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.
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 . Soon the article  appeared in
the USA which revealed the personal
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
“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:
The Soviet scientific community tears away
from you the mask of an honest scientist, leaving you in the altogether,
and so you appear before the eyes of the world as a paltry individual
who pretends to champion “pure science” but betrays the interests of science,
merchandizing it to appease you former bosses—the present-day masters
of faschistoid science. The Soviet community will perceive the story
about Academician Luzin as another object-lesson of the fact that
the adversary never lays down his arms, that he camouflages himself
more skilfully, that the methods of his mimicry becomes more
diverse, and that vigilance remains the most demanded trait of every
Bolshevik and every Soviet citizen.
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
Investigation was launched that time by
my father (seemingly, with Lyusternik and Lavrentiev, the latter knowledgable
about the Party circles).
They found out there there was a letter from
P. Alexandroff to some influential guy,
Khvorostin by name.4
This letter narrated the nasty deeds of Luzin. Khvorostin
resided in Saratov and had great connections within the C[entral] C[ommittee of the Party].
He hated Luzin, which was known to everyone. It was Khvorostin as they
guessed out who submitted materials to the CC and initiated the article.
Pavel Sergeevich was a great master of a billiard shot!
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
Suslin called them A-sets. But he never told that he called them so in my honor.
In his reminiscences of 1979 he claimed quite the opposite:7
It was exactly then that Suslin proposed to call the
new set theoretic operation that I had constructed the A-operation
while calling A-sets those that
result from application of the operation to closed sets.
Doing so, he emphasized that he was suggesting this terminology in my honor
by analogy with Borel sets which were customarily called B-sets those days.
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
During our rather often meetings in the second
half of the 1970s, I repeatedly asked P. S. about the history of
the discovery of A-sets. One day he rang me up and suggested that
I would come to his apartments at an appointed time when he would stay alone.
I had to enter into the waiting room without ringing the door bell, and P. S.
would be seated on a chair quite opposite to the door. All happened
exactly as planned. His narration was lengthy. I wrote it down.
On the next day I brought the typewritten text of my record, and P. S. told that
it conforms completely with what he had said, but stipulated the condition that
the record be never published during his life time.
When P. S. had passed away in 1982,
I decided to take the advice of A. N. [Kolmogorov (S. K.)].
After listening the text, A. N. told me that to publish it was still too early.
Now there are neither P. S. nor A. N., and I have nobody else
to take advice of. I decided to seal the narration of P. S.
Alexandroff in an envelope and put it to the Archive of
the Academy of Sciences of the USSR for deposition in the Alexandroff Fond
with the inscription: “Received from A. P. Yushkevich.
Open only after 10 years since his death.”9
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
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
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.
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  in Russian Mathematical Surveys
on the occasion of the ninetieth 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. 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
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
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
Ihr führt in's Leben uns hinein,
Ihr lasst den Armen Schuldig werden
Dann überlasst Ihr ihn der Pein,
Denn jede Schuld rächt 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.13
In his terminal years Luzin saw the bottom of the sour bowl of
the revenge that was described by
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
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.
But 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. Alexandroff, A. N. Kolmogorov
told in 1982:15
My entire life as a whole was full of happiness.
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
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.
But nobody could be more amazed than me. Mr. Luzin
feels himself happy only when he has managed to ascribe his own discoveries to
The students were “more Catholic than
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
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
In his letter as of June 27, 1935—which was a year
ago—Mr. Luzin wrote:
“Returning now to my very difficult self-defence
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 self-defence was provoked by
a very grave and absolutely impending danger. Mr. Alexandroff
has 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 plausible.”
When I was in Moscow in September, 1935,
Mr. Alexandroff assured me that the apprehensions of Luzin
are purely imaginary and that he respects Luzin, his former teacher.
In my presence Alexandroff shook hands with Luzin and declared that he
would always be a friend of Luzin.
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
L. S. Pontryagin (1908–1988)
wrote on December 24, 1946:20
You are asking about cooperation of Kolmogorov and Luzin.
Surely, this needs to be narrated rather that written since the mode of voice is essential to
render all properly. In summer Kolmogorov told me that his only concern
about the election of Alexandroff consists in the fact that
he became an obvious candidate four months before the elections.
carried out a great preparatory work in the sense that
entered into various agreements with academicians. For instance, there was a promise to
Vinogradov that Kolmogorov would support Lavrentiev in the event that Vinogradov
would support Alexandroff. All in all it seemed that everyone will vote for
Alexandroff. For example, Bernstein had nominated Alexandroff at a meeting of the
[Steklov] Institute as well as Chebotarëv, I must mention for the sake of truth.
Kolmogorov had made an agreement with the bosses of the Academy that he will be
a member of the Board of Experts.22 The first annoying news was the fact
that he had not been assigned to the Board, but he still hoped that this was not essential already.
After the session of the Board of Experts there were a few
closed meetings of all academicians where they discussed the candidates, and only at that stage
Kolmogorov became aware that none of the members of the Board of Experts had supported
Alexandroff. On the contrary, Bernstein vigorously objected against him,
claiming that Alexandroff's area of research is harmful. Bernstein's behavior
still seems highly illogical for me; probably he had just quarreled with
Pusiks. All the rest is rather comprehensible.
Lavrentiev turned out an unquestionable candidate somehow and he had no need in the
support of Kolmogorov who was not a member of the Board at that.
Therefore, Vinogradov had no need in Kolmogorov and Pusik.
As regards Sobolev and Khristianovich, the former deeply hated Pusik
for expelling Sobolev from the directorship [of the Steklov Institute (S.K.)],
while the latter is a crony and companion of Sobolev.
In these circumstances there was practically no hope of success.
The only remaining possibility was that some academicians among mathematicians
would support Alexandroff, for physicists wanted to support him but surely
that could not confront all mathematicians.
Luzin became the hope of
He was invited to Komarovka
and promised his support.
But he spoke against Alexandroff at the final closed meeting.
Departing from this meeting, Kolmogorov was absolutely upset and stung.
He came to Luzin and 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 then answered him: “So what shall I do to you:
spit at your physiognomy or slap your mug?” After a short thought, he dared
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
Now about another matter: the time is coming of the elections to the Academy.
It would be an utmost injustice, had these be happened without Pavel Sergeevich.
His works whose echoes are met throughout the world literature,
his splendid ripe years—the completion of maturity and wisdom and he himself as
the man of perfect attraction—all these made us see in him a worthy candidate
whose activity is invaluable for the Academy.
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
Since for many years I am engrossed in preventing the various random and immaterial
circumstances to hinder the election of Pavel Sergeevich which would be
a rather just event in my opinion; therefore, I indeed appraise very highly your
readiness to support all necessary actions for the success when this is really desired.
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
... it should be noticed there was some rather unsavory particularity:
sometimes he lost his temper.
Andrei Nikolaevich was never too good-natured and he narrated not without pride about his
clash with police at the Yaroslavl Railway Station.
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”
accepted at the country house of A. N. Kolmogorov and P. S. Alexandroff
in Komarovka before the
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
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 on 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 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.
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
Letters to Luzin as well as to 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. V. I. Vernadsky remarked:34
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.
And on July 11 S. A. Chaplygin (1869–1942) wrote to V. I.
The article about Luzin is completely outrageous: Supposing
that he committed the sin
of misjudging some applicant for a scientific degree or title, but how
is it possible to jump to the conclusion of sabotage from that?! ...
As far as the accusations, slipping through the article, of fascism
and his enlisting the old reactionary Moscow school of mathematics,
I am complete unable to understand these.
There remains the critical evaluation of Luzin's contributions. But in this regard
I must say only that this discloses the complete incompetence of the authors which
proves their minor and superficial acquaintance with his works and their
deliberate distortion of correct evaluation.
His authority is incomparable with that of Khinchin
who is counterpoised to him. But what should be done right away? How can we help N. N.?
I did only one thing yet: I sent N. N. a cable whose copy I attach:
"Dumbfounded by absolutely undeserved newspaper attacks against you.
Your high world-wide acknowledged scientific authority cannot be
shaken. I hope definitely that you will find
the inner forces to face this inauthoritative criticism of your contributions calmly.
I avoid mentioning the completely groundless accusations of the other sort.
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.
You will see that it was not yesterday when the attacks on Luzin began with the aim
of firing him and emptying place for Alexandroff. 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 Alexandroff. 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 Alexandroff has never cited me anymore
since he must now speak badly of me in his struggle against Luzin!
Another evidence of W. Sierpinski is as follows:37
I share the opinion and the same opinion
is shared by my Polish colleagues that the presence of
Alexandroff, 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.
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
The acrimonious class struggle in the USSR has pushed the right-wing professoriate into the
camp of the counter-revolution. The reactionary professoriate headed all sabotaging
organizations and counter-revolutionary parties that have been disclosed recently.
Owing to the meritorious actions of the OGPU39
there are divulged the crimes of the whole bunch of scientific bonzes who can
artfully hide themselves under various masks—from that of cold loyalty to Soviet
power to highly-advertised profound affection to Soviet power.
Even in the community of mathematicians some active counter-revolutionaries
were found out. Under arrest for participation in a counter-revolutionary organization
is Professor Egorov, the undisputed leader of the Moscow mathematical school,
the Chairmen of the Moscow Mathematical Society, the former Director of the Mathematical
Institute, and the candidate of Moscow mathematics to the Academy of
Sciences—the very same Egorov, the savior of the academic traditions, whom the proletarian
student body had been struggling against for a long time but whose defence was
a practically unanimous decision of the community of Moscow mathematicians.
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
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. 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
Vladimir Ivanovich, the candidates in mathematics—Sobolev and Kolmogorov—are good.
I will vote for them.
A broad campaign against Luzin and “Luzinism” waged over this country
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
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
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
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.
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
As regards the last paragraph of the article in Pravda where
the monstrous accusations were made against me in servitude to
the present-day masters
of faschistoid science, I state with the full understanding of my political
responsibility of a scientist of international reputation and a citizen of
the USSR that the Editorial Board of Pravda was deliberately
misled to delusion by the persons who had informed it about this.
This is refuted by my whole life and activities as a scientist and a person.
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
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.
Antipenko L. G.,
“N. N. Luzin: Letters to V. I. Vernadsky
(Archive of the Academy of Sciences of the USSR, Moscow Affiliation, Fond 518, Description 3, Item 995).”
The Russian Thought, No.1–2, 103–117 (1993).
Bogolyubov A. N. and Rozhenko N. M.,
“The Experiment of ‘Implanting’ Dialectics into Mathematics from the End of the 1920s to
the Beginning of the 1930s.” Problems of Philosophy, No. 9, 32–43 (1991).
Pontryagin L. S.
The Life Description of Lev Semënovich Pontryagin
as Compiled by Himself. Born 1908, Moscow.
Moscow: IPE "Prima V," 1998.
Sobolev Institute of Mathematics
Novosibirsk February 7, 2007–May 9, 2011
very grateful to Professor W. A. J. Luxemburg for
attracting my attention to the inadvertent omission
of a reference to  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]).
6Cp. [1, p. 90].
7Cp. [6, p. 235].
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].
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].
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.
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
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
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
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.  and .
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].
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).
Every now and then I still hear quite a few questions to me
Luzin case. In my opinion three of them deserve public answers.
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?
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:
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.
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?
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
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
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
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.”
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?
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.