Pages 1--8 from SOURCE; The Influence of P. A. FLorensky on N. N. Luzin

SOURCE

The Influence of P. A. Florensky on N. N. Luzin

Charles E. Ford

Department of Mathematics and Computer Science, Saint Louis University,

Saint Louis, Missouri 63103

The study of the early history of the Moscow school of the theory of functions has been

greatly enhanced by the discovery of correspondence between one of its founders, N. N.

Luzin, and the priest, theologian, philosopher, and scientist P. A. Florensky. The correspon-dence

reveals that Luzin experienced a profound spiritual crisis in 1905 when his materialist

worldview collapsed. This crisis continued for three years and was finally resolved when Luzin

had a decisive encounter with the religious philosophy of Florensky. After this, Luzin's interest

in mathematics gradually revived until he was able, by 1909, to commit himself to a career

in mathematics. Ó 1998 Academic Press

Les e´ tudes concernant l'histoire des de´ buts de l'e ´ cole moscovite de la the´ orie des functions

ont e´ te´ grandement e´ claire´ es par la de´ couverte d'une correspondance entre l'un de ses fonda-teurs,

N. N. Luzin, et P. A. Florenski, un preà tre, the´ ologien, philosophe, et savant. Cette

correspondance re´ ve` le que Luzin a traverse´ une crise spirituelle profonde a` partir de 1905,

lorsque sa perspective mate´ rialiste du monde s'est effondre´ e. Cette crise a dure´ trois ans, et

a trouve´ sa re´ solution dans la rencontre de´ cisive de Luzin avec la philosophie religieuse de

Florenski. Par la suite, l'inte ´ reà t de Luzin pour les mathe´ matiques s'est progressivement

ravive´ , jusqu'a` ce qu'il soit en mesure de de´ cider, en 1909, de consacrer sa vie aux

mathe´ matiques. Ó 1998 Academic Press

Ó 1998 Academic

Press

MSC 1991 subject classification: 01A30, 01A60, 01A80, 03-03.

Key Words: religion; philosophy; materialism; Luzin; Florensky; Moscow.

INTRODUCTION

Nikolai Nikolaevich Luzin (1883± 1950) is a major figure in the history of 20th-century

mathematics [8]. He is particularly important as a founder of the Moscow

school of the theory of functions [2, 35; 8, 277]. The early history of the Moscow

school has been greatly illuminated by the recent discovery that a close relationship

had developed between Luzin and the philosopher, theologian, and scientist, Pavel

Aleksandrovich Florensky (1882± 1937) [1; 6].

332

0315-0860/ 98 $25.00 Copyright Ó 1998 by Academic Press

All rights of reproduction in any form reserved.
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This paper aims to highlight, through their correspondence [4], the profound

influence of Florensky on Luzin as the latter struggled to find an appropriate

worldview. Like many intellectuals of the early 20th century, Luzin embraced a

materialist worldview, which collapsed around the time of his graduation from

Moscow University in 1905. The ensuing crisis engulfed him for the next four years

and was ultimately resolved when Luzin had a decisive encounter with the religious

philosophy of Florensky. This enabled Luzin to launch his career as a mathematician.

Florensky entered Moscow University in 1900 and Luzin in 1901, both as students

in mathematics and physics. Florensky left the University upon graduation in 1904

to enter the Moscow Theological Academy. Upon graduation in 1908, he was

appointed directly to the faculty in the history of philosophy. In the spring of 1908

he wrote the treatise '' On Spiritual Truth. '' This was expanded into what became

his first doctoral dissertation in 1914. It was published under the title '' The Pillar

and Foundation of Truth'' [5] and has become one of the most famous works of

modern Russian theology.

THE CORRESPONDENCE

For the preservation of this correspondence we are indebted to the family of

Florensky, especially to his courageous wife, Anna Mikhailovna. After his arrest

she preserved much of his archive, including many unpublished manuscripts, papers

from his student years, and correspondence, including the letters he had received

from Luzin. The friendship between Florensky and Luzin had extended to include

their wives.

Toward the end of his life, Luzin burned his diaries. After his death in 1950, his

wife could easily have destroyed his remaining papers. Fortunately, she chose instead

to give the letters her husband had received from Florensky to his widow, along

with other related correspondence. Thus, at least parts of both sides of the corre-spondence

have been preserved.

The publication of this correspondence, by Sergei Demidov and his colleagues,

is a major event in the history of mathematics in Moscow. The correspondence has

been augmented with excellent footnotes and significant quotations from related

correspondence, as well as an informative introduction [3]. Another paper based

on this correspondence traces Luzin's early mathematical and philosophical devel-opment.

Most of the correspondence covers the period from the time Florensky left

Moscow for the Theological Academy in Sergiev Posad in 1904 until he moved

back to Moscow in January 1921. Luzin frequently visited Sergiev Posad (renamed

Zagorsk during the Soviet period and located about 30 miles northeast of Moscow)

and often spent the summer there. He came to love the town and especially valued

the opportunity to meet with Florensky. We can find echoes of their conversations

in the correspondence. The correspondence shows the powerful influence Florensky

had on turning Luzin toward an interest in the '' general questions'' of philosophy

and science.

One feature of the correspondence that is lost in translation is its formality. As
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with several European languages, Russian has two forms of the second person

singular pronoun '' you. '' One form is familiar, the other formal. In this correspon-dence

the latter is always used. This is rather surprising, given that the two had been

students together and enjoyed a long and intimate relationship. In this connection, it

may be noteworthy that the signatures at the end of the letters always include last

names. After being ordained, Florensky nearly always signed himself as '' priest. ''

Perhaps the formality reflects the somewhat unequal relationship between them, a

sign of Luzin's deference to the more mature Florensky. This deference is most

pronounced in spiritual matters, in which Luzin repeatedly seeks the advice of

Florensky. Whatever the case, the formality does not seem to be an obstruction to

the closeness of the relationship, and, if anything, makes the (often religious)

greetings in the correspondence seem the more intense.

SPIRITUAL CRISIS

After graduation, in the fall of 1905, Luzin left on his first commission to study

abroad. Florensky wrote to him in the spring of 1906, by which time he was in

Paris, in the midst of a deep spiritual crisis. Luzin responded to Florensky on 1

May 1906, in a letter [4, 135± 138] which sheds light on the long period of indecision

that he experienced before finally, in 1909, committing himself to mathematics. The

letter confirms the account by Esther Phillips [7, 283] that Luzin considered studying

medicine and attending lectures of a more philosophical nature, before finally

settling on a career in mathematics in 1909. More than indecision, Luzin was

experiencing an identity crisis that was tied up with his relationship with Florensky

[6, 28] and that had begun a year earlier in the spring of 1905, shortly before he

graduated from Moscow University.

Throughout this letter, Luzin addressed Florensky by the name Pyotr Afanasye-vich,

which has the same initials as Pavel Aleksandrovich, Florensky's real name.

The reason for this is not known, but may have some religious significance, possibly

connected with the names of Saints Peter and Athanasius. The editors note [4,

138± 139, n. 1] that at this time Florensky was preparing a work entitled '' Spiritual

Renaming. '' Florensky was very interested in the question of names. The editors

also remark [4, 138, first, unnumbered footnote] that the letter is addressed to '' His

Eminence P. A. Florensky'' at the Theological Academy in Sergiev Posad, so there

is no question that it was written to Florenksy. (Emphasis here and in succeeding

passages is in the original.)

I received your letter three weeks ago, and only now am I able (perhaps) to reply. . . . Life

is too depressing for me, sometimes agonizingly depressing. I am left with nothing, no solid

worldview; I am unable to find a solution to the '' problem of life. '' My self-image is so frequently

changing that life has become pure torment. That is why I was unable to reply to you immedi-ately.

You would not believe how precious your letter and your concern for my inner life were

to me. It is horrible, horrible, infinitely horrible to feel yourself surrounded by egoism, nothing

but unrelieved egoism.... There is such a lack of respect for people and even life itself. . . . If

I were sure that in fact there is not and cannot be any absolute respect in the world for the

soul of another, I would kill myself immediately. I cannot imagine living without that hope.

Why? I do not know. . . .
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By now you will have understood how precious to me, against the background of the vast

and empty night that oppresses the soul, the heart, and the brain to madness, how precious

to me is your concern for my inner life.

I have found myself abroad, in Paris, I don't know how, seemingly by chance.

You found me a mere child at the University, knowing nothing. I don't know how it happened,

but I cannot be satisfied any more with analytic functions and Taylor series.... Tobeprecise,

it happened about a year ago. . . . To see the misery of people, to see the torment of life, to

wend my way home from a mathematical meeting, to wend my way through the Aleksandrovsky

Garden [on the side of the Kremlin nearest the University], where, shivering in the cold, some

women stand waiting in vain for dinner purchased with horrorÐ this is an unbearable sight.

It is unbearable, having seen this, to calmly study (in fact to enjoy) science. After that I could

not study only mathematics, and I wanted to transfer to the medical school. I don't know what

stopped me. All I know is that it had nothing to do with thoughts of a career. It seems to have

been the thought: '' Would this be the right decision? '' Then came the terrible days for us all

[the 1905 revolution], for me in particular.... Ibarely remember what happened to me. I could

not work in science, and I seem to have begun to lose my mind as a result of the impossibility

of living quietly and understanding where, where the truth is. Dmitrii Fedorovich (Professor

Egorov), seeing me in such a state, sent me here to Paris. That is how I got here. . . . I have

been here about 5 months, but have only recently begun to study. I lacked the self-awareness.

[4, 135± 136]

Thus, although the specific catalyst of the crisis was the sight of women reduced

to prostitution, there are larger questions at issue. His letter continues by elaborating

on this, revealing that his previous (materialist) worldview had collapsed.

Life is painfully depressing for me Pyotr Afanasyevich! The worldviews that I have

known up to now (materialist worldviews) absolutely do not satisfy me. I may be wrong,

but I believe there is some kind of vicious circle in all of them, some fatal reluctance to

accept the contingency of matter, some reluctance, which I find absolutely incomprehensible,

to sort out the fundamentals, the principles. I have only recently come to understand this.

I used to believe inmaterialism, but I was not able to live according to it, and was

miserable, infinitely miserable.

Yes, I now understand that '' science, '' in essence, is metaphysical and based on nothing.

The scientific quest for '' differential resolvents for equations of degree six'' is absolutely

incomprehensible.... At the moment my scholarly interests are in principles, symbolic logic,

and set theory. But I cannot live by science alone. . . . I have nothing, no worldview, and no

education. I am absolutely ignorant of the philological sciences, history, philosophy.... It is

painfully clear to me that it makes no sense to settle for a '' scientific'' education. To see all

around that fatal lack of respect for the soul of another, its trampling underfoot, to see all

this, and not to know the right way to deal with people, not to know how to stand up for

them, to sense the mad folly of human relations and not to have or know the truthÐ Lord!

what pain this is....

My dear Pyotr Afanasyevich! Forgive me, for God's sake, for such a personal letter, but

I am so depressed that I can't see help anywhere.... Professor Egorov advised me to read

Kant. But Kant's assumptions seem to me to be ultra-shaky, to say nothing of Poincare´ 's

squalid philosophy.... I am willing to give up my personal life just to find out where to

seek the truth. For to know what the truth is and not to go there is unthinkable and

impossible.... Life depresses me perhaps because I don't understand what I need. What

I am now thinking about doing is, upon returning to Moscow, to attend lectures in the

Department of History and Philology. I am absolutely ignorant of these subjects, and I

cannot live on just mathematics and natural science. This Department may perhaps enable

me to make sense of human relations.... If I do not find a path to seek the truth . . . then

I will not go on living. [4, 136± 137]
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TOGETHER AGAIN

Luzin wrote again to Florensky for guidance on 14 March 1908. '' I want to see

you, and only you.... Thelonger I live, the more I feel that we must live differently

. . . '' [4, 142]. Luzin described his current studies as follows. '' I am studying mathe-matics

a little. I don't want to. I am more looking through historical and philological

journals and news of the theory of electrons'' [4, 142]. He added as a postscript,

'' I cannot become a specialist: I have been poisoned by you. I thank you for that''

[4, 143].

Amonth later, 11 April 1908, Luzin wrote an enthusiastic letter with a particularly

strong religious greeting, indicating that it was probably written just after Easter:

'' Christ is Risen! Dear Pavel Aleksandrovich! It is a shame that it was not possible

to greet you personally with these holy words on the Resurrection of Life itself''

[4, 144].

Luzin was now spending all his time studying number theory. '' It's a mysterious

area that envelops me deeper and deeper'' [4, 145]. He explained that his personal

life had changed profoundly. '' I have gotten married and am no longer alone'' [4,

145]. He was as anxious as ever to meet with Florensky and to read his works,

especially now because '' my wife is also very interested and shares my commitment

to the search for the profound truths of life'' [4, 145].

Luzin spent the summer of 1908 with his parents at the Chernigov Skeete, a

monastery near Sergiev Posad. In a long letter to his wife [4, 149± 151, n. 2], he

described a visit that he made to Florensky. By chance, Luzin's visit came at the

very moment of Florensky's appointment to the faculty of the Moscow Theological

Academy, to teach the history of philosophy. In the letter Luzin offers this evaluation

of Florensky's mathematical work: '' But as soon as he showed me his works in

mathematics, my old opinion came back to me: that all his works are of no value

in the area of mathematics. Suggestive hints, beautiful analogiesÐ very attractive

and promising, provocative, beckoning, but without any results'' [4, 150].

This statement is somewhat surprising because Luzin knew that Florensky aimed

not to produce results of interest to mathematicians, but rather to use the results

of mathematics in his philosophical and theological writings. In fact, earlier in the

letter Luzin described in great detail a discussion he had with Florensky about the

'' question about 'the number three' . . . why is God in three persons, not in two, not

in four . . .'' [4, 149]. They had an extended discussion about this issue, including

the drawing of diagrams and attempts at mathematical proofs. Luzin concluded

'' We were not able to do it after much thinking'' [4, 150].

In any case, the crisis that Luzin had been experiencing continued. Indeed it

seems to have reached its peak during the summer of 1908.

THE PILLAR AND FOUNDATION OF TRUTH

On 10 June 1908 Florensky defended his thesis '' On Religious Truth. '' Florensky

wanted to invite Luzin to attend the defense but was unable to reach him. That

same month, Florensky's thesis was published under the title '' The Pillar and Foun-dation

of Truth. '' An expanded version with the same title appeared in 1914.
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The book made a profound impact on Luzin. He wrote about it in a long letter

to his wife on 29 June 1908 [4, 146± 148, n. 3].

Today I want to write at length from my personal experienceÐ I don't know whether I'll

be able. I had to endure a lot as a result of the work of Florensky: '' The Pillar and Foundation

of Truth. . . .'' I read it all at once in a single dayÐ skipping a lot, but the impression was

overwhelming. As I read it, I was STUNNED the entire time by blows from a battering ram

against a stronghold.... [4, 146]

As Luzin described it, Florensky had destroyed the foundation of contemporary

intellectual life, which rejected religion in the name of reason, and he had brilliantly

but logically defended religious concepts which were scorned or ignored by the

contemporary intelligentsia. Luzin saw this as '' a worldwide tragedy of life and

reason. ''

I don't hesitate to use such words, they are completely appropriate here. Yes precisely a

world drama. For this is the stronghold by which the '' essence'' of our intelligentsia lives and

moves. By which it thinks and lives. And not only ours. I repeat, the issue here is the human

mind, its life and drama....

Our life, the life of the XIX and XX centuries, is full of confusion, full of contradictions.

This was not true earlier, it was not true of the Greeks (hence their strength, born of unity

and soundness). One need only to look at our intelligentsia [to see the confusion] ....

Our culture is such, as you have said many times yourself while thinking out loud, that it is

impossible to continue in it any further without harm to those of us who live in it.

The work of Florensky is one solution to this impossible situation. [4, 146± 147]

Luzin admitted that this solution lay '' in sub-logical soil, and this means foreign

to reason'' [4, 147]. It could be understood in apocalyptic terms, '' in the transforma-tion

of all flesh and all creation under the spirit of the judgment of God'' [4, 147].

'' How to respond to it, '' he asked. '' By feeling or by reason? Are such matters

amenable to reason? '' Luzin believed that Florensky had created '' a scandal for

university philosophy. ''

Because, in addition to discussing understanding through the senses ('' Physics, '' '' Natural

Science'') and understanding through the mind ('' Mathematics, '' '' Logic''), Florensky has given

equal rights to another kind of understanding, which you never hear about at the university,

namely '' intuitive± mystical understanding'' (Hindu). This is a great scandal. [4, 147]

Florensky had used '' philosophical research'' to give '' a brilliant psychological

analysis of the mind. '' Luzin regretted that this included so much scholarly material,

otherwise it '' would be understood by everyone, and cause everyone to turn pale''

[4, 147]. Florensky had portrayed '' the search of a mind suffering in a philosophical

hell, a search for religion, '' and continued with

a description of the psychic and somatic change at embarking on the Christian way and

prospering in it. Then comes a theological defense of disputed points of doctrine: a defense

of the doctrine of the Holy Spirit, a defense of the idea of that there is no contradiction between

religion and the mind. Then a brilliant defense of the doctrine of hell and its torments, a logical

defense, just brilliant.... Here there is a very good description of temptation by loveÐ which

perhaps Florensky has experienced himself. . . . [4, 147]
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In summary he wrote:

This work is so valuable because it deals with the most fundamental questions of life, not

by taking anything on faith, but on the contrary, by showing the limits of the mind, and then

going beyond, logically, intuitively, but based on reason. No work on religious questions has

ever presented so little fantasy and so much logic, which religious people are usually criticized

for lacking. . . .

The greatest of discoveries is when a pioneer builds a bridge between unconnected areas and

passes over it.... Ifthis work is completed, it will bring a wholeness to everything. [4, 147± 148]

This powerful experience for Luzin came at the very time when he was con-templating

suicide. Luzin explained this in a letter of 15 July 1908. He began by

thanking Florensky '' with all the gratitude of which I am able'' for the conversations

they had had that summer. '' Two times I was very close to suicideÐ then I came

here . . . looking to talk with you, and both times I felt as if I had leaned on a 'pillar'

and with this feeling of support I returned home. Excuse my openness and don't

think of it as anything negative: I owe my interest in life to you . . . ''[ 4, 148]. Over

the next year, Luzin would find his interest in mathematics gradually reviving.

AFTER THE REVOLUTION

Luzin was appointed to the Mathematics Faculty at Moscow University in 1917,

just before the Revolution. Florensky continued to live in Sergiev Posad until the

beginning of 1921.

In his final letter to Florensky, written 5 May 1919 (following the new calendar),

Luzin turned anew to Florensky for spiritual guidance. It appears that the Revolu-tion

had precipitated a strong desire in Luzin for a renewed spiritual life. He turned

to Florensky in '' deep inner need. '' '' I am overcome by a feeling of emptiness and

isolation from a source of spiritual life'' [4, 187]. On the outside nothing had

changed, but inside '' something has broken. ''

I have to admit it: clearly, mistakes were made, requiring correction. I fear for the future,

because for me it is now indefinite.

It is difficult to say just why, but I need to stop and examine my inner life and this is

inextricably connected with the need to draw closer to the way which you have followed and

continue to follow.... That is why I ask you, dear Pavel Aleksandrovich, to help me.... I

would like to have, if possible, all your published works. I do have many, but do not have

your big works, the latest lectures on philosophy (it is said that they are already published)

and above all, I do not have your thesis '' The Pillar and Foundation of Truth. '' [4, 187± 188]

This is the treatise that made such a profound impression on Luzin when he read

it in preliminary form in June 1908. When he saw the completed version in 1914,

he was rather critical of it. He now deeply regretted that he had not bothered to

preserve a copy of this '' basic and fundamental work. '' Knowing that the book was

now very valuable and difficult to obtain, he turned to Florensky for help. He

wanted not just to borrow a copy but to purchase one. '' I do not want just to read

it, it is necessary for me to absorb it. '' Luzin apologizes for imposing on Florensky,

but has been overcome by '' this overpowering spiritual need. '' '' I need it 'now' not

'later' . . . '' [4, 188].
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The correspondence ended much as it began, with Luzin again experiencing a

strong desire to follow Florensky in matters of '' the inner life. '' Florensky was

always the more emotionally mature of the two and Luzin seems to have depended

on this. This was also recognized by Luzin's wife, in two letters that she wrote to

Florensky on her husband's behalf, which are included among the 39 letters pub-lished

([ 4, 184± 186]). The editors have also included a footnote about two letters

that she wrote to Florensky in 1914, when she and Luzin had temporarily separated.

In response, Florensky noted

Nikolai Nikolaevich is a very sweet and fine person; but in personal relationships he is not

at all mature, especially in intuitively perceiving the hidden currents of life. You, as a woman

and on the strength of that alone, would have a sense for the inner life. You will have to take

the relationship in hand and create a family tone, simplicity. Instead, as I perceive it (excuse

me, perhaps I am mistaken!), you have established the tone of an acquaintanceship rather

than a family. [4, 175, n. 1]

In addition, the editors quote a letter she wrote to Florensky in 1915 [4, 183± 184,

n. 1] and one she wrote to his mother-in-law [4, 186, n. 1]. In the former, she pointed

out how valuable Florensky's visits were for Luzin, and urged him to visit more often.

CONCLUSION

The influence of Florensky was decisive in turning Luzin toward religious philoso-phy.

It was probably his friendship with Florensky that caused Luzin's materialist

worldview to collapse in the first place, especially after Florensky gave up a promis-ing

career in mathematics to study theology. The Revolution caused Luzin to seek

to reestablish and deepen his relationship with Florensky.

I express my sincere gratitude to an anonymous referee for generously providing

the translation of the entire letter of 1 May 1906, and overall for helpful suggestions

and comments.

REFERENCES

1. Sergei S. Demidov, On an Early History of the Moscow School of Theory of Functions, Philosophia

Mathematica 3 (1988), 29± 35.

2. Sergei S. Demidov, The Moscow School of the Theory of Functions, in Golden Years of Moscow

Mathematics, ed. Smilka Zdravkovska and Peter L. Duren, History of Mathematics, vol. 6, Providence,

RI: Amer. Math. Soc., 1993, 35± 53.

3. Sergei S. Demidov, Aleksei N. Parshin, and Sergei M. Polovinkin, On the Correspondence of N. N.

Luzin with P. A. Florensky, Istoriko-Matematicheskiye Issledovaniya 31 (1989), 116± 124. [In Russian]

4. Sergei S. Demidov, Aleksei N. Parshin, Sergei M. Polovinkin, and Pavel V. Florensky, ed., The

Correspondence of N. N. Luzin with P. A. Florensky, Istoriko-Matematicheskiye Issledovaniya 31

(1989), 125± 191. [In Russian]

5. Pavel A. Florensky, The Pillar and Foundation of Truth, Moscow: Put, 1914 [in Russian]; facsimilie

edition printed by Gregg International, Westmead, Farnborough, England, 1970.

6. Charles E. Ford, Dmitrii Egorov: Mathematics and Religion in Moscow, The Mathematical Intelligencer

13( 2) (1991), 24± 30.

7. Esther R. Phillips, Nicolai Nicolaevich Luzin and the Moscow School of the Theory of Functions,

Historia Mathematica 5 (1978), 275± 305.
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