saqarTvelos mecnierebaTa erovnuli akademiis moambe, t. 175, ½4, 2007 BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol. 175, no. 4, 2007 History of Mathematics twentieth century, has had a world- wide impact. If you go today to the mathematics department of Moscow University, where this movement began, you might see on a bulletin board, as I have seen, a genealogical chart de- picting the founders of this impres- sive mathematical movement and their succeeding generations of students. Mathematicians or those familiar with the world of mathematics would rec- ognize the names of some of the most influential mathematicians of the last century: for example, Andrei Kolmogorov, perhaps the greatest probabilist of the twentieth century; Sergei Novikov; Vladimir Arnol’d; Lev Pontriagin; Pavel Aleksandrov; and Mstislav Keldysh, onetime president of the Soviet Academy of Sciences and the theoretician of the Soviet space program. Russian Religious Mystics and French At the top of the genealogical tree * are Egorov and Luzin. Who were Rationalists: Mathematics, 1900-1930 these men? Where did they come from? What motivated them? How did they differ from other leading math- ematicians, especially the French who Loren Graham and Jean-Michel Kantor were at the time considered pioneers in the same fields? My colleague from Paris, Jean-Michel Kantor, and I have This presentation was given at the 1884th Stated Meeting, held at the been investigating these questions, House of the Academy on November 10, 2004. and we have come to a conclusion that surprises us and runs counter Loren Graham is Professor of the contribution that Russians made in to our own secular predispositions: History of Science in the Program in the twentieth century, I would answer, at the heart of the birth of the Mos- Science, Technology, and Society at the without much hesitation, mathemat- cow School of Mathematics was a Massachusetts Institute of Technology. ics and fields closely connected with mystical religious impulse. This mys- He has been a Fellow of the American it, such as theoretical physics. The tical doctrine was defined by the es- Academy since 1981. Jean-Michel Kantor is a mathematician Moscow School of Mathematics was tablished Russian Orthodox Church at the Institut Mathématiques de one of the most influential move- as a heresy and hence condemned. Jussieu, Université Paris. ments in twentieth-century mathemat- Yet the heresy, known as Name Wor- ics. In particular, the study of func- shipping (imiaslavie), never died and tions and the descriptive theory of it even has a small life in Russia to- Loren Graham sets (the application to real numbers day; indeed, it has gained some of set theory), initiated by Dmitrii strength in recent years. Several out- If someone were to ask me what I Egorov, Nikolai Luzin, and their stu- standing mathematicians are in- think was the greatest intellectual dents in the first decades of the volved with it at present, but their * Reprinted with the permission of the American Academy of Arts & Sciences from Bulletin of the American Academy, vol. LVIII, No. 3, 2005. © 2007 Bull. Georg. Natl. Acad. Sci. Russian Religious Mystics and French Rationalists: Mathematics, 1900-1930 45 that we were dancing in what had once been a church, nor did we have any idea that this place would be- come important to my research. I asked the Moscow mathematician how I would know when I had reached the spot sacred to Name Worshippers. He told me that I would know when I got there. I went there this past July and wandered around, searching the whitewashed walls of the basement. Then I found a pecu- liar corner, and I knew immediately I was in the right place. On the walls were two photographs of the two men who were instrumental in estab- lishing Name Worshipping among mathematicians, namely, Dmitrii Egorov and Pavel Florenskii. Dmitrii Egorov (1869 – 1931) and Nikolai Luzin (1883 – 1950) founded the Moscow School of Mathematics. They had close connections with French and German mathematicians. Egorov spent the year of 1902 in Paris, Berlin, and Göttingen and talked with, among others, the math- ematicians Henri Lebesgue, Henri Poincaré, Jacques Hadamard, and Kurt Hensel. Luzin first went to west- ern Europe in 1905, later visited France and Germany a number of times, and had frequent contacts with interest in it remains hidden, as it al- Worshipping cannot be done openly mathematicians there. ways has been. in established churches or cathedrals because the official church disap- In the first years of the twentieth cen- During the last two years, I have been proves of the practice. He added, tury, Luzin studied mathematics in in Moscow a number of times, and I however, that there was one place Moscow University under Egorov have visited with Russian scholars particularly sacred to Name Worship- and as a fellow student with Pavel who are familiar with the Name Wor- pers: the basement of the Church of Florenskii (1882 – 1937), who were in- shipping movement. One of them was Saint Tatiana the Martyr in Moscow. fluential in forming the ideas of the a mathematician – a rather well known I knew where this church was. Be- Moscow School. In their mature and one whom I prefer not to name in fore the Russian Revolution it was professionally active years, all three order to preserve his privacy. I knew the official church of Moscow Uni- men – Florenskii, Egorov, and Luzin that he was philosophically and reli- versity, and now that the Soviet – were deeply religious. Florenskii, giously interested in Name Worship- Union has disappeared, it has be- disappointing his teachers, aban- ping, and so I asked if it would be come so again. For many years the doned mathematics for religious stud- possible to witness Name Worship- mathematics department of the uni- ies and became a priest. Egorov and pers practicing their faith. His answer versity was located next to it. During Luzin went on to become outstand- was no: “Name Worshipping is an in- the Soviet years it was converted ing mathematicians who helped cre- timate practice that is best done into a sort of student club, and one ate an explosion of mathematical re- alone.” I asked if there was any place time in the early 1960s I went to a search in Moscow in the 1920s and where Name Worshippers particularly dance there with my young wife, early 1930s. Florenskii and Egorov liked to worship. He replied that Name Patricia. We did not know at the time would eventually be arrested by the Bull. Georg. Natl. Acad. Sci., vol. 175, no. 4, 2007 46 Loren Graham and Jean-Michel Kantor Communist’ authorities, accused of 1905, but the trip did not solve Many of the ideas Luzin found stimu- mixing mathematics and religion. Luzin’s spiritual and intellectual prob- lating and reassuring were presented They subsequently died in prison. lems. Not only did Luzin’s materialist in an essay Florenskii wrote in 1903, (Parenthetically I would observe that worldview collapse, but his faith in when he was only twenty-one years it is one of the cruel ironies of his- science and mathematics did as well. old and still a mathematics student at tory that the Communists’ charge that He was totally without a purpose in Moscow University. In this essay, Florenskii and Egorov mixed math- life. In despair on May 1,1906, he entitled “The Idea of Discontinuity as ematics and religion was correct; al- wrote Florenskii from Paris: an Element of World View,” Florenskii though contrary to the assumption displayed a characteristic that was of the Communists, the mixture was You found me a mere very common among members of the amazingly fruitful to the field of math- child at the University, know- Russian intelligentsia of his time: the ematics.) Luzin narrowly escaped im- ing nothing. I don’t know belief that all intellectual life forms a prisonment, even though he was put how it happened, but I can- connected whole and that therefore on “trial” for ideological deviations not be satisfied any more with ideas in mathematics and philosophy and severely reprimanded. Florenskii the analytic functions and could be extended to the social and is credited with developing a new Taylor series... To see the mis- moral realms, and vice versa. ideology of mathematics and religion ery of people, to see the tor- that played a role in the pioneering ment of life ... this is an un- Florenskii thought that much of the mathematics work of Egorov, Luzin, bearable sight... I cannot live nineteenth century had been a disas- and their students. by science alone...I have noth- ter from the standpoint of philoso- ing, no worldview, and no phy, religion, and ethics and that the Florenskii was one year older than education. I am absolutely ig- particular type of mathematics that Luzin and entered Moscow University norant of the philological sci- reigned during that century was one in 1900; Luzin followed him in 1901. ences, history, philosophy. of the important causes of this mis- Both studied with Egorov, who was a fortune. The governing mathematical young professor of mathematics. Luzin In a long correspondence and in nu- principle of the nineteenth century, at that time was not the religious be- merous meetings at Sergeev Posad, which Florenskii saw as responsible liever that he later became. By his own Zagorsk, a monastery town outside for ethical decline, was deterministic admission he was a “materialist,” like Moscow, Florenskii, already a devout “continuity”: the belief that all phe- many other young Russian intellectu- believer, supplied Luzin with a new nomena pass from one state to an- worldview. It combined both religion als, and he knew very little about phi- other smoothly.