Naming God, Naming the Infinite:

 

Mathematics and Religious Heresy

 

 


Loren Graham

 

Jean-Michel Kantor



 
Naming God, Naming the Infinite:  Mathematics and Religious Heresy
 
One-Page Synopsis
 
This story combines mathematics and religious heresy, and is a tale in which mathematicians who were religious heretics triumphed over those who were secular rationalists.  In this one-page synopsis we will, in the first paragraph, briefly explain the mathematics involved and its connection with religion; in the second paragraph we will describe the dramatic political and personal events in which these mathematicians participated.  Then in the proposal that follows we will expand on this summary. 
 
In the early twentieth century mathematicians developing set theory faced a major problem: it was possible to conceive of sets of infinite numbers, sets which could not be given rigorous definitions.  But was it mathematically sound to work with such sets?  Two groups of mathematicians intensively studied this question, the French in Paris and the Russians in Moscow.  The French subscribed to rationalist views that caused them to doubt that such sets were justified; the Russians were involved in a religious heresy that emboldened them to create such sets.  The Russians noted that they could not give a rigorous definition of either “God” or their new sets, but they nonetheless had faith in the reality of both.  They answered the question “How do we know such sets of infinite numbers exist?” in the same way they answered the question “How do we know God exists?”:  “We know both exist,” they maintained, “because we can name both and treat them as real.”  These Russian mathematicians were called “Name Worshippers” and were a part of a religious heresy spreading in Russia.  The French considered such an attitude mystical nonsense, and they refused to go forward.  The Russians, emboldened by their faith, plunged ahead and created a new field of mathematics, establishing at the same time the Moscow School of Mathematics, still famous throughout the world of mathematicians.
 
All this was embedded in a fascinating story of politics and colorful personalities that continues to the present and can be told without difficult mathematics.  On the French side, the mathematicians included people with deep political interests, one of whom became a minister in the French government.  But the French lost their nerve over set theory.  One of them eventually committed suicide and another abandoned set theory out of fear of “serious illness” if he continued his work.  The Russians, exhilarated by their conviction that they could freely create and name new mathematical sets, did not have these mental problems but they soon encountered grave political ones.  They were criticized by the established Church even before the Russian Revolution of 1917 but soon thereafter were caught in a political upheaval whose leaders denied the place of religion and persecuted religious believers of all types, orthodox and heretical.  The Russian mathematicians worked in secret and made their breakthrough before they were caught.  However, eventually most of them were seized by the Soviet authorities and some were executed for “mixing mathematics and religion.”  But the heresy continued underground and is alive in Russia today, although it is still banned by the established Orthodox Church.  This story differs from the usual science vs. religion scenario, or freedom vs. communism struggle, because both the Church and the Communists, dogmatists alike, opposed the heretical mathematicians.  And yet, in a sense, the “heresy” won.
 
(for a brief explanation of mathematical “sets” see the last page of proposal)[1]

 

Proposal

                  Early in the morning of July 3, 1913, two ships from the Imperial Russian Navy, acting on tsar Nicholas II’s orders, steamed into the azure waters surrounding the holy mountain of Mt. Athos in Greece, a center of Orthodox Christianity for over a thousand years.  The ships, the Donets and the Kherson, anchored near the Pantaleimon Monastery, a traditional center of Russian Orthodoxy and residence of hundreds of Russian monks.   Small boats loaded with armed Russian marines made their way to the dock, where the men disembarked.  The marines proceeded to the central room of the monastery, which served as the dining hall, at that moment nearly empty.  There the officer in charge met with several monks and told them that they were to inform all their brethren to leave their cells and assemble in the dining hall.  When the other monks learned of the order, they barricaded the doors of their cells with furniture and boards.  Inside they fell on their knees and began crying “Lord, Have Mercy!” (Gospodi pomilui) and many of them launched into a unique prayer, one causing controversy in the Church, called “The Jesus Prayer.”
 The Russian officer demanded that the monks come out.  When his warning was ignored, he ordered his marines to tear down the barricades and aim water from fire hoses at the Russian monks inside.  The marines flushed the monks from their cells and herded them into the dining hall.  There the officer announced to the soaked and terrified monks that they must either renounce their heretical beliefs or be arrested.  Only a few stepped forward and promised to obey.  The others remained obstinate, crying that the marines represented the “Anti-Christ.”  The officer ordered the marines to force the recalcitrant monks onto the waiting ships which took them to the Russian city of Odessa, on the Black Sea.  In all, approximately 1000 monks were detained in this fashion.
  In Odessa the monks were told that the Holy Synod in St. Petersburg -- the highest authority of Russian Orthodoxy -- had condemned them as heretics for engaging in the cult known as “Name-Worshipping.”   The monks were forbidden to return to Mt. Athos or to reside in the major cities of St. Petersburg and Moscow.  They were also warned that they must not practice their deviant religious beliefs in the established churches of Russian Orthodoxy on penalty of excommunication.  Otherwise they were free to go.  The unrepentant monks dispersed all over rural Russia where they often lived in remote monasteries, far from central authorities, and continued there to practice their heresy and to propagate their religious faith.
                  Instead of dying out, as the tsarist authorities obviously hoped that it would, the heresy continued to spread surreptitiously.  With the outbreak, a year later, of World War I the attention of the tsarist government shifted elsewhere.  Name-Worshipping silently increased in strength, gradually moving from the countryside to the cities, where it attracted the attention of the intelligentsia, especially mathematicians, some of whom believed it contained profound insights for their field.
What was “Name-Worshipping,” and how could this religious movement have anything to do with mathematics?  The dispute over this “heresy” is rooted in the ancient question “How can humans worship an unknowable diety?”  If God is in principle beyond the comprehension and description of mortals (and holy scripture contains many such assertions), how, in complete ignorance of His nature, can human beings worship Him?  What does one worship?  The most common response given to this dilemma throughout religious history has been the resort to symbols:  icons, prayers, names, rituals, music, relics, scents, tastes.  Symbolism is the use of a perceptible object or activity to represent to the mind the semblance of something which is not shown but realized by association with it.  The religious worshipper believes he or she makes contact with an unknowable God through the use of these religious symbols. 
In the years 1907-1917 a particular prayer, “The Jesus Prayer,” became very popular among some members of the Russian Orthodox Church as a symbolic means of connecting with Jesus and God.  In the Jesus Prayer the religious believer chants the names of Christ and God over and over again, hundreds and hundreds of times, “praying without ceasing,”until the believer’s whole body reaches a state of religious ecstasy in which even the beating of his heart, in addition to his breathing cycle, is supposedly in tune with the chanted words “Christ” and “God” (a state vividly described by J. D. Salinger in Franny and Zooey).[2]
 When the Bolsheviks took over Russia in the Revolution of October/November 1917 they announced their determination to suppress religion as an obscurantist, irrational worldview, and they made no distinction between orthodox believers and heretics.  However, as adherents of an underground faith the Name Worshippers had an unusual advantage in resisting the Communists’ campaign against religion.  Centered in no specific church and practiced usually in isolation by a single person, Name Worshipping was not a form of organized religion that could be easily suppressed.  A monk could practice it alone in his cell, as could a professor in his or her study.  It needed no church hierarchy or particular physical setting.  There was no obvious way to identify who was a Name Worshipper and who was not.   
Gradually Name Worshipping gained a foothold in Moscow even though its followers were not only hunted by the Soviet secret police but also proscribed by the beleaguered Orthodox Church itself.   Among intellectuals Name Worshipping became particularly popular.  Philosophically and artistically it was in harmony with the symbolist movement that had swept Russian culture in the last years of tsarism and remained strong in the early Soviet period.  That movement affected ballet, music, literature, art, and poetry, as the names Diaghilev, Stravinsky, Belyi, Stanislavsky, Nemirovich-Danchenko and Meyerhold remind us.  Now we should add mathematicians  to such lists.  Indeed, there was even a connection between the literary and mathematical movements.  Andrei Belyi, the symbolist poet, was the son of a Moscow mathematician, and had majored in mathematics at Moscow University; he was familiar with Name-Worshipping.  Belyi once wrote an essay called “The Magic of Words” in which he asserted, “When I name an object with a word, I thereby assert its existence.”
                   In the nineteen twenties a “Name Worshipping Circle” met regularly in the old Arbat region of Moscow  -- the traditional home of intellectuals and artists – often in the apartments of mathematicians, philosophers, physicists, and writers.  A Western journalist, René Fulop-Miller, met many of these dissident believers at this time; in his book about his experiences he wrote: “Name Worshipping is a movement to which a great part of the intelligentsia as well as a considerable part of the peasantry belong.  The best men of Russia lead this school . . . .”  
                  Among “the best men of Russia” who became interested in Name Worshipping were two of the most gifted mathematicians in that country, Dmitrii Egorov and Nikolai Luzin.
Dmitrii Egorov (1869-1931) was a brilliant lecturer and prominent mathematician, but somewhat reserved personally, and a deeply devout man.  He began teaching at Moscow University in 1894 and was associated with the university almost all the rest of his life.  A friend of many philosophers and writers, he lived on Boris-and-Gleb Street, in the center of the city and a few  blocks from the university.   He was in his prime the best-known mathematician in Russia, and president of the Moscow Mathematical Society.  He had the ability to attract many devoted students, although he remained a rather aloof professor of the old European style.
Nikolai Luzin (1883-1950) was born in far-away Tomsk, and came to Moscow as a university student.  He was perhaps the most brilliant of Egorov’s pupils, and a man with a different temperament.  In contrast to the scholarly steadiness of his teacher, Luzin was charismatic, even electric.  After he joined Egorov as a professor at Moscow University, his students revered him, although in later years a few of them turned against him, accusing him of moodiness and instability.  Luzin as a youth preferred radical politics, but after 1905 he went through a psychological transformation which resulted in a turn to more conservative politics and also to religion. .  When he studied in Paris intermittently in the period 1906-1914 the concierge of the hotel where he stayed near the Pantheon, the Hotel Parisiana, marveled at his devout religious practices.  In Moscow Luzin lived on “Arbat Street,” the center of intellectual and artistic life in the city, and only a few blocks from the home of his teacher Egorov..  Luzin’s apartment building today bears a plaque citing him as “the founder of the Moscow School of Mathematics,” although that honor should be shared with his teacher Egorov.  The plaque may have been placed on Luzin’s home at a time when Egorov, who was imprisoned by the Soviet authorities, was still a “non-person.”    (There is no plaque even today on Egorov’s building.)
Egorov and Luzin believed that Name Worshipping could help them make their way through a crisis that was affecting their colleagues throughout the world of mathematics.  Both Egorov and Luzin studied mathematics in Western Europe, and they were thoroughly at home with contemporary problems in their field.
             As a result of the work and interests of people like Egorov and Luzin, the Name Worshipping cult became a factor in the development of mathematics.  At this time the leading mathematicians of Europe were discussing the use of infinity in set theory, first developed several decades earlier in Germany by Georg Cantor.   Since the time of the ancient Greeks the Infinite was connected with deity, God, the absolute or “the One.”   Among the conceivable sets were non-finite sets like that of all numbers, or the continuum.  But should mathematicians consider such sets to be legitimate?  Should they work with them?     
These questions led to a great debate among mathematicians.  The French, led by such eminent mathematicians as René Baire, Henri Lebesgue, and Emile Borel, were products of a very powerful tradition in mathematics, and one would expect them to excel over the Russians.
 
ADD PERSONAL DETAILS ON BAIRE, LEBESGUE AND BOREL
 
 The Russians from Moscow, led by Dmitri Egorov and Nikolai Luzin, were the newcomers in the mathematical debates, and at first learned from their French colleagues more than they taught.  But the two groups followed different approaches, and in the end these differences would turn out to be more important than the traditional strengths of the respective mathematical schools.  The French subscribed to rationalism and to a limited view of mathematics.  The Russians, on the other hand, were deeply religious, and they relied on mystical intuition as they approached the same mathematical  problems which were troubling their French colleagues.   And ultimately it was the Russians who made the mathematical breakthrough.
A contrast between the cold logic of the French and the spirituality of the Russians is not new in the history of culture.  Leo Tolstoy in War and Peace compared Napoleon’s Cartesian logic in his assault on Russia with his opponent Kutuzov’s emotional religiosity.  After the critical battle of Borodino the novelist described the Russian general Kutuzov kneeling in gratitude before a holy icon in a church procession while Napoleon rationalized his “miscalculation.”  Tolstoy saw Borodino as a victory of Russian spirit over French rationalism.
But can a similar comparison be made in that realm that seems farthest from human concerns, mathematics?  Actually, in the history of science irrational elements have often played important roles in what were later considered to be positive developments.  Newton not only believed in astrology and alchemy, but was convinced that his system of the Universe revealed the grandeur of God.  Part of his motivation for pushing forward with that system despite all difficulties was undoubtedly religious.   The astronomer Kepler was enamored with the “harmony of the spheres” and thought each of the orbits of the planets could be circumscribed within one of the Platonic perfect solids.  The beauty of his vision drove him to a frenzy of work.  Many other examples of the interaction of mystical and rational elements can be found in the history of science.  In the case of mathematics in the early twentieth century the mystical beliefs possessed by a few Russian mathematicians supplied them with the motivation to dream of new concepts in mathematics that later, more rational, mathematicians would come to accept even if they did not agree with the original motivation.
The Russian who was more influential than any other in mixing the worlds of religion and mathematics in the first decades of the last century was Pavel Florenskii, a student of Egorov and a classmate and friend of Luzin.   Florenskii became the intellectual architect of the edifice that, in his opinion, united religion and mathematics.  He studied mathematics at Moscow University in the years 1900-1904 and excelled in the field.  His professor, Egorov, recognizing his great talent, urged him to continue graduate studies in mathematics, but Florenskii refused, and entered religious studies instead.  Eventually he became a priest.  Despite Florenskii’s departure from professional mathematics, all three men -- Florenskii, Luzin, and Egorov – remained in contact.
Florenskii, in his defense of “Name-Worshipping,” emphasized the importance of “naming” in mathematical set theory.    Mathematicians created mathematical realities by naming sets in the same way that worshippers created a religious reality by naming God.  A new form of mathematics was coming, said Florenskii, and he suggested that his former professor and classmate – Egorov and Luzin – be leaders in this new mathematics.  And so they became.
The idea that “naming” is an act of creation goes back to the beginning of religious and mythological thought.  In Genesis we are told, “God said ‘Let there be light and there was light’.”  In other words, He gave the thing a name before He created it.  The ancient Egyptian God Ptah is described in Memphite theology as creating with his tongue that which he first conceived in his head.  Naming God is forbidden in the Jewish tradition, and in the mystical Kabbala (Book of Creation, Zohar) there is a belief in creation through emanation.  In the first verse of the gospel according to St. John we read “In the beginning was the Word, and the Word was with God, and the Word was God.”  Words are names, and one of the leaders of the Russian Name-Worshippers, the monk Ilarion, said “the name of God is God!” (“Imia Bozhie est’ sam Bog”)
Ilarion’s statement was one of the main reasons that the established Orthodox Church in Russia condemned Name-Worshipping as a heresy.  According to the leaders of the Church the Name-Worshippers were heretics because they allegedly confused the symbols of God with God Himself. 
Nikolai Luzin followed in mathematics an approach that was similar to that of the Name Worshippers in religion.  Going deep inside the mysteries of subsets of the mathematical continuum he went as far as he could in “naming” new mathematical objects, thus creating “descriptive set theory.”  Remaining in his personal archive in Moscow today is his hand-written comment “To name something is to give it individuality.”  Like Ptah, he was creating with his tongue that which he conceived in his head.  At another moment he scribbled, “Everything seems to be a daydream, playing with symbols, which, however, yield great things.”
Western rationalists like the French mathematicians reacted to the mathematical Name Worshippers by objecting, “But naming is not identical with creating.  I can name a ‘unicorn’ but that does not make unicorns real.”  And such a rationalist might go even further by maintaining that Name Worshipping was really nothing “new” since it displayed similarities with many other types of religious and meditation practices, including variants of Hinduism, Buddhism, Judaism, and Islam (the evangelical Protestant tradition of “speaking in tongues” is also similar).  The endpoint, as in Name Worshipping, is a state of ecstasy. 
                  But these legitimate objections miss the uniqueness of the situation mathematicians were in during the early years of the last century.  Everybody knows unicorns are fanciful, but mathematicians in these years truly differed among themselves about the existence of various infinite sets.  The French, with their secular, rationalist worldview, had neither the courage nor the motivation to enter the frightening world of infinite sets, particularly non-denumerable ones.   Several leading French mathematicians actually feared that submersion in the subject could bring on mental problems.  Georg Cantor, the German founder of set theory, had his first serious attack of depression in 1884.  René Baire, who originally showed some enthusiasm for set theory, fell badly ill in 1898, as if being punished for his flirtation with the new ideas.  He stopped working in 1900, became “neurasthenic,” and finally, in 1932, killed himself.  Emile Borel, after referring to the illnesses of Cantor and Baire, told his friend Paul Valéry in 1923 that he had to abandon set theory because it “made him fear and foresee in himself serious illness if he persisted in that work.”   The Russians from Moscow did not have these problems.  The Name Worshippers, in particular, were exhilarated by what they saw as their absolute freedom to invent mathematical objects, and to give their inventions names.  Following their approach the Russians created a new field, descriptive set theory, at a time when the French faltered.
                  Looking back at the crucial moments in this story today, one can see that the French mathematicians felt that they were very near the edge of the possible and the justifiable, and perhaps even of sanity itself; they therefore drew upon their cultural resources to steady themselves.  The French fell back on the clarity of Cartesian logic, which gave them reason to hesitate.  No one knew where set theory would go, so it was better to pause.  The Russians drew on their own cultural traditions, including mystical religious beliefs, and found encouragement to push ahead, name new sets, create new mathematical objects.  In sum, the cultural resources of the French served as cautionary, retarding factors; the cultural resources of the Russians were promoting factors.
The circle of eager students at Moscow University which formed around Egorov and Luzin at about the time of the beginning of World War I and continued throughout the early twenties was known as “Lusitania,” and even today this group is considered the cradle of the illustrious Moscow School of Mathematics.    Lusitania was at first a small secret society, and the place of religion in that society is illustrated by the fact that Egorov was called “God-the-Father,” Luzin was “God-the-son,” and each of the students in the society was given the monastic title of “novice.”  They all went to Egorov’s home three times a year:  Easter, Christmas, and Egorov’s Name-Day (again, the emphasis on “names”).  Three students were given “offices” in the society:  Pavel Alexandrov was named “the creator,” Pavel Uryson “the keeper”, and Viacheslav Stepanov “the herald of the mysteries” of Lusitania.  The religious and mystical overtones of Lusitania took on deeper, even dangerous, implications after the Russian Revolution of 1917, when the new Soviet regime began to persecute religious believers.
Pavel  Florenskii, who espoused the fusion of mathematics and religion, was a priest and a professor in the Ecclesiastical Academy, but also a heretic who advanced many ideas that did not fit comfortably with the established Church, including an unusual doctrine of philic love.  One American professor who studied his religious writings called them “the first Christian theology to place same-sex relationship at the center of its vision.” And homosexuality did play a role in Lusitania, although not between Luzin and Egorov.  Two of the first student officers of Lusitania, the gifted mathematicians Pavel  Alexandrov,  the “creator,” and Pavel Uryson, the “keeper,” a Christian and a Jew, soon became steadfast partners who loved to work, travel, and swim together.  Working jointly they made advances in topology that are still valued today.  On trips to France and Germany they met the great mathematicians of those countries, and also vacationed, enjoying their sport of swimming together, often in dangerous ocean waters.  On August 17, 1924, Uryson was tragically killed by a rogue wave off the coast of Brittany despite Alexandrov’s efforts to save him. 
In later years Alexandrov made a homosexual liaison with another member of Lusitania, a young man who became one of the Soviet Union’s most famous mathematicians, Andrei Kolmogorov.  Alexandrov and Kolmogorov owned jointly a dacha outside Moscow, near the Kliazma River, and frequently worked and swam together, often in the nude.  (We are told of their habit of both swimming and working on mathematics “desnudos” by two Cuban mathematicians who did doctoral studies with them in Moscow and later wrote a book about their experiences published in Spain.)  Under Stalin homosexuality became a grave crime in the Soviet Union, and consequently Alexandrov and Kolmogorov were always in danger.  But instead of arresting them for homosexuality, the Soviet secret police used their knowledge of their habits to control them.  When the police wanted them to give their support to a certain Soviet cause, the police could simply ask and receive.  Alexandrov and Kolmogorov believed they had no choice but to obey.   This power explains why the two men often signed public statements in support of repressive Soviet policies, such as the condemnation of dissidents like Andrei Sakharov.  Kolmogorov once told a colleague “I will fear them [the secret police] until my death.  Someday people will understand my behavior.”  He died in 1987, five years after his friend Alexandrov.
Although Egorov and Luzin were both devout believers before and after the Russian Revolution,  their outward behavior began to diverge in the nineteen twenties, after the Soviet authorities made it clear that they were going to try to suppress religion.  Egorov continued to defend not only his personal religious beliefs but those of others.  Luzin retreated inward, stopped going to meetings of the Name Worshippers, and eventually turned to applied problems in mathematics.  As a result, Egorov suffered more than Luzin.  In 1924 Egorov was fired from a part-time teaching position he held in a Moscow engineering institute, and was attacked by ideologists as a “reactionary supporter of religious beliefs, a dangerous influence on students, and a person who mixes mathematics and religion.”  Yet Egorov was respected so much by his colleagues that the administration of the engineering institute had difficulty finding anyone who would “replace” him.  The first candidate, the mathematician Nikolai Chebotaryov, resigned when he learned why his predecessor Egorov had been fired.  This same Chebotaryov -- a significant mathematician known today for the “Chebotaryov Density Theorem” -- would later fight to save Egorov’s life in prison.
The Soviet authorities in the late twenties and afterward moved heavily against the Name Worshippers.  They arrested Father Florensky, perhaps the main ideologist of mathematical Name-Worshipping, and sent him to a labor camp in the Solovetsky Islands, far north in the Arctic Ocean, where he continued to do scientific work.  On December 8,1937, he was executed by firing squad.  In one of his last letters to his son, who lives in Moscow today, Florensky wrote, “Above all I think about you, but with worry.  Life is dead.”  All Florensky’s voluminous writings were removed from Soviet libraries, and even mentioning his name was forbidden.
Dmitrii Egorov, president of the Moscow Mathematical Society, was arrested in 1930 and sent to a camp near Kazan, on the Volga River.  There he went on hunger strike because the prison guards would not permit him to practice his religious faith.  Near death, Egorov was sent to a local hospital where he was recognized by the wife of the mathematician Chebotaryov, mentioned above.  The two Chebotaryovs did everything they could to try to save Egorov’s life, but it was too late.  We are told that he died in the arms of Dr. Chebotaryova, murmuring the Jesus Prayer.  Egorov’s name, like Florensky’s, was not to be mentioned in Soviet society.  These Name Worshippers became the object of name censorship. 
The philosopher A. F. Losev, who along with Egorov was a prime mover in the “Name Worshipper Circle” in Moscow, was arrested in 1930, sentenced to ten years in prison, but released in 1933.  He lived on until 1988; his wife is still alive and maintains a museum with much Name-Worshipping material in Losev’s old apartment (Arbat 33, apt. 20).  Many other members of that circle were arrested, imprisoned and/or executed.
The most talented of the mathematicians connected with religious movement, Nikolai Luzin, was subjected to a show trial, known even today as the “Luzin Affair.”   One of the ideological charges against him was that he “loved” capitalist France, where he often worked, and was a friend of the French mathematician Emile Borel (a colleague in set theory) who was at that moment Minister of the Navy in the French government, and therefore was obviously a “militarist” eager for aggression against the Soviet Union.  In a great act of heroism, one of the most famous physicists in the Soviet Union, Peter Kapitsa, wrote a confidental letter to the Soviet leaders Molotov and Stalin, pleading for mercy for “one of our greatest mathematicians, known throughout the world.”  Luzin was reprimanded but miraculously saved, and continued mathematical work until his death in 1950, although no longer in set theory and no longer in communication with his French friends.
The persecution of the Name Worshippers continued throughout the Soviet period, with arrests as late as the nineteen eighties, up to the Gorbachev period starting in 1985.  Even today the state-supported Orthodox Church considers Name Worshippers to be heretics, and moves against them whenever a visible spike of their activity appears.  Yet the heresy has never died out, and, in fact, is currently enjoying a small resurgence of interest among intellectuals, especially mathematicians.
In the summer of 2004 one of the co-authors of this proposed book, Loren Graham, met with a prominent mathematician in Moscow known to be in sympathy with Name-Worshipping.  The mathematician implied he was a Name-Worshipper without stating it outright.  His apartment was decorated with the symbols of Name-Worshipping, including photographs of its leaders.  His library was filled with rare books and articles on Name-Worshipping.  Loren asked if it would be possible for him to witness a Name-Worshipper in the Jesus Prayer trance.  “No,” replied the mathematician, “this practice is very intimate, and is best done alone.  For 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.”  Loren knew about this church; forty-five years earlier he had attended a student dance in the building after the church itself had been eliminated by Soviet authorities and converted into a student club and theater.  Now, in the post-Soviet period, it has been restored as the official church of Moscow University, as it was before the Revolution.  It is located on the old campus near the Kremlin, in a building next to the one that housed the Department of Mathematics when Egorov and Luzin dominated that department.  It is the church where they often prayed.  Loren asked the mathematician, “When I go into the basement, how will I know when I have reached the sacred spot?”  The mathematician replied, “You will know when you get there.”
The next day Loren went to the Church of St.  Tatiana the Martyr, and made his way to the basement.  There he found a particular corner where the photographs of Father Florenskii and Dmitri Egorov, founders of mathematical Name-Worshipping, faced each other, and he knew that he was in the sacred spot where Name Worshippers liked to come, alone, to practice the Jesus Prayer.  (Photographs of the spot taken by him at that time are appended to this proposal.)  But six months later, in December 2004, Loren visited the same spot again and found that it had been eliminated by the Church, which had finally realized that Name Worshippers were coming to the basement to celebrate their faith.  Now an official chapel of the Church occupies the basement spot, with a priest guarding over it and ensuring the orthodoxy of all worshippers.  Jesus Prayers are not practiced there any more.  Thus, the struggle over Name-Worshipping continues today.
We have attached to this proposal several other illustrations which depict people and places important to the history that we wish to tell.  The first is a genealogical  chart of the members of the Moscow Mathematical School – approximately 120 mathematicians who are descendants of Egorov and Luzin,  some of them world-famous.  A number are alive today, working not only in Russia, but also in Western Europe and the United States.  In 2004 the other co-author making this proposal, Jean-Michel Kantor, visited the spot in Batz-sur-Mer on the Brittany coast where Uryson and Alexandrov swam and Uryson died.  The photograph taken by Kantor depicts Uryson’s  tombstone, maintained today by the Russian embassy in Paris, which notes the mode of his death and his achievements in topology. 
Last summer Loren Graham also journeyed to a cemetery in Kazan, on the Volga river, and took a photograph of the gravesite of Dmitrii Egorov, the starving heretic.    While he was photographing Egorov’s tombstone he was approached by a man wearing a tuba  musical instrument  (see photograph).  The musician was in the habit of playing funeral dirges whenever he saw someone grieving in the cemetery, in the hopes of receiving a few rubles in return.  When the tuba player saw Loren looking at Egorov’s grave he asked “Did you know this man Egorov?”  Loren replied that he did not know him personally but greatly respected him.  Loren then asked the musician, “Do you know who Egorov was?”   The itinerant instrumentalist replied, “I have no idea who he was, but I’ll tell you something:  there is something very strange about this tombstone.  The lower bar of the Orthodox cross goes, left-to-right, upwards instead of downwards, as is required by the Church.  I think this man must have been a heretic.”  Loren replied, “He was a heretic.” A photograph of that tombstone is also appended.
  We also include photographs of Alexandrov and his lover Kolmogorov at their dacha and in the Kliazma river.  We propose to visit the island in the Arctic Ocean, and to photograph, the place where Pavel Florenskii, the inspirer of Name Worshipping as an approach to mathematics, was shot.  And we also wish to visit and photograph the Pantaleimon Monastery in Mt. Athos where the forced dispersion of the Name-Worshipping monks stimulated the story.
  Loren Graham is a specialist in the history of Russian science who has written many books and articles on the subject, including Science and Philosophy in the Soviet Union (Knopf), which was a finalist for a National Book Award.  Jean-Michel Kantor is a French mathematician and popular writer on science in la Quinzaine Littéraire  who is a specialist in topology and set theory.  Both of them have researched the story of Name-Worshipping and are acquaintances of the Russian mathematician described above who lives in Moscow at the present time and who sympathizes with the “heresy.”  (It perhaps should be noted that both Graham and Kantor are secularists and rationalists, and do not themselves subscribe to the mystical beliefs of the Name Worshippers.  But they believe that this remarkable story should be told.)  The two co-authors possess the knowledge (French and Russian history, history of science, mathematics) and the language skills (French, Russian, German, Spanish, English) necessary for the project.   They have already written together an academic article on the Name-Worshippers, pending publication.  They now propose to write a book on the same subject that will appeal to a broad audience.


[1] Explanation of meaning of the term “set”:  A “set” is a collection of entities that are identified by a common characteristic or rule of formation.  As Georg Cantor said, “A set is a Many that allows itself to be thought of as One.”  In other words, a set is a collection formed following a precise rule that allows one to decide whether a given entity belongs in the collection or not.  An example would be the collection of all giraffes living in South Carolina.  We know that according to the rule by which this set was created that giraffes in Massachusetts do not belong in the set, nor do donkeys in South Carolina.  The set of all odd whole numbers less than 10 would contain five entities (1, 3, 5, 7, 9).

 

[2] Salinger has Franny observing to her incredulous friend Lane, “If you keep saying that prayer [the Jesus Prayer] over and over again – you only have to just do it with your lips at first – then eventually what happens, the prayer becomes self-active.  Something happens after a while.  I don’t know what, but something happens, and the words get synchronized with the person’s heartbeats, and then you’re actually praying without ceasing.  Which has a really tremendous, mystical effect on your whole outlook.  I mean that’s the whole point of it, more or less.  I mean you do it to purify your whole outlook and get an absolutely new conception of what everything’s about.”  J. D. Salinger, Franny and Zooey, (Little Brown and Company:  Boston, 1961), pp. 36-37.