Roots of Luzin’s case

Abstract

This is a brief overview of the so-called “case of Academician Luzin” as well as the mathematical and humanitarian roots of
the affair.

Full text

ISSN 1990-4789, Journal of Applied and Industrial Mathe matics, 2007, Vol. 1, No. 3, pp. 261–267. c
Pleiades Publis hing, Ltd., 2007.
Original Russian Text c
S.S. Kutateladze , 2007, published in Sibirski i Zhurnal Industrial’noi Mate matiki, 2007, Vol. X, No. 2(30), pp. 85–92.
Roots of Luzin’s Case
S. S. Kutateladze*
Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
Received March 8, 2007
Abstract—This is a brief overview of the so-called “case of Academician Luzin”as well as the
mathematical and humanitarian roots of the affair.
DOI: 10.1134/S1990478907030015
On the Occasion of the 50th Anniversary of
the Siberian Division of the Russian Academy of Sciences
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. Aleksandroff(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 mathe-
maticians.
The outstanding roles in the development of mathematics in Siberia were performed by Lavrentiev
and Lyapunov, Luzin’s direct descendants as well as Academicians A. I. Maltsev (1909–1967) and
A. A. Borovkov, students of Kolmogorov.
1. 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 Professor 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,”stands close to the ideology of the “black hundred,”orthodoxy, and monarchy
“fascist-type modernized but slightly.”
All Russian scientists of the elder generation knew about the Pravda editorial and the savage
dissolution of “luzinism.”The newly-published archive files open to the public that some students of
Luzin were the active participants of the political assault on their teacher. The key role was played
by P. S. Aleksandroffwho headed the Moscow topological school. Also 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
*E-mail: sskut@member.ams.org
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.
261

262 KUTATELADZE
of the Commission read as follows: “Everything of the above, summarizing the overwhelming material
evidence in possession of the Academy of Sciences, completely ascertains the characteristics of Luzin
in the Pravda newspaper.”
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.
2. 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 [3] in Russian
Mathematical Surveys on the occasion of the 90th anniversary of the birth of Luzin. He also included
this article in the collection of his papers on the general issues of science and life [4]. 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 the birth of Luzin. P. S. Aleksandroffand 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. Alek-
sandroffand 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 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.
However, we should distinguishthe 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. Aleksandroffwrote in his reminiscences [6]:
“Knowing Luzin in his green creative years, I got acquaintance with a truly inspired teacher and
scholar who lived only by science and in the name of science. I met a person who resided in the sphere
of the sublime human treasures which is forbidden for any rotten ghost or spirit. When a human being
leaves this sphere (and Luzin had left it once), he is doomed to surrender to the forces that were described
by Goethe as follows:
Ihr f ¨
uhrt in’s Leben uns hinein,
Ihr lasst den Armen Schuldig werden
Dann ¨
uberlasst Ihr ihn der Pein,
Denn jede Schuld r ¨
acht sich auf Erden.
Into our life you lead us in,
The wretch’s guilt you bring to birth,
Then bring affliction down on sin,
For all guilt takes revenge on Earth.2
In his terminal years Luzin saw the bottom of the sour bowl of the revenge that was described by
Goethe.”
It is worth observing that Khinchin, hostile to Luzin, commented on the accusations that Luzin drove
Suslin to death [5]: “Suslin is called the student perished by N. N. Luzin. Why, when a man dies from
typhus fever this is a rather exaggerated expression. In fact Suslin could possibly get typhus fever in
Ivanovo. Furthermore, in the common opinion it was N. N. who tried and expelled Suslin from Ivanovo.
2P. S. Aleksandroffcited 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).
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007

ROOTS OF LUZIN’S CASE 263
However, the transfer from Moscow to Ivanovo I view as a favor to Suslin who was not hostile to Luzin
in those days.”
Narrating his reminiscences of P. S. Aleksandroff, A. N. Kolmogorov told in 1982 [7]: “My entire life
as a whole was full of happiness.”Neither he nor Aleksandroffnor 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, Lebesgue wrote in his preface to the Luzin book on analytic sets as follows: “Anyone will be
astonished to find out from Luzin’s book that I had incidentally invented the sieve method and was
the first to construct an analytic set. However, nobody could be more amazed than me. Mr. Luzin
feels himself happy only when he has managed to ascribe his own discoveries to someone else”[8].
The students were “more Catholic than the Pope.”3
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. Aleksandroffin the elections to a vacancy
of an academician despite his personal letter of support of Aleksandroffto A. N. Kolmogorov. Well, there
is nothing untypical of the academic manners or extraordinary in Luzin’s conduct, is 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: “In his letter as of June 27, 1935—which was a year
ago—Mr. Luzin wrote: ‘Returning now to my very difficult selfdefence against the ascription to Suslin
of the results which he had no rights to and which were absent even in his thoughts, I must say that this
selfdefence was provoked by a very grave and absolutely impending danger. Mr. Aleksandroffhas dreams
of entering the Academy of Sciences as a full member by dismissing me. To this end he requests that my
contributions be reconsidered, claiming that I has no right to be a member of the Academy since all my
ideas are stolen from Suslin. This reconsideration is rather likely and feasible.’ When I was in Moscow
in September, 1935, Mr. Aleksandroffassured me that the apprehensions of Luzin are purely imaginary
and that he respects Luzin, his former teacher. In my presence Aleksandroffshook hands with Luzin and
declared that he would always be a friend of Luzin”[9].
The pretentious reconciliation of P. S. Aleksandroffwith Luzin which was described by Sierpinski
and which was later publicly refuted by P. S. Aleksandroffis in no way similar to the refusal of Luzin
to support the election of P. S. Aleksandroffas 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. 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. Aleksandroffand
A. N. Kolmogorov. Luzin was granted “mercy”and accepted at the country house of A. N. Kolmogorov
and P. S. Aleksandroffin Komarovka before the elections.4
3The corresponding excerpt of the shorthand notes of the meeting of the Commission on July 13, 1936 reads as follows:
[1, pp. 196–197]:
Aleksandroff.As regards obsequiousness, I suggest that we will usethe genuine words of the lips of Lebesgue: (Readsin 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 Lebe sgue his belongings and he did it in so dopey
manner. No sane person would e ver ascribe them to Lebesgue . The thing is that doing so he c reates his reputation of the person w ho ascribes his own ideas to someone else; but when
the matter concerns his own stude nts then he robbed their belongings wh ile 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 thesewords about him?
Aleksandroff.This is an obsequious system since it is uncustomary in academic circles to ascribe som eone’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.
4L. S. Pontryagin (1908–1988) wrote on December 24, 1946 [13, Letter No. 49]: “Luzin became the hope of Pusiks [with
the letter upronounced as oo in soon; the collective equivocal nickname of Aleksandroffand Kolmogorov (S. K.)]. He
was invited to Komarovka and promised his support. However, he spoke against Aleksandroffat the final closed meeting.
Departing from this meeting,Kolmogorov was absolutely upset and stung. He came to Luzinand said that he would have
nothing in common with Luzin ever since. Luzin pretended that he did not understand anything and began to talk as
follows: ‘Dear me, calm down. Forget it. You are ill. Relax.’ This is what must be narrated with expression. Kolmogorov
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007

264 KUTATELADZE
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: “We then must think over the following matter. This fall the
elections are in order and we are hinted that there will be vacancies for 30 new academicians and 60
new corresponding members. We are to refresh the body of the Academy, and by the Assembly of
the Academy in September you have to ponder over and decide the following matter: Whom you will
recommend to be elected as corresponding members and academicians. This will be the best outcome of
the work of this Commission.”No elections to the Academy were arranged in 1936. The great elections
happened only on January 29, 1939 (cf. [14, No. 241; No. 242]). 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.
3. THE CONTEMPORARY REACTIONS TO THE LUZIN CASE
All moral accusations against Luzin are absolutely 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. Vernadsky wrote in his diary on
the next day “Letters to Luzin, Chaplygin, and Fersman about him. Majority treats as demonstrated
the slander and insinuations. M[ay] b[e], he [is needed] abroad but not at home. I am afraid that this
disgusting article will affect him much. Many conversations and many impressions.”On the same day
he sent a letter to Academician A. E. Fersman (1883–1945), a member of the Commission. Vernadsky
wrote: “I think that such an episode would eventually be perilous to the Academy were it led to the
expulsion of N. N. [Luzin] from the Academy or any similar actions. We would slide down the slippery
slope”[10].
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: “You will see that it was not yesterday when
the attacks on Luzin began with the aim of firing him and emptying place for Aleksandroff. You will see
there that I was already mixed in this by contrasting ‘my’ science, which is bourgeoise and useless, to
analysis situs [topology], a proletarian and useful science. Since the former was the science of Luzin;
whereas the latter, the science of Aleksandroff. What is curious is that he begins as Urysohn whose
papers he inherited at the same starting point that was mine. With the only difference that Urysohn
cited me whereas Aleksandroffhas never cited me anymore since he must now speak badly of me in his
struggle against Luzin!”[9].
Another evidence of Sierpinski: “I share the opinion and the same opinion is shared by my Polish
colleagues that the presence of Aleksandroff, Khinchin, Kolmogorov, and Shnirelman who confronted
their former teacher in the most dishonest manner and slanderously accused him is intolerable at any
meeting of decent persons”[9].
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. Gel-
fond, and L. S. Pontryagin (1908–1988) claimed that “there appeared active counter-revolutionaries
among mathematicians”[5]. Some of these were pointed out, namely, D. F. Egorov (1869–1931),
a teacher of Luzin. Shortly before D. F. Egorov had been arrested, and Luzin decided it wise to leave
then answered him: ‘So what shall I do to you: spit at your physiognomy or slap your mug?’ After a short thought, he
dared the latter.”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.
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007

ROOTS OF LUZIN’S CASE 265
the university (he was later accused of this removal by his students). In his life’s-description, dated as of
the late 1970s, Academician Pontryagin wrote [11]: “The two public actions, in 1936 as regards Luzin
and in 1939 as regards elections, were the important stages of my uprising as a public person. In my
opinion both were the struggle for rightful ends.”
This is totally inconsistent with the position of Luzin who wrote in his letter of 1934 to L. V. Kanto-
rovich (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”[12].
A broad campaign against Luzin and “luzinism”waged over this country in 1936 [15, pp. 757–767].
Fortunately, Luzin was not repressed nor expelled from the Academy. Some historians opine that there
was a relevant oral direction of I. V. Stalin.5However, 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.
4. MATHEMATICAL ROOTS OF THE LUZIN CASE
The human passions and follies behind the 1930s tragedy of mathematics in Russia are obvious: love
and hatred, jealosy 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 collec-
tivism and individualism. Many particular phenomena of life and culture reflect their distinction. The
dissolution of monarchism and tyranny were 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
5It was disclosed recently that the above-mentioned letter of Kapitsa to 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.
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007

266 KUTATELADZE
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. We do not worry 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 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, topology
began when the idea of the ultimate unique foundation was ruined for ever. K. G ¨
odel (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 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.
5. 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 Moscow Mathematical Society and the Academy of Sciences. These scientific
institutions are alive.
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. Evil and genius coexist from time to time. Mathematics
does not inoculate morality. Manuscripts do not burn...
REFERENCES
1. The Case of Academician Nikolai Nikolaevich Luzin, Ed. by S. S. Demidov and B. V. Levshin (Russian
Christian Humanitarian Inst., St. Petersburg, 1999) [in Russian].
2. G. G. Lorentz, “Mathematics and Politics in the Soviet Union from 1928 to 1953,”J. Approx. Theory 116,
169–223 (2002).
3. M. A. Lavrentiev, “Nikolai Nikolaevich Luzin (on the 90th Anniversary of His Birth),”Uspekhi Mat. Nauk
29 (5), 177–182 (1974).
4. M. A. Lavrentiev, Science. Progress in Technology. Cadres (Nauka, Novosibirsk, 1980) [in Russian].
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007

ROOTS OF LUZIN’S CASE 267
5. A. P. Yushkevich, “The ‘Case’ of Academician N. N. Luzin,”in Science Under Repressions (Nauka,
Leningrad, 1991), pp. 377–394.
6. P. S. Aleksandroff,“Pages from an Autobiography,”Uspekhi Mat. Nauk 34 (6), 219–249 (1979).
7. V. M. Tikhomirov, Andrei Nikolaevich Kolmogorov (Nauka, Moscow, 2006) [in Russian].
8. H. Lebesgue, “Introduction to the Book by N. N. Luzin Lectures on Analytic Sets and Applications,”
Uspekhi Mat. Nauk 40 (3), 9–14 (1985).
9. P. Dugac, “The ‘Case’ of Luzin and French Mathematicians,”Istoriko-Mat. Issledovaniya 5(40), 119–142
(2000).
10. V. I. Vernadsky, Dairies. 1935–1941, Book 1: 1935–1938 (Nauka, Moscow, 2006) [in Russian].
11. L. S. Pontryagin, The Life Description of Lev Semenovich Pontryagin as Compiled by Himself. Born
1908, Moscow (IPE “Prima V,”Moscow, 1998) [in Russian].
12. Yu. G. Reshetnyak and S. S. Kutateladze, “A Letter of N. N. Luzin to L. V. Kantorovich,”Vestnik Ross. Akad.
Nauk 72 (8), 740–742 (2002).
13. E. I. Gordon, “Letters from L. S. Pontryagin to I. I. Gordon,”Istoriko-Mat. Issledovaniya 9(44), 27–208
(2005).
14. V. D. Esakov, The Academy of Sciences in the Resolutions of the Political Bureau of the Cental
Committee of the RCP(B)–AUCP(B ) –CPSU. 1922–1952 (The Russian Political Encyclopedia, Moscow,
2000) [in Russian].
15. `
E. I. Kolchinskii, “Science and Condolidation of the Soviet System in the Prewar Years,”in Science and
Crises. Historico-Comparative Essays (Dmitrii Bulavin, St. Petersburg, 2003) [in Russian].
JOURNAL OF APPLIED AND INDUSTRIAL MATHEMATICS Vol. 1 No. 3 2007