . Chasing, . ourtesy of atilde arcolli. p. 2 Photograph of atilde arcolli. ourtesy of atilde arcolli. p. 22 Photograph of aroslav eetil. Private archive of author. p. 2 Image of Lszl oholy-agy’s Radio Tower Berlin. Private archive of authors. p. 2 Photograph of aroslav eetil. Private archive of author. p. 2 Photograph of iroslav Petek. Private archive of author. p. 2 Opening photograph of oth onversation article. Andras leyer gives per- mission to publish this photograph only in this book (Art in the Life of Mathematicians) and will retain the copyright. p. 2 Photograph of laus oth. Photo courtesy of the oyal Society, used with permission. p. 2 Photograph of alsz Szegedy. ourtesy of alsz Sgezedy. p. 2 Photograph of alsz Szegedy. ourtesy of alsz Sgezedy. p. 22 Photograph of dric illani. ourtesy of erv Thouroude. p. 2 Photograph of dric illani. opyright S Photolibrary/Sebastien Godefroy. p. 22 Photograph of bird. ourtesy of ladimir oevodsky. p. 2 Photograph of ladimir oevodsky. Photo taken by iana oevodsky. ourtesy of ladimir oevodsky. p. 2 Photograph of frog. ourtesy of ladimir oevodsky. p. 2 Photograph of turtles. ourtesy of ladimir oevodsky. p. 2 Photograph of bird in fl ight. ourtesy of ladimir oevodsky. p. 2 Photograph of bee. ourtesy of ladimir oevodsky. p. 2 Photograph of plant. ourtesy of ladimir oevodsky. p. 2 Photograph of mushrooms. ourtesy of ladimir oevodsky. p. 2 Photograph of forest. ourtesy of ladimir oevodsky. p. 22 Photograph of sun refl ecting off water. ourtesy of ladimir oevodsky. p. 2 Photograph of spider and web. ourtesy of ladimir oevodsky. I have always admired the abstraction ability of composers. The ingenious construction of beautiful patterns that can evoke such powerful emotions seems nothing short of magical. While mathematicians too construct beautiful patterns, I fear that few outside the math community appreciate that beauty or fi nd any magic in it. I hope that this wonderful collection of articles, written by mathematicians who are themselves artists, will help better explain the many varied connections between mathematics and the arts, and illu- minate better the beauty and magic in math. —Avi Wigderson, Institute for Advanced Study, Princeton Much has been written about the close relationship of mathematics and music. It is a rather one-sided affair because mathematicians are usually very musical while musi- cians—including myself—are considerably less knowledgeable on matters of science. However we are all eager to learn from each other and the present volume is a most valu- able contribution to this interesting dialogue. —Sir Andras Schiff, pianist and conductor Creativity, Originality and Imagination are three common features of mathematicians and artists. This inspiring book contains much more about the similarities between art and mathematics, as described by outstanding mathematicians with a wide range of artistic interests. —Noga Alon, Tel Aviv University Mathematics and art are intertwined on so many levels… It is exciting to see such a broad treatment of this important theme. —Charles Simonyi, Chairman of the Board, Institute for Advanced Study, Princeton *** tŚLJĂƌĞŵĂƚŚĞŵĂƟĐŝĂŶƐĚƌĂǁŶƚŽĂƌƚ͍,ŽǁĚŽƚŚĞLJƉĞƌĐĞŝǀĞŝƚ͍tŚĂƚŵŽƟǀĂƚĞƐƚŚĞŵ ƚŽƉƵƌƐƵĞĞdžĐĞůůĞŶĐĞŝŶŵƵƐŝĐŽƌƉĂŝŶƟŶŐ͍ŽƚŚĞLJǀŝĞǁƚŚĞŝƌĂƌƚĂƐĂĐŽŶǀĞLJĂŶĐĞĨŽƌ ƚŚĞŝƌŵĂƚŚĞŵĂƟĐƐŽƌĂŶĞƐĐĂƉĞĨƌŽŵŝƚ͍tŚĂƚĂƌĞƚŚĞƐŝŵŝůĂƌŝƟĞƐďĞƚǁĞĞŶŵĂƚŚĞŵĂƟĐĂů ƚĂůĞŶƚĂŶĚĐƌĞĂƟǀŝƚLJĂŶĚƚŚĞŝƌĂƌƟƐƟĐĞƋƵŝǀĂůĞŶƚƐ͍tŚĂƚĂƌĞƚŚĞĚŝīĞƌĞŶĐĞƐ͍ĂŶĂƚŚĞĂƚͲ ƌŝĐĂůƉůĂLJŽƌĂǀŝƐƵĂůŝŵĂŐĞĐĂƉƚƵƌĞƚŚĞďĞĂƵƚLJĂŶĚĞdžĐŝƚĞŵĞŶƚŽĨŵĂƚŚĞŵĂƟĐƐ͍^ŽŵĞŽĨ ƚŚĞǁŽƌůĚ͛ƐƚŽƉŵĂƚŚĞŵĂƟĐŝĂŶƐĂƌĞĂůƐŽĂĐĐŽŵƉůŝƐŚĞĚĂƌƟƐƚƐ͗ŵƵƐŝĐŝĂŶƐ͕ƉŚŽƚŽŐƌĂƉŚĞƌƐ͕ ƉĂŝŶƚĞƌƐ͕ĚĂŶĐĞƌƐ͕ǁƌŝƚĞƌƐ͕ĮůŵŵĂŬĞƌƐ͘/ŶƚŚŝƐǀŽůƵŵĞ͕ƚŚĞLJƐŚĂƌĞƐŽŵĞŽĨƚŚĞŝƌǁŽƌŬĂŶĚ ƌĞŇĞĐƚŽŶƚŚĞƌŽůĞƐƚŚĂƚŵĂƚŚĞŵĂƟĐƐĂŶĚĂƌƚŚĂǀĞƉůĂLJĞĚŝŶƚŚĞŝƌůŝǀĞƐ͘dŚĞLJǁƌŝƚĞĂďŽƵƚ ĐƌĞĂƟǀŝƚLJ͕ĐŽŵŵƵŶŝĐĂƟŽŶ͕ŵĂŬŝŶŐĐŽŶŶĞĐƟŽŶƐ͕ŶĞŐŽƟĂƟŶŐƐƵĐĐĞƐƐĞƐĂŶĚĨĂŝůƵƌĞƐ͕ĂŶĚ ŶĂǀŝŐĂƟŶŐƚŚĞǀĂƐƚůLJĚŝīĞƌĞŶƚƉƌŽĨĞƐƐŝŽŶĂůǁŽƌůĚƐŽĨĂƌƚĂŶĚŵĂƚŚĞŵĂƟĐƐ͘

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