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Naming Infinity: a True Story of Religious Mysticism And Naming Infinity Naming Infinity A True Story of Religious Mysticism and Mathematical Creativity Loren Graham and Jean-Michel Kantor The Belknap Press of Harvard University Press Cambridge, Massachusetts London, En gland 2009 Copyright © 2009 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America Library of Congress Cataloging-in-Publication Data Graham, Loren R. Naming infinity : a true story of religious mysticism and mathematical creativity / Loren Graham and Jean-Michel Kantor. â p. cm. Includes bibliographical references and index. ISBN 978-0-674-03293-4 (alk. paper) 1. Mathematics—Russia (Federation)—Religious aspects. 2. Mysticism—Russia (Federation) 3. Mathematics—Russia (Federation)—Philosophy. 4. Mathematics—France—Religious aspects. 5. Mathematics—France—Philosophy. 6. Set theory. I. Kantor, Jean-Michel. II. Title. QA27.R8G73 2009 510.947′0904—dc22â 2008041334 CONTENTS Introduction 1 1. Storming a Monastery 7 2. A Crisis in Mathematics 19 3. The French Trio: Borel, Lebesgue, Baire 33 4. The Russian Trio: Egorov, Luzin, Florensky 66 5. Russian Mathematics and Mysticism 91 6. The Legendary Lusitania 101 7. Fates of the Russian Trio 125 8. Lusitania and After 162 9. The Human in Mathematics, Then and Now 188 Appendix: Luzin’s Personal Archives 205 Notes 212 Acknowledgments 228 Index 231 ILLUSTRATIONS Framed photos of Dmitri Egorov and Pavel Florensky. Photographed by Loren Graham in the basement of the Church of St. Tatiana the Martyr, 2004. 4 Monastery of St. Pantaleimon, Mt. Athos, Greece. 8 Larger and larger circles with segment approaching straight line, as suggested by Nicholas of Cusa. 25 Cantor ternary set. 27 Émile Borel. Reproduced by permission of Institut Mittag-Leffler andActa Mathematica. 44 Henri Poincaré. Reproduced by permission of Institut Mittag-Leffler andActa Mathematica. 46 Henri Lebesgue. Reproduced by permission of L’enseignement mathématique. 48 René Baire. Reproduced by permission of Institut Mittag- Leffler andActa Mathematica. 52 Arnaud Denjoy. 54 Illustrations Jacques Hadamard. Reproduced by permission of Institut Mittag-Leffler andActa Mathematica. 57 Charles-Émile Picard. Reproduced by permission of Institut Mittag-Leffler andActa Mathematica. 60 Hotel Parisiana on the rue Tournefort in Paris, c. 1915. Reproduced from Anna Radwan, Mémoire des rues (Paris: Parimagine, 2006), p. 111. 81 Nikolai Luzin in 1917. Courtesy of Uspekhi matematicheskikh nauk. 85 Pavel Florensky. From Charles E. Ford, “Dmitrii Egorov: Mathematics and Religion in Moscow,” The Mathematical Intelligencer, 13 (1991), pp. 24–30. Reproduced with the kind permission of Springer Science and Business Media. 89 Building of the old Moscow State University where the Lusitania seminars were held. Photograph by Loren Graham. 104 Luzin’s apartment on Arbat Street, Moscow. Photograph by Loren Graham. 107 Interior of Church of St. Tatiana the Martyr, Moscow. Photograph by Loren Graham. 111 Nikolai Luzin, Waclaw Sierpinski, and Dmitri Egorov in Egorov’s apartment in Moscow. Photograph courtesy of N. S. Ermolaeva and Springer Science and Business Media. 120 Otto Shmidt. Courtesy of the Shmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow. http://www.ifz.ru/schmidt.html. 123 “A Temple of the Machine-Worshippers.” Drawing by Vladimir Krinski, c. 1925. 128 { viii } Illustrations Ernst Kol’man. Reproduced with the permission of Chalidze Publications from Ernst Kol’man, My ne dolzhny byli tak zhit’ (New York: Chalidze Publications, 1982). 130 Nikolai Chebotaryov. Courtesy of the State University of Kazan, the Museum of History. 133 Hospital in Kazan where Maria Smirnitskaia tried to save Egorov. Photograph by Loren Graham, 2004. 137 Dmitri Egorov’s gravestone, Arskoe Cemetery, Kazan. Photograph by Loren Graham, 2004. 139 Nina Bari. Courtesy of Douglas Ewan Cameron, from his collection of pictures in the history of mathematics and Uspekhi matematicheskikh nauk. 154 The Luzins with the Denjoy family on the island of Oléron, Brittany. Courtesy of N. S. Ermolaeva. 156 Peter Kapitsa. Courtesy of the Institute of the History of Science and Technology, Academy of Sciences, Moscow, and Sergei Kapitsa. 159 Genealogical chart of the Moscow School of Mathematics. 163 Ludmila Keldysh. Courtesy of A. Chernavsky, “Ljudmila Vsevolodovna Keldysh (to her centenary),” Newsletter of the European Mathematical Society, 58 (December 2005), p. 27. 165 Lev Shnirel’man. Courtesy of Uspekhi matematicheskikh nauk. 168 Pavel Alexandrov, L. E. J. Brouwer, and Pavel Uryson in Amsterdam, 1924. Courtesy of Douglas Ewan Cameron, from his collection of pictures in the history of mathematics. 176 { ix } Illustrations Grave of Pavel Uryson (Urysohn) at Batz-sur-Mer, France. Photograph by Jean-Michel Kantor. 178 Pavel Alexandrov. Courtesy of Douglas Ewan Cameron, from his collection of pictures in the history of mathematics. 179 Andrei Kolmogorov. Courtesy of Uspekhi matematicheskikh nauk. 181 Pavel Alexandrov swimming. Courtesy of Douglas Ewan Cameron, from his collection of pictures in the history of mathematics. 183 Alexandrov and Kolmogorov together. Courtesy of Douglas Ewan Cameron, from his collection of pictures in the history of mathematics. 185 { x } Naming Infinity Introduction In the summer of 2004 Loren Graham was invited to the Mos- cow apartment of a prominent mathematician known to be in sym- pathy with a religious belief called “Name Worshipping” that had been labeled a heresy by the Russian Orthodox Church. The mathe- matician implied he was a Name Worshipper without stating it out- right, and he intimated that this religious heresy had something to do with mathematics. Graham had sought out the Russian scientist at the suggestion of a French mathematician, Jean-Michel Kantor, with whom he had be- gun discussions of religion and mathematics three years earlier. Gra- ham, an American historian of science, had long known that there was an interesting unexplored story about the beginnings of the famed Moscow School of Mathematics early in the twentieth cen- tury. After reading a book by Graham that hinted at this story, Kan- tor immediately contacted Graham to tell him that he knew some- thing about these events. The two met in 2002 and found, to their mutual excitement, that their respective pieces of the narrative had many things in common. Moreover, Kantor told Graham that the story was not just about Russian mathematicians, but about French and world mathematics as well. As Kantor put it, in the early years of the twentieth century mathematics had fallen into such strong con- tradictions that it was very dif fi cult for mathematicians to see how to { 1 } naming infinity go forward. The French, leading in the field, and the Russians, try- ing to catch up, took two different approaches to the same problems. The French had mixed feelings about the issues; they engaged in passionate discussions, and important breakthroughs were made by Émile Borel, René Baire, and Henri Lebesgue, but they ended up sticking to their rationalistic, Cartesian presuppositions. The Rus- sians, learning the new mathematics from the Paris seminars they attended, were stimulated by mystical and intuitional approaches connected to a religious heresy, Name Worshipping, to which sev- eral of them were loyal. The two of us began digging more deeply into the story, reading ev ery thing we could find about the beginnings of set theory in France and Name Worshipping in Russia, and looking for people in both countries who could tell us more. The trail led to the Russian math- ematician in Moscow who agreed to talk to Graham about Name Worshipping. The mathematician’s apartment was a typical one built in Soviet times — small and cramped, with just enough space to live and work. The hallway connecting the apartment’s four rooms was lined with bookcases filled with works on mathematics, linguistics, philos- ophy, theology, and rare books on Name Worshipping. In one of the few empty wall spaces hung framed photographs of two men who, according to the mathematician, were early leaders of Name Worshipping: Professor Dmitri Egorov and Father Pavel Florensky. Another photograph showed the Pantaleimon Monastery on Mt. Athos in Greece, which the mathematician asserted was the early home of Name Worshipping. Yet another photo displayed a book cover with the title “Philosophy of the Name,” written by a Russian philosopher who had subscribed to Name Worshipping in the 1920s. Graham asked if it would be possible to witness a Name Worship- per in the Jesus Prayer trance, which he had recently learned was at the center of the Name Worshipping faith. “No,” replied the math- ematician, “this practice is very intimate, and is best done alone. For { 2 } Introduction you to witness it would be considered an intrusion. However, if you are looking for some evidence of Name Worshipping today I would suggest that you visit the basement of the Church of St. Tatiana the Martyr. In that basement is a spot that has recently become sacred to Name Worshippers.” Graham knew about this church; de cades earlier it had been closed down during an anti- religious campaign by Soviet authorities and converted into a student club and theater. Now, in the post- Soviet period, it has been restored as the offi cial church of Moscow Univer- sity, as it was before the Russian Revolution. It is located on the old campus near the Kremlin, in a building attached to the one that housed the Department of Mathematics in the heyday of Dmitri Egorov and Nikolai Luzin, founders of the Moscow School of Math- ematics. It is the church where they often went to pray. Graham asked the mathematician, “When I go into the basement, how will I know when I have reached the sacred spot?” The mathematician re- plied, “You will know when you get there.” What was the connection between Name Worshipping and math- ematics? And why did the mathematician speak of Name Worship- ping in such a cautious way? The next day Graham went to the Church of St.
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