The Tragedy of Mathematics in Russia

The Tragedy of Mathematics
IN RUSSIA

Contents

Nikolai Luzin

Nikolai Nikolaevich Luzin (1883–1950) was one of the founding fathers of the Moscow mathematical school. The list of his students contains Full Members of the Academy P. S. Alexandroff (1896–1982), A. N. Kolmogorov (1903–1987), M. A. Lavrentiev (1900–1980), P. S. Novikov (1901–1975); Corresponding Members L. A. Lyusternik (1899–1981), A. A. Lyapunov (1911–1973), D. E. Menshov (1892–1988), A. Ya. Khinchin (1894–1959), L. G. Shnirelman (1905–1938); and many other mathematicians.
The outstanding roles in the development of mathematics in Siberia were performed by M. A. Lavrentiev and A. A. Lyapunov, Luzin's direct descendants as well as Academicians A. I. Maltsev (1909–1967) and A. A. Borovkov, students of Kolmogorov.

The Case Against Luzin

Tsunami swept over the Russian mathematical community in 1999 after publication of the complete shorthand notes of the meetings of the notorious Emergency Commission of the Academy of Sciences of the USSR on the case of Academician Luzin [1]. Soon the article [2] appeared in the USA which revealed the personal testimony of G. G. Lorentz (1910–2006) about the mathematical life of that time in the USSR.1
The Commission for the “hearing of the case of Ac[ademician] Luzin” was convened by the Presidium of the Academy of Sciences of the USSR after the article “Enemies under the Mask of a Soviet Citizen” in the Pravda newspaper on July 3, 1936.
Luzin was accused of all theoretically possible instances of misconduct in science and depicted as an enemy that combined “moral unscrupulousness and scientific dishonesty with deeply concealed enmity and hatred to every bit of the Soviet life.” It was alleged that he publishes “would-be scientific papers,” “feels no shame in declaring the discoveries of his students to be his own achievements,” and stands close to the ideology of the “black hundred,” orthodoxy, and monarchy “fascist-type modernized but slightly.” The closing of the lampoon read:
All Russian scientists of the elder generation knew about the Pravda editorial and the savage dissolution of “Luzinism.” There was no denying that the initiation of the campaign for discrediting Luzin was carried out by the symbiosis of the party and repressive machinery of the USSR. Behind the scenes of the campaign loomed the grim figures of E. N. Kolman (1892–1979) and L. Z. Mekhlis (1889–1953), typical representatives of the Oprichnina of the Stalinist epoch. The former was Head of the Department of Science of the Moscow Urban Committee of the All-Union Communist Party (Bolsheviks), while the latter was Editor-in-Chief of Pravda.
The Luzin case had been considered only within the context of the general crimes of the Stalin totalitarianism for a long while. The newly-published archive files have opened to the public the new circumstances—some students of Luzin were rather active participants of the political assault on their teacher. The key role among them was played by P. S. Alexandroff who headed the Moscow topological school.
S. P. Novikov2 wrote in his reminiscences:3
Luzin was especially annoyed by the invectives of P. S. Alexandroff which were aimed at the declension of Luzin's contribution to analytic set theory.5 It is now in common parlance to call an analytic set the continuous image of a Borel subset of the reals. These sets are often associated with the names of P. S Alexandroff and M. Ya. Suslin and called A-sets or Suslin sets. Note that P. S. Alexandroff commented at the meeting of the Commission on July 6, 1936 as follows:6
In his reminiscences of 1979 he claimed quite the opposite:7
There was a mysterious relevant episode about the history of the discovery of A-sets which was narrated by A. P. Yushkevich (1906–1993) not long before his death:8
Rather active at the meetings of the Commission were A. N. Kolmogorov, L. A. Lyusternik, A. Ya. Khinchin, and L. G. Shnirelman. The political attacks on Luzin were vigorously supported by members of the Commission S. L. Sobolev (1907–1989) and O. Yu. Schmidt (1891–1956). A. N. Krylov (1863–1945) and S. N. Bernstein (1880–1968) revealed valor in the vigorous defence of Luzin. The final clause of the official Resolution of the Commission read as follows:10
All participants of the events of 1936 we discuss had left this world. They seemingly failed to know that the files of the Commission are all safe and intact. Today we are aware in precise detail of what happened at the meetings of the Commission and around the whole case. The mathematical community painfully reconsiders the events and rethinks the role of the students of Luzin in his political execution.

Roles of Luzin's Students

P. S. Novikov and M. A. Lavrentiev were not listed as participants of the public persecution of Luzin (despite the fact that both were mentioned at the meetings of the Commission among the persons robbed by Luzin). It transpires now why M. A. Lavrentiev was the sole author of a memorial article [7] in Russian Mathematical Surveys on the occasion of the ninetieth anniversary of the birth of Luzin. He also included this article in the collection [8] of his papers on the general issues of science and life. M. A. Lavrentiev was the chairman of the editorial board of the selected works of Luzin which were published by the decision of the Academy of Sciences of the USSR after the death of Luzin on the occasion of the 70th anniversary of his birth. P. S. Alexandroff and A. N. Kolmogorov were absent from the editorial board.
Practically the same are the comments on their relationship with Luzin which were left by P. S. Alexandroff and A. N. Kolmogorov. Their statements are still shared to some extent by their numerous students. It is customary to emphasize that Luzin was not so great a mathematician as his students that had persecuted him. Some moral fault is persistently incriminated to Luzin in the untimely death of M. Ya. Suslin (1894–1919) from typhus fever. Luzin is often blamed for all his disasters at least partly. He is ascribed such traits of character as theatricality, envy of others' success, hypocrisy, plagiarism, and inclination to intriguing.11 He is said to deserve all punishments and if not all then it is not his students' fault but Stalinism and the curse of the epoch. These arguments reside in the minds of not only the elders but also the youngsters. The best of them view the Luzin case as the mutual tragedy of all participants.
We should however distinguish the personal tragedy of Luzin from the tragedy of the Moscow school and the tragedy of the national mathematical community. The students of Luzin who participated in the persecution of the teacher never considered their own fates tragical.
P. S. Alexandroff wrote in his reminiscences:12
It is worth observing that A. Ya. Khinchin, hostile to Luzin, commented on the accusations that Luzin drove M. Ya. Suslin to death as follows:14
Narrating his reminiscences of P. S. Alexandroff, A. N. Kolmogorov told in 1982:15
Neither he nor Alexandroff nor other participants of the persecution of Luzin had ever treated the Luzin case as a common tragedy with Luzin. They were correct in this judgement but on the grounds completely different from those they declared.
If Luzin were guilty then his fault would belong to the sphere of the personal mathematical relations between a teacher and a student. No convincing evidence of Luzin's plagiarism was ever submitted. The alleged accusations that he ascribed to H. Lebesgue (1875–1941) or kept a grip of Suslin's results are poorly disguised and baseless. To prove the scientific misconduct of Luzin it was alleged that Luzin ingratiated and flattered H. Lebesgue by ascribing Luzin's sieve method to H. Lebesgue. On the other hand, H. Lebesgue wrote in his preface to the Luzin book on analytic sets:16
The students were “more Catholic than the Pope.”17
In any case, we cannot help but ascertain that there clearly was a conflict of generations—the precipice of alienation and misunderstanding between Luzin and his most successful students. It is easy to assume the genuine or imaginary injustice and prejudice of Luzin in citing his students as well as the genuine or imaginary feebleness of Luzin in overcoming mathematical obstacles. We may agree to see hypocrisy in Luzin's decision to vote against P. S. Alexandroff in the elections to a vacancy of an academician despite his personal letter of support of P. S. Alexandroff to A. N. Kolmogorov. Well, there is nothing untypical of the academic manners or extraordinary in Luzin's conduct, isn't there? It is the true background of the Luzin case, isn't it?
Available is the following testimony of W. Sierpinski (1882–1969), a famous Polish mathematician who was declared to be a “blatant black hundredist” at the meetings of the Commission of the Academy of Sciences of the USSR on the Luzin case:18
The pretentious reconciliation of P. S. Alexandroff with Luzin which was described by W. Sierpinski and which was later publicly refuted by P. S. Alexandroff is in no way similar to the refusal of Luzin to support the election of P. S. Alexandroff as an academician, isn't it? It is in general belief that this refusal was the reason for A. N. Kolmogorov to slap the face of Luzin publicly in 1946.19 L. S. Pontryagin (1908–1988) wrote on December 24, 1946:20
V. M. Tikhomirov disclosed the correspondence between Luzin and A. N. Kolmogorov on the eve of the elections of P. S. Alexandroff. In the fall of 1945 Luzin wrote to A. N. Kolmogorov:24
A. N. Kolmogorov overestimated the position of Luzin who had written nothing more than that he was going to support P. S. Alexandroff as a nominee for the elections (which Luzin fulfilled in due time).
In the reply letter of October 7, 1945 A. N. Kolmogorov remarked:25
Clearly, A. N. Kolmogorov decided without proper grounds that Luzin would support the election rather than nomination of P. S. Alexandroff. Luzin however promised nothing of the sort in his letter. It is the tradition of a long standing that nomination and election to the Academy of Sciences and other similar institutions are sufficiently independent procedures.
Usually A. N. Kolmogorov was viewed as a calm person not liable to fits and extremes of temper. Therefore, he seemingly needed some special provocation from Luzin for slapping in Luzin's face, which led to some apocrypha about an obscene remark from Luzin at the elections of 1946.26 An analogous version was mentioned by V. I. Arnold in private correspondence. It is not excluded that the available hints on topolozhstvo27 is a produce of the 1950s put in gossips for rehabilitation of the instigators of the “Luzin case.” But the students of A. N. Kolmogorov indicated one quite unknown trait of his personality. V. M. Tikhomirov wrote:28
V. I. Arnold (1937–2010) witnessed:29
Luzin was twenty years older than A. N. Kolmogorov. Luzin was a teacher of A. N. Kolmogorov and carried the heavy burden of political accusations that were imposed on Luzin with participation of P. S. Alexandroff and A. N. Kolmogorov. Luzin was granted “mercy” and accepted at the country house of A. N. Kolmogorov and P. S. Alexandroff in Komarovka before the elections.30 Everyone at the meeting remembered the most important matter that Luzin was victimized and must surrender to the noble victors, didn't he? It transpires now, doesn't it? We can compare the internal academic matters, say Luzin's misconduct and even plagiarism, with the accusations of subversive activities against the Soviet life, can't we? These grave and vexed questions...
Closing the meeting on July 13, 1936, Academician G. M. Krzhyzhanovskii (1872–1959), Chairman of the Commission, told in particular:31
No elections to the Academy were arranged in 1936. The great elections took place only on January 29, 1939.32 The following mathematicians were elected to the Department of Mathematical and Natural Sciences of the Academy: A. N. Kolmogorov and S. L. Sobolev became full members, while A. O. Gelfond, L. S. Pontryagin, and A. Ya. Khinchin became corresponding members.

Reactions of Luzin's Contemporaries

All moral accusations against Luzin are rather inconvincible. That which was submitted as proofs was inadequate even in the times of the Commission neither for P. L. Kapitsa (1894–1984), nor V. I. Vernadsky (1863–1945), nor A. Denjoy (1884–1974), nor Lebesgue, nor many other elder persons.
The objections of Kapitsa were expressed on July 6 in his letter to V. M. Molotov who was the Chairmen of the Council of the People's Commissars of the USSR. V. I. Vernadsky noticed in his diary on the next day:33
On the same day he sent a letter to Academician A. E. Fersman (1883–1945), a member of the Commission. V. I. Vernadsky remarked:34
And on July 11 S. A. Chaplygin (1869–1942) wrote to V. I. Vernadsky:35
Lebesgue's letter of August 5, 1936 is in order now. I remind that H. Lebesgue was elected in 1929 to the Academy of Sciences of the USSR for his outstanding contribution to mathematics. The great Lebesgue, the author of that very "Lebesgue integral" which is indispensable in modern mathematics, was in the state of utmost indignation and anger. He wrote:36
Another evidence of W. Sierpinski is as follows:37
The method of political insinuations and slander was used against the old Muscovite professorship many years before the Pravda article. The declaration of November 21, 1930 of the “initiative group” of the Moscow Mathematical Society which consisted of L. A. Lyusternik, L. G. Shnirelman, A. O. Gelfond, and L. S. Pontryagin and K. P. Nekrasov claimed:38
D. F. Egorov (1869–1931) was the teacher of Luzin. Shortly before D. F. Egorov had been arrested, and Luzin decided it wise to leave the university (he was later accused of this removal by his students).
In his life's-description, dated as of the late 1970s, L. S. Pontryagin asserted:40
This is totally inconsistent with the position of Luzin who wrote in his letter of 1934 to L. V. Kantorovich (1912-1986) after the ugly declaration signed by A. O. Gelfond that his choice in Moscow for the forthcoming election of corresponding members of the Academy “will be Gelfond who has recently made a discovery worthy of a genius.”41
And in 1939 Luzin wrote to V. I. Vernadsky:42
A broad campaign against Luzin and “Luzinism” waged over this country in 1936.43 Fortunately, Luzin was not repressed nor expelled from the Academy. Some historians opine that there was a relevant oral direction of I. V. Stalin.44 But the badge of an enemy under the mask of a Soviet citizen was pinpointed to Luzin during 14 years up to his death. The monstrosity over Luzin is absolutely incomparable with the alleged accusations of moral misconduct.

Mathematical Roots of the Luzin Case

The human passions and follies behind the 1930s tragedy of mathematics in Russia are obvious: love and hatred, jealousy and admiration, vanity and modesty, generosity and careerism, etc. But was there a mathematical background? Some roots are visible.
We are granted the blissful world that has the indisputable property of unicity. The solitude of reality was perceived by our ancestors as the ultimate proof of unicity. This argument resided behind the incessant attempts at proving the fifth postulate of Euclid. The same gives grounds for the common search of the unique best solution of any human problem.
Mathematics has never liberated itself from the tethers of experimentation. The reason is not the simple fact that we still complete proofs by declaring “obvious.” Alive and rather popular are the views of mathematics as a toolkit for natural sciences. These stances may be expressed by the slogan “mathematics is experimental theoretical physics.” Not less popular is the dual claim “theoretical physics is experimental mathematics.” This short digression is intended to point to the interconnections of the trains of thought in mathematics and natural sciences.
It is worth observing that the dogmata of faith and the principles of theology are also well reflected in the history of mathematical theories. Variational calculus was invented in search of better understanding of the principles of mechanics, resting on the religious views of the universal beauty and harmony of the act of creation.
The twentieth century marked an important twist in the content of mathematics. Mathematical ideas imbued the humanitarian sphere and, primarily, politics, sociology, and economics. Social events are principally volatile and possess a high degree of uncertainty. Economic processes utilize a wide range of the admissible ways of production, organization, and management. The nature of nonunicity in economics transpires: The genuine interests of human beings cannot fail to be contradictory. The unique solution is an oxymoron in any nontrivial problem of economics which refers to the distribution of goods between a few agents. It is not by chance that the social sciences and instances of humanitarian mentality invoke the numerous hypotheses of the best organization of production and consumption, the most just and equitable social structure, the codices of rational behavior and moral conduct, etc.
The twentieth century became the age of freedom. Plurality and unicity were confronted as collectivism and individualism. Many particular phenomena of life and culture reflect their distinction. The dissolution of monarchism and tyranny was accompanied by the rise of parliamentarism and democracy. Quantum mechanics and Heisenberg's uncertainty incorporated plurality in physics. The waves of modernism in poetry and artistry should be also listed. Mankind had changed all valleys of residence and dream.
In mathematics the quest for plurality led to the abandonment of the overwhelming pressure of unicity and categoricity. The latter ideas were practically absent, at least minor, in Ancient Greece and sprang to life in the epoch of absolutism and Christianity. G. Cantor (1845–1918) was a harbinger of mighty changes, claiming that “das Wesen der Mathematik liegt gerade in ihrer Freiheit.” Paradoxically, the resurrection of freedom expelled mathematicians from the Cantor paradise.
Nowadays we are accustomed to the unsolvability and undecidability of many problems. We see only minor difficulties in accepting nonstandard models and modal logics. It does not worry us that the problem of the continuum is undecidable within Zermelo-Fraenkel set theory. However simple nowadays, these stances of thought seemed opportunistic and controversial at the times of Luzin. The successful breakthroughs of the great students of Luzin were based on the rejection of his mathematical ideas. This is a psychological partly Freudian background of the Luzin case. His gifted students smelled the necessity of liberation from description and the pertinent blissful dreams of Luzin which were proved to be undecidable in favor of freedom for mathematics. His students were misled and consciously or unconsciously transformed the noble desire for freedom into the primitive hatred and cruelty. This transformation is a popular fixation and hobby horse of the human beings through the ages.
Terrible and unbearable is the lightheaded universal fun of putting the blame entirely on Luzin for the crimes in mathematics which he was hardly guilty of with the barely concealed intention to revenge his genuine and would-be private and personal sins. We should try and understand that the ideas of description, finitism, intuitionism, and similar heroic attempts at the turn of the twentieth century in search of the sole genuine and ultimate foundation were unavoidable by way of liberating mathematics from the illusionary dreams of categoricity. The collapse of the eternal unicity and absolutism was a triumph and tragedy of the mathematical ideas of the first two decades of the last century. The blossom of the creative ideas of Luzin's students stemmed partly from his mathematical illusions in description.
The struggle against Luzin had mathematical roots which were impossible to extract and explicate those days. We see clearly now that the epoch of probability, functional analysis, distributions, and topology began when the idea of the ultimate unique foundation was ruined for ever. K. Gödel (1906–1978) had explained some trains of thought behind the phenomenon, but the mathematicians par excellence felt them with inborn intuition and challenge of mind.
It was Luzin whom the vision of the Moscow school of today had started with. Luzin was interested in foundations, and description for him was the method of understanding the whole of mathematics. Sprang to life as the theory of measurability, description has not passed away—it is alive in recursive analysis and other ideas related to computability and the Church thesis.
Description plays the same role in regard to finitism and intuitionism as absolute geometry plays in regard to elliptic and hyperbolic geometries. The procedures and ideology of description are the forerunners of the ideas of computability and algorithm. The creative contribution of A. N. Kolmogorov into algorithm theory, computability, and complexity comprises the component that stems from description. Probability theory, turbulence, and analysis constitute the component that is rooted in the refusal from description. Mathematics reduces to neither finitism, nor intuitionism, nor description. It is not categorical—it is free. In the twentieth century the freedom of mathematics was best demonstrated in Russia by A. N. Kolmogorov, a student of Luzin and the teacher of the new generations of mathematicians in this country. He harbored more freedom in mathematics, which made him a greater mathematician.
It is the tragedy of mathematics in Russia that the noble endeavor for freedom had launched the political monstrosity of the scientific giants disguised into the cassocks of Torquemada.

A Few Lessons

History and decedents are out of the courts of justice. Scientists and ordinary persons must see and collect facts. Never accuse the passed away, but calmly and openly point out that which was in reality. Explain the difference between moral accusations and political insinuations to the youth. Demonstrate the difficulty and necessity of the repairing of mistakes and repentance. Show how easy it is to forgive oneself and accuse the others.
We must work out and transfer to the next generations the objective views of the past. Of its successes and tragedies. With love and doubts, with the understanding of our unfortunate fate and the honor of objectivity. It is the personal faults and failures that we are to accuse and repair first of all. They knew even in Ancient Rome that we should tell nothing or good about the dead. Facts did never pass away. Luzin was accused by the community of Moscow mathematicians as well as by the Academy of Sciences.
The defence of Stalinism consists often in proclaiming that the ugly misdeeds and crimes of Stalinism are the fault of Stalin, Beriya, Mekhlis, Kolman, and the hord of their minor clones and replicas, while in fact Stalinism was created by millions. Stalinism in science was mainly raised by scientists themselves. It is indecent to pretend that Luzin's students safeguarded their teacher and science from Stalinism. Luzin was a victim of social ostracism and lived with the brand and stigma of an adversary with a Soviet mask during fourteen years up to his death. He became an exemplary outcast for Stalinism—an adversary at large. Luzin's colleagues and students lowered and neglected him, which culminated in slapping in his face and spitting on his tomb. Luzin has passed away but the false accusations in sabotage and obsequiousness are still effective.
We cannot forget the words of Luzin:45
Any attempt at discerning morality in the past immorality is dangerous since it feeds this immorality by creating the comfortable environment of immorality in the present and future. The stamina of a scientist by belief is a discontinuous function. Science does not inoculate morality. Evil and genius coexist from time to time.
History is a branch of science, but science goes hand in hand with conscience. Therefore history is not only a scientific discipline but also a matter of responsibility of the present. No one can change the history but we, the humankind, are not indifferent onlookers on the past. History is not anything existant without people. The past is the past of the present and as such it is part of the present-day responsibility. The alive rather than the dead are responsible for what was done in the past. It is we who change life so creating the future. History awakens our conscience and hits in our hearts alike the ashes of Claes' did in Till Eulenspiegel's.

Acknowledgements

This essay summarizes the author's position at the informal lobby discussions at the Mini-Symposium on Convex Analysis which was held at Lomonosov Moscow State University, February 2–4 (2007). The author is especially grateful to Professor V. M. Tikhomirov, Chairman of the Mini-Symposium, for endurance, friendliness, and hospitality.
This article is an expanded and updated version of the author's article “Roots of Luzin's case.”46
Working on the article the author has appreciated and enjoyed the helpfull and encouraging attitude of many other scientists among which of the utmost importance for the author was the highly-principled moral views of V. I. Arnold, A. A. Borovkov, and Ya. G. Sinai, the direct students of A. N. Kolmogorov.
The author has received many comments and replies with criticism and advice all aiming at the improvement of the article, as well as containing the indication of some new documentary sources and reminiscences. The author thanks all his readers and correspondents.

References

[1] Demidov S. S. and Levshin B. V. (Eds.), The Case of Academician Nikolai Nikolaevich Luzin. St. Petersburg: Russian Christian Humanitarian Institute, 1999.
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[5] Yushkevich A. P., “My Few Meetings with A. N. Kolmogorov.” In: Kolmogorov in Reminiscences, (Ed. A. N.Shiryaev), Moscow: Fizmatgiz (1993), 602–617.
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[8] Lavrentiev M. A., Science. Progress in Technology. Cadres. Novosibirsk: Nauka Publishers, 1980.
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S. Kutateladze
Sobolev Institute of Mathematics
Novosibirsk
February 7, 2007–May 9, 2011


Footnotes:

1I am very grateful to Professor W. A. J. Luxemburg for attracting my attention to the inadvertent omission of a reference to [2] in the draft of this paper.
2Sergei Petrovich Novikov is a Fields medalist, the son of L. V. Keldysh and P. S. Novikov who were students of Luzin.
3Cp. [3, p. 45].
4G. K. Khvorostin (1900–1938) was an educated mathematician, Rector of Saratov State University in 1935–1937. A. Ya. Khinchin qualified him as “the Party youth” (cp. [1, p. 100]).
5Cp. [4].
6Cp. [1, p. 90].
7Cp. [6, p. 235].
8Cp.  [5].
9 J.-M. Kantor informed me that his attempts, and the attempts by S. S. Demidov either, were in vain to find this envelope in the Archive of the Russian Academy of Sciences (S. K.).
10Cp. [1, p. 296].
11No person with these defects of personality could ever become the founder of “Lusitania”—the most successful mathematical school in the history of world science. Therefore, there exists a rather likely theory of “two Luzins”: one of the epoch of Lusitania and the other of the times of the Luzin case.
12Cp. [6, p. 90].
13 P. S. Alexandroff cited the poem Harfenspieler dated as of 1795 by Johann Wolfgang von Goethe (1749-1832) and gave a rough translation into Russian. The lines in English here belong to Vernon Watkins (1906–1967).
14Cp. [5, p. 391]
15Cp. [11, p. 10].
16Cp.  [12].
17 The corresponding excerpt of the shorthand minutes of the meeting of the Commission on July 13, 1936 is as follows: [1, p. 196–197]:
Alexandroff. As regards obsequiousness, I suggest that we will use the genuine words of the lips of Lebesgue: (Reads in French). Concerning this matter, I have explanations that I can explicate as thoroughly as need be. The "strange mania" in question, I would say, is a deeply premeditated idea. He ascribed to Lebesgue his belongings and he did it in so dopey manner. No sane person would ever ascribe them to Lebesgue. The thing is that doing so he creates his reputation of the person who ascribes his own ideas to someone else; but when the matter concerns his own students then he robbed their belongings while hiding behind this screen.
Lyusternik. This kind of defence sounded at the meeting in the [Steklov (S. K.)] Institute. Precisely this way of defence that was clearly inspired by him: How might it happen that N. N. grips the results of the others if Lebesgue himself writes these words about him?
Alexandroff. This is an obsequious system since it is uncustomary in academic circles to ascribe someone's own results to anybody else. Therefore, we see here, on the one hand, his flattery of Lebesgue and, on the other hand, the arranging of the screen that allows him to behave so.
18Cp. [13, p. 124].
19About various versions of this episode see the recent book by L. Graham and J.-M. Kantor [14, p. 186] as well as the reminiscences of S. M. Nikolskii [15, p. 155] and S. P. Novikov [3, p. 22].
20Cp. [16, Letter No. 49, p. 89–91].
21With the letter u pronounced as oo in soon, Pusiks was the collective equivocal nickname of P. S. Alexandroff and A. N. Kolmogorov. The singular Pusik was applied only to P. S. Alexandroff. For the English ear the word Pusiks has an obscene connotation, but this effect is completely absent in Russian.
22This is an interim committee convened at the elections that discusses all nominees and chooses those that are recommended to be elected. The names of the recommended nominees appear at the top on voting bulletins, which prompts the choice of those unacquainted with the candidates.
23 The elections to the Academy of Sciences of the USSR in 1946 took place on November 30. It was M. A. Lavrentiev and I. G. Petrovskii (1901–1973) who were elected to fill the mathematical vacancies of a full member in the Division of Physics and Mathematics. A. D. Alexandrov (1912–1999), N. N. Bogolyubov (1909–1992), L. A. Lyusternik, and V. V. Stepanov (1889–1950) became corresponding members of the Academy.
24Cp. [11, p. 80].
25Cp. [11, p. 82].
26E.g., see [14, p. 186] and [3, p. 22].
27This is a portmanteau of the Russian words for topology and pederasty—something like “topologasty” in English.
28Cp. [11, p. 83].
29Cp. [17, p. 50].
30V. M. Tikhomirov wrote about the meeting in Komarovka: “The correspondence of L. S. Pontryagin and his student and friend I. I. Gordon reveals that Luzin was accepted and served a meal in Komarovka.” Cp. [11, p. 83].
31Cp. [1, p. 196].
32Cp. [23,No. 241, No. 242].
33Cp.  [18, p. 92].
34Cp. [18, p. 94]
35Cp. [19, p. 106–107].
36Cp. [13, p. 127].
37Cp. [13, p. 125].
38Cp. [10] and [20].
39This is the standard abbreviation in Russia of the political police of those years which was called the United State Political Department.
40Cp. [21, p. 91].
41Cp. [22].
42Cp. [19, p. 105].
43Cp. [24, p. 757–767].
44It was disclosed recently that the above-mentioned letter of P. S. Kapitsa to V. M. Molotov was multiplied in 16 copies for the members of the Political Bureau of the All-Union Communist Party (Bolsheviks) and discussed over with other letters in support of Luzin.
45Cp. [1, p. 73].
46J. Appl. Indust. Math., 1: 3, 261–267 (2007).


The Presidium of the Russian Academy of Sciences dismissed the Luzin case by Resolution No. 8 of January 17, 2012:
This act annuls the Resolution of the Presidium of the Academy of Sciences of the USSR of August 5, 1936 (Protocol 16).

The decision followed the appeal to the Presidium of the Russian Academy of Sciences signed by A. A. Borovkov, V. E. Zakharov, I. A. Ibragimov, V. E. Nakoryakov, A. K. Rebrov, and Yu. G. Reshetnyak.

An Epilog

   Every now and then I still hear quite a few questions to me concerning the Luzin case. In my opinion three of them deserve public answers.
Question: Why do you avoid properly evaluating the role of Arnošt Kolman who was almost surely the author of the anti-Luzin letters in the Pravda newspaper and who was an agent of Stalin's totalitarianism in the scientific life of Russia in that epoch?
Answer: There is no doubt that Kolman was a rapscallion and a vilest skunk who authored many anonymous and signed lampoons. But Kolman was not a working mathematician, and his attempts at implanting Bolshevism in mathematics had vanished quickly and left practically no aftermaths. Kolman was not a member of the Emergency Commission of the Academy of Sciences of the USSR on the Case of Academician Luzin. He never took the floor at the meetings of the Commission, and he never wrote a word about the Luzin case in his reminiscences, which demonstrates that he had viewed the Luzin case neither among his successes nor among his crimes. Practically no one of the younger generations has ever heard about Kolman. Some students of Nikolai Luzin and Pavel Alexandroff did flirt with Kolman, which implies nothing but the negative characterization of these students and their truculent roles in hounding Luzin. The Luzin case was a message to Stalin and his myrmidons: “We will trample anyone down—just give a sign.” The scenario of the Luzin case was clearly written in the Central Committee of the All-Union Communist Party (Bolsheviks), while it was the students of Luzin who had instigated the case and played key roles at the meetings of the Emergency Commission.
   The list of the members of the Commission is now in order: Chairman G. M. Krzhizhanovsky; Members of the Commission—A. E. Fersman, S. N. Bernstein, O. Yu. Schmidt, I. M. Vinogradov, A. N. Bakh, N. P. Gorbunov, L. G. Snirelman, S. L. Sobolev, P. S. Alexandroff, and A. Ya. Khinchin.
Question: Why do you not see that Luzin's students, their friends, and G. M. Krzhizhanovsky made all they could to save Luzin from death, although Luzin had pushed his students away by his misconduct, hypocrisy, plagiarism, unfair reviews of feeble papers, and so on?
Answer: I do not see anything that is absent. Completely preposterous is the suggestion that the Academy of Sciences and Luzin's students had protected Luzin from Stalinism. The facts destroy the possibility of their noble defence of Luzin and science from Stalin. The hypothesis that Stalin stood behind the Luzin case has no documentary justifications. This hypothesis is clearly of a contrive and a posteriori nature. Luzin was made the target of the attack by some of his students—is fecit, cui prodest. That is exactly how the Luzin case was viewed by virtuous contemporaries. The documentary evidence of that is galore. Krzhizhanovsky position is completely characterized by the fact that he never eliminated the political flavor of the abominable trial.
   It suffices today to read what was said by the Luzin judges at the meetings of the Commission. Also, we must never forget that the participants of the trial had kept silence during half a century. They had concealed all documents and had never spoken about any attempts of theirs at protecting their teacher from Stalinism, Alexandroff wrote about just revenge to Luzin in 1979, while Kolmogorov had slapped the face of Luzin in 1946 and tried to justify this by Luzin's misconduct in the 1980s. But we know nothing about any attempts of the students to apologize for their ugly deeds against Luzin. The truth about the Luzin case became known to the public contrary to the will of the participants of the trial of Luzin. Luzin's students had elaborately concealed their participation in the Luzin case. And there were good reasons for that: Luzin was accused in servitude to the masters of “fascistoid science,” and the accusation was never disputed at the meetings of the Commission by anyone but Luzin. The Commission completely ascertained the characteristics of Luzin in the Pravda newspaper. “Completely” means that it ascertained the servitude of Luzin to the obviously foreign “masters of fascistoid science.” Bernstein was the only member of the Commission who defended Luzin.
    The minutes of the meetings of the Emergency Commission are historical documents. Anything written is much stronger that any ad hoc hypothesis. It stands to reason to look at some excerpts from the minutes.
  • Krzhizhanovsky. N.N. said that he confesses to this, confesses to cowardice. But we see here either the absence of at least a tiny bit of Soviet patriotism and even, I would say, of the Soviet feeling—the feeling of a Soviet citizen. I would like to clarify: He is an academician, a Soviet academician who works at the highest headquarters, at the scientific headquarters of this country; and he reveals lack of courage [and cowardice] in this matter.
  • Krzhizhanovsky. There is no shred of a doubt that he is a boundless coward. And this boundless cowardice led him to the complete loss of any principles and to double-dealing. He is a coward not only in regard to the Soviet reality but also to the All-Slavic Congress and Lebesgue. This is a typical double-dealing for the two sides: here and there. This is proven.
  • Sobolev. A comment about the policy of N.N. when on the agenda was the election of corresponding members of the Academy of Sciences of the USSR and similar matters. I recall for instance the elections of 1934 when N.N. implemented a very strange policy. Indeed, S[ergei] N[atanovich] [Bernstein] had presented a rather large list of serious scientists so that we treated the responsible task with due respect and had a possibility of discussing who really deserved the merit and who could be elected. The list had included the most capable young persons like A. Kolmogorov, Gelfond, and others. The list had been compiled rather objectively in my opinion. And the only thing left was to evaluate each candidate seriously in the [mathematical] group of the Academy. But N.N. used formalities like something was absent or some report that can appear the next day was not submitted in time. In other words, using some trifles exaggerated by him, he requested in a completely hysterical tone that no candidacy but he had nominated should be considered. In fact he made impossible any discussion of the candidates and put the group into the position when the sole candidate was nominated. I will not discuss whether this candidate deserves election, maybe this is so, but the fact of refusal of discussion and election of proper candidates speaks for itself. I for myself saw in this simply that N.N. was in fact utterly reluctant to have some suddenly elected representative of the youth like A.N. Kolmogorov whom N.N. had no intention to admit to the Academy. After the meeting of the group I told N.N. that this was an outrage, N.N., that what you had been doing. And he answered to me that those were the sacred traditions of the Academy of Sciences, etc.
       I think that he adhered in the Academy to the policy that, by all means, caused harm to the Academy of Sciences. Maybe, he made this pursuing his private rather than political ends—this is possible. We may assume that he had thought that this would be bad for him if such and such persons were elected. But it is possible that the utter contempt to our Academy of Sciences resulted in the desire of arranging some cosy group around himself.
  • Alexandroff. I agree about the first part with S[ergei] L[vovich]. I see too that N.N. was completely outrageous in all his public activities. I'll say it clearly that there is no doubt that N.N. could transform any public activity to something ridiculous. But I consider as wrong the statement of S[ergei] L[vovich] that N.N. did not respect the Academy of Sciences. I think that my meetings with him in the recent years corroborate me full and firm belief in that. On the contrary, N.N. appraises nothing under the Sun as much as the title of academician. And those who had contacted him in person got in a predicament because of that, since N.N. has demonstrated every now and then that an academician is a person of a completely different composition that any other mortal. This was so definite that it often gave a comical impression. N.N assessed his title of academician quite highly but reflected in some crooked mirror of his.
       As regard his antisocial deeds, these are many to be recalled. I view N.N., while this might be a rather rude expression, as an intriguer—a person who is always concerned about having a surrounding group of minions who are loyal to him and stare at his mouth. And it is this that explains many of his appraisals of inappropriate applicants to varios scientific degrees. For instance, the situation with Kudryavtsev. In the same spirit N.N. wrote prefaces, funny and risible, to many books. And even if N.N. had a police, this policy was of a purely personal nature: N.N. desired to gain “popularity” among this kind of commonplace scientific workers. He would say a compliment to everyone. He wanted tro have all votes in his favor irrespectively of the objective weight of a voter. It seems to me that the facts that the facts outspoken by S[ergei] L[vovich], are unquestionable, but they relate to personal intriguing rather than political sabotage.
  • Kolmogorov. Would you please read the clause about his article in the Izvestiya newspaper? (Krzhizhanovsky reads it.) I think this is a weak formulation since the article clearly contradict facts, and we must formulate this stronger.
  • Alexandroff. One of the clauses of the resolution pinpoints the contemptuous attitude of N.N. to Soviet science. I think that the mode of discussion we are having is a compelling justification of the clause since the mode cannot be qualified as anything else but demonstration of contempt to all who are present. N.N. systematically argues with sophisms obvious to anyone or with appealing to the three lines crossed out by Borel. This witnesses the fact that N.N. did not respect this assembly since otherwise he would never allow himself to give these arguments for this assembly consists of the persons experienced in such matters. And the fact that N.N. gives these feeble arguments with such a persistence I qualify as contempt to the assembly.
  • Krzhizhanovsky. He indicates only that the result was obtained in another manner. So he ascribed a half of what is done to himself without any remorse, and in closing he points out that Novikov obtained this in another manner. This is a theft in my opinion!
  • Shnirelman. If we raise the question as follows: Is N.N. a man who is actively loyal to the interests of the Soviet state, then I think we will all answer unanimously that we have no grounds to think so but we have all grounds to think contrary-wise, since any man actively loyal to the Soviet state would firstly consider the interests of the cause he write his review for, the interests of the institution he is the head of, etc. We have no facts for many years which enable us to state that N.N. is an active Soviet citizen.
       I think that this conclusion which is made with unambiguous clarity proves with utmost lucidity and in its own right that N.N. could not be trusted to deal with any public matter of the scientific community. We must formulate this exactly as it is in reality.
       The second question: Is he is an active counter-revolutionary or a conscious but possibly peculiar saboteur? I think that we cannot answer this question yet since we have no data. I assume that to answer the question (which is necessary since the question is very important) we must proceed as follows: we must delegate this to the competent institution that has all data in its possession.
   This is exactly how the judges of Luzin defended him from Stalinism. All meetings of the Commission are common examples of the collective execution of an a priori convicted person. Finally, it seems reasonable to recall that the Resolution of the Emergency Commission has the following particular clause: “N.N. Luzin inflicted explicit damage on Soviet science.”
Question: Why do you qualify the Luzin case as the tragedy of mathematics in Russia for in fact this was an ordinary episode of the crimes of Stalin's totalitarianism which did not greatly affected the development of mathematics in Russia?
Answer: The true initiators of hounding Luzin were some of his students who struggled for liquidation of the Luzin influence on the mathematical infrastructure of the epoch. Kolman was used by mathematicians as a weapon of the political execution of Luzin. The understanding of the filthy evil done had come with time, but the participants of the trial never repented and simply concealed the truth about their participation in hounding Luzin. It was neither Stalin nor Kolman who destroyed the official minutes of the meetings of the Emergency Commission of the Academy of Sciences of the USSR, but this was done by those who were interested in concealing the truth about the Luzin case. The figure of silence of the participants of the trial of Luzin had played the role of immoral mutual cover-up.
   In actuality, most but happily not all prominent students of Luzin who took the roles of scientific and moral leaders of mathematics in the USSR possessed, at least to some extent, the deficiencies of personality which they had ascribed to Luzin. The principal difference between Luzin and the students that betrayed him is as follows: Luzin never participated in any political trials against his students and never flirted with Stalin's regime.
   The rotten stuff produces rotten stuff, and filth brings about filth. The tragedy of mathematics in Russia consists in the fact that the skyscraper of mathematics in the USSR was erected on the political tomb of Luzin whose execution had involved his outstanding students. The virulent miasma of this foundation had fed the filth that rotten the mathematical life in the USSR: careerism, political intriguing, xenophobia, collective trials of anyone unpleasant under the banners of Soviet patriotism and hypocritical struggle for the moral dignity of the profession.
   The sources of the Luzin case are not localized in some specific totalitarian mechanisms of the Stalinist USSR of the 1930s. The standards of life in Russia have changed but there are still many who believe that Luzin got what he deserves since he was a poorer mathematician as compared with his students. Careerism, servility, making gods from bosses and teachers are common phenomena. There is little pleasure in discovering that great scientists and pious saints can be rapscallions, but to conceal unpleasant facts is unobjective. On the contrary, such cases are most important for raising integrity and morality. The Bible tells a story of the sort.
   The historical nihilism of these days intertwines rather tightly with nihilism in morality. “The past crimes are buried in the past. The past is absent at present. Therefore, the past crimes are absent now. So, let bygones be bygones.” This sophism underlies the delusive appeal to ignore the old crimes and manifestations of subjectivism, monopolism, protectionism, and even nastier isms in view of the period of limitations.
   This is ultimately ridiculous to refer to the period of limitations in regard to the matters of science and morality. No period of limitations is ever met over there. The period of limitations never eliminates any mistakes—mistakes disappear only when repaired. It is much easier to make mistakes than to repair them. It is much more difficult to repair mistakes of the past and mistakes of the others. When we manage to do this, the number of mistakes diminishes. We must separate ourselves from the mistakes of the past, destroy their sources and repair their consequences, rather them hide ourselves under the false argument of the period of limitations.
   For 75 years the Luzin case had been spoiling the academic atmosphere with lies, the concealed misdeeds of the past, the instances of willing or unwilling justification of political slander towards colleagues and competitors in order to free the lanes of promotion and the roads to top offices. Now this source of evil is closed, and science becomes a bit purer. Luzin will never recognize this, but his memory has become brighter, shedding more light on the way of young generations in science. Luzin's honor is a part of the personal honor of many scientists. The honor of science is slightly safer now, at least in Russia.

S. Kutateladze

January 13, 2013


Some versions are available:

“Roots of Luzin’s Case.”
J. Appl. Indust. Math., 2007, V. 1, No. 3, 261–267.

The Tragedy of Mathematics in Russia.
Preprint No. 268
Sobolev Institute of Mathematics, Novosibirsk (2011)
arXiv:math/0702632v6 [math.HO]

“The Tragedy of Mathematics in Russia.”
Siberian Electronic Mathematical Reports, 2012, V. 9, A85–A100.

“An Epilog to the Luzin Case.”
Siberian Electronic Mathematical Reports, Vol. 10, A1–A6.


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