# Andrej N. Kolmogorov’s in front of the “affaire Lysenko”: an episode in
mathematics and ideology in the 20th century

Fascitiello Isabella University of Roma Tre, Department of Mathematics and
Physics  Fascitiello Isabella

###### Abstract

Andrej N. Kolmogorov’s life and outstanding mathematical work was intertwined
with the political and cultural evolution of the Russian Empire from the
Tzarist regime to the establishment and development of the Soviet Union. His
early involvement in scientific education (and his own education) was marked
by the progressive education movement continuing under the Lenin rule. Under
the dramatic years of Stalin rule he was involved in the process against
Nikolai N. Luzin but had a conflict in 1940 with Trochym D. Lysenko, thus
founding himself in accordance and then in opposition to Ernst Kol’man
(1892–1979), a very influential figure in mathematical circles. Kolmogorov’s
political views had been considered either that of a authentic Marxist (Graham
1993) loyal to the regime or that of a great scientist, a member of the
intelligentsia science, who lived through the 1930s and 1940 acting sometimes
against his principles (Arnold 2000, Lorentz 2002).

In this paper the context of the 1940 mathematical paper by Kolmogorov on
Mendel’s laws of genetics is considered, also thanks to a recent study by
Stark and Seneta (2011). Kolmogorov’s vision of the relationship between
mathematics and science in the understanding of the natural world appears to
have encouraged him in tacking part in the discussions around Mendelism in
while Lysenko’s position against it was becoming the only permissible for
Soviet Union biologists.

###### Contents

  1. 1 Kolmogorov, a representative of Russian “intelligentsia science” and his education
  2. 2 Living through the 1930’s and 40’s: Kolmogorov and science under Stalinism
  3. 3 On a new confimation of Mendel’s Laws: Kolmogorov participates in the polemic on genetics in the USSR 1940
    1. 3.1 The Lysenko affair
    2. 3.2 Kolmogorov against Lysenko and Kol’man
  4. 4 Final remarks
  5. Bibliography

##  1 Kolmogorov, a representative of Russian “intelligentsia science” and his
education

The young Kolmogorov, born two years before the 1905 upheavals that marked the
final years of the Tzarist regime, was raised in an environment soaked by
progressive education: after some years of home schooling at his grandfather
home until 1910 under the guidance of his aunts, which adhered to the
principles of advanced "democratic" pedagogy then in vogue in Russia and which
were the heart of school policy in the first years after the October
Revolution and until 1931111See [Karp, Vogeli 2010], [Karp 2012] and [Karp,
Schubring 2014], since the age of 7 he attended a private gymansium in Moscow,
founded by two woman, Evgenja (Evgeniya) Albertovnava Repman and Vera
Fedorova222See [Tikhomirov 1988]. E.A. Repman (1870-1937), founder and
director of the school, was the eldest daughter of Albert Hristianovitch
Repman (1834-1917), sinced 1889 director of the section on applied physics of
the Polytechnical Museum of Moscow (founded by the zar Alexander II in 1870 as
Museum of Applied Knowledge). After 1917, it was renamed Section grade school
no. 23. Biographical essays [Tikhomirov 1988] and [Shyraev 2000] draw many
informations from Kolmogorov’s reminiscences included in his posthumous book
on mathematics as science and as a profession [Kolmogorov 1988] published in
Russian in a series by the magazine Kvan. In 1942 Kolmogorov would marry Anna
Dmitrievna Egorova, whose first husband was the mathematician and painter
Sergei Mikhailovich Ivashyov-Musatov, the mother of Oleg Sergeyevich Ivashyov-
Musatov, who majored in mathematics with his stepfather. Kolmogorov, Anna
Dmitrievna Egorova and her ex-husband were former students of the Repman
school. Thus, the final years of highschool and those as university student
were marked by the end of Tzarist monarchy in October 1917 – he was 14 years
old – and the rise of bolshevism under Lenin. He had to leave Moscow in
1918-20 with his family, as he himself recounts in [Kolmogorov 1988]:

In 1918-1920 life in Moscow was not easy. In schools, only the most persistent
were seriously engaged. At that moment, together with my elders, I had to
leave for the construction of the Kazan-Ekaterinburg (now Sverdlovsk) railway.

By the cultural atmosphere of his early years, he was imbued by the patriotic
scientism of Russian radical intelligentsia, and no wonder that in 1920 he
enrolled both at the Physics and Mathematics Department of Moscow University
and at the Institute of Chemical Engineering “D.I. Mendeleev”. Engineering was
then perceived as something more serious and necessary than pure science, he
would say in 1963 during and interview with the magazine Ogonek. Furthermore
in 1922 – he was he was enrolled as a teacher of mathematics and physics and
boarding school educator in a secondary school of the network under the
administration of the People’s Commissariat of Education (known as
Narkompros), led by Anatoly Lunacharsky (1875-1933) with Lenin’s wife,
Nadezhda Konstantinovna Krupskaya (1869-1939):

Now I remember with great pleasure my work at the Potylikha Experimental
School of the People’s Commissariat of Education of the RSFSR. I taught
mathematics and physics (at that time they were not afraid to entrust the
teaching of two subjects to 19-year-old teachers at the same time) and took an
active part in the life of the school (I was the secretary of the school board
and a boarding school educator).333Although perhaps this early involvement in
elementary education it began as a job out of necessity rather than will,
[Abramov 2011] shows that in the 1960s and 1970s he returned to his interest
in education, marked by his own experience, participating in efforts to
improve the secondary mathematics education in the USSR.

Alexander Karp has descrived the influence on mathematical education in the
Russian Empire of the modern school movement; his description help us
understanding the cultural atmosphere in which the young Kolmogorov work as
mathematics and physics teacher:

In place of all existing types of educational institutions, a statute of 1918
established the so-called unified labor schools. These schools were divided
into two stages, and the network of first-stage schools, which were far more
numerous to begin with, continued to be intensively developed.
$[...]$ The goal was to eliminate from schools anything reminiscent of former
discipline and drills, including exams, textbooks, and even separate subjects
(including mathematics). The ideas of American progressive educators were
taken up and developed in Russia (Soviet Union); schools made use of projects,
laboratory work, group work, and, above all, "complexes".
“Complexes” had to link through one overarching theme topics that had
previously been studied in different subject classes. For example, teachers
could use a theme such as “The Post Office” to get their students to do some
writing, to perform some computations, to talk about geography, and even to
discuss the difficult position of the working class in other countries. [Karp
2014, p. 315].

His career as a research mathematician was already starting. That same year
1922 he proved his first famous result, in the field of trigonometric series,
building an almost everywhere divergent Fourier-Lebesgue series; it was
published the following year in the new Polishjournal Fundamenta
Mathematicæ444This journal, founded in 1920 by a group of Polish
mathematicians to strenghten the mathematical homeland culture in the years of
restoration of Poland independence after the end of the First World War, was
at the same time intended with a deep international vocation..
On the 21st January 1924 Lenin died. Under the first years of Joseph Stalin’s
rule Kolmogorov’s career and prestige took off: he graduated in 1925, and
after his postgraduate period, in 1929 he was enrolled in the Moscow
University Institute of Mathematics of Mechanics. After ten years, in the
dramatic years of the Stalinist terror, Kolmogorov was elected a full member
of the USSR Academy of Sciences. In 1933 he had published, in German, his
revolutionary treatise on the foundations of probability theory: Grundbegriffe
der Wahrscheinlichkeitsrechnung, laying the axiomatic foundations of the
theory of probability.

##  2 Living through the 1930’s and 40’s: Kolmogorov and science under
Stalinism

Despite the change of regime in the Russian Empire, in the 1920s and early
1930s scientist’s in the USSR maintained and developed the ongoing
international relationships, specially with Germany, France – a center of
emigrés intellectuals after the 1905 upheaval –, and the United States. Legacy
of the schools of Dmitry Fëdorovič Egorov555Dmitry Fëdorovič Egorov (Moscow,
1869- Kazan, 1931) was a Russian mathematician who mainly dealt with
differential geometry and mathematical analysis. and Luzin, Kolmogorov had
tight connections in France.666For more details on relations between France
and Russia, see [Deminov 2009].
During a journey with Pavel Alexandrovich Aleksandrov in Germany and France
between 1930 and 1931, he met the French mathematicians Maurice Fréchet, Émile
Borel and Henri Léon Lebesgue. Deminov asserts that the intense relations
between these two countries seemed more flourishing than ever, with no clouds
on the horizon:

Au début des années 30, la recherche mathématique semblait donc pouvoir se
poursuivre sans obstacle. La vie normale de la communauté scientifique,
interrompue par la première guerre mondiale, avait repris et la collaboration
des mathématiciens français avec leurs collègues soviétiques se développait
dans les meilleures conditions.777Eng.tr.: At the beginning of the 1930s,
mathematical research seemed to be able to continue without obstacles. The
normal life of the scientific community, interrupted by the First World War,
had resumed and the collaboration of French mathematicians with their Soviet
colleagues was developing under the best conditions. [Deminov 2009, p 130]

But in the time of the great purges starting at the mid 1930s the connections
almost collapsed. As early as 1932, Luzin was denied participation in the
International Congress of Mathematicians in Zurich and, two years later,
Kolmogorov was unable to go to Paris, despite a scholarship granted by the
Rockefeller Foundation. Since the late 1930s, scientist in the Soviet Union
hardly traveled abroad. Kolmogorov could not leave the Soviet Union until
September 1954, when the Russians were finally able to take part again in the
International Congress of Mathematicians in Amsterdam, albeit with a tiny
delegation of four people (Alexandrov, Kolmogorov, V. Kozetsky e Sergej
Michajlovich Nikolskij).888Already suspended in 1936, the congress was only
reinstated in 1950, but, on that occasion, the entire Russian academic
community did not participate in the event. For more details, see in the
Proceedings of the ICM 1950, Cambridge, Massachusetts, [Graves, Hille, Smith,
Zariski 1955, p 122]
During my research work on the cultural origins of the theorem and the
research project on classical mechanics and the theory of dynamical systems,
which Kolmogorov presented at the Amsterdam congress, I was led to consider
his scientific work during the time of terror Stalinist. In fact, he seems to
have devoted himself, in a hidden way, to topics of classical mechanics
related to Poincaré’s research999see in this regard the preprint [Fascitiello
2022] Thirty years after: insights on the cultural origins of Andrej N.
Kolmogorov’s 1954 invariant tori theorem from a short conversation with
Vladimir I. Arnold, thus continuing an incipient interest in the theory of
dynamical systems, in particular in Vito Volterra’s seminal studies on
population dynamics, as the beginning of a mathematical theoretical biology
[Kolmogorov 1935, 1936]. Kolmogorov recalled his early interest in astronomy,
thanks to the works of Camille Flamarion (1842–1925), and also in biology:

[…] For a time, interest in other sciences took over. The first big impression
on me of the strength and significance of scientific research was made by the
book by K. A. Timirjazev101010He refers to Kliment Arkad’evič
Timirjazev(1843-1920), a Russian plant physiologist and a major proponent of
the Evolution Theory of Charles Darwin in Russia. The Life of Plants.

The 23 editions published between 1898 and 1962 in 5 languages - therefore
before and after October 1917 - of the famous book by the botanist Timiryazev
show his adherence to radical and scientistic ideals and to the vision of
science in the Soviet Union. Requirements of Soviet science well described in
[Nicolaidis 1990]:

After 1928 however, the Stalinist regime proclaimed a so called "Marxist"
official ideological line concerning science. This ideological line became the
official line of Soviet astronomy in 1931 Its principles were the following:
(1) There are two sorts of astronomies Soviet and bourgeois. This principle
comes from the dogmatic principle that a capitalist regime restrains the
scientific evolution while on the contrary, the construction of the socialist
regime implies in addition the construction of a new, superior science. This
principle of "two sciences" was the main Stalinist principle concerning all
scientific fields. We will see that in astronomy, the application of this
principle was to have terrible consequences for the leading Russian
astronomers.
(2) Soviet astronomy must serve Soviet society more precisely astronomy must
serve ideology and the economy.
But how could astronomy serve Stalinist ideology? […] Astronomy was a
scientific tool that would help to disprove what Stalinists called "religious
myths". In a more specifically scientific field, soviet astronomy was ordered
to fight against what was termed idealistic western cosmological theories, and
especially against the theory of general relativity and the concept of a
finite universe - because to put limits and an age to the universe would imply
the Creation and so the existence of a God.
The relation between astronomy and the Soviet economy was a more complicated
concept.
The general line that all activities in the USSR must serve the "building of
socialism" implied that research in astronomy must also have industrial
applications It was difficult to make applications concrete, and so the
ideological line spoke about researches concerning Earth Sun relations and
geodesy. [Nicolaidis 1990, pp. 346-347]

The risk of researching questions linked to 19th century open problems in
celestial mechanics during those years seems very high, taking into account
the “purge of astronomers” in years 1936-37 which involved not scientist in
various disciplines (celestial mechanics, geology, geophysics, geodesy)
working in the wide network of astronomical observatories in the Russian
Empire.111111The causes and evolution of this series of arrestations,
emprisonments and murders have been studied in [McCutcheon 1991], [Nicolaidis
1990] and [Eremeeva 1995]; an relevant role was played by the close connection
between astronomy and (Orthodox Christian) religion
Kolmogorov has often been credited with fully sharing the communist ideals of
the Soviet regime. The aim of the present paper is not to fully analize such
an issue121212The question of science in the Soviet Union, its impressive
devolopment, in the context of an evolution starting in the last fifty years
of the Tzarist regime has been paid considerable attention since the
dissolution of the USSR and the establishment of the Russian Federation
[Kojelnikov 2002], [Gordin et al 2008].. Nevertheless, there are two opposite
interpretations of his behaviour and writings. Loren Graham, in his book
Science in Russia and the Soviet Union. A short History [Graham 1993],
describes Kolmogorov as one of the leading figures in USSR science:

Most people now assume that all influence of Marxism on Soviet science was
deleterious. On the contrary, in the works of scientists such as L. S.
Vygotsky, A. I. Oparin, V. A. Fock, O. Iu. Schmidt, and A. N. Kolmogorov, the
influence of Marxism was subtle and authentic. [Graham 1993, p 3-4].

In his discussion of USSR mathematics, he writes:

A. N. Kolmogorov, one of Shmidt’s authors in the first edition of the Large
Soviet Encyclopedia, wrote the entry "Mathematics." […] I will briefly compare
Kolmogorov’s article with those in the Encyclopedia Britannica written by
Frank Plumpton Ramsey and Alfred North Whitehead at approximately the same
time as the first edition of Kolmogorov’s article.
The points of difference arise on the most essential questions of mathematics:
What are the origins of mathematics? and What is the relationship between
mathematics and the real world? According to Kolmogorov, mathematics is "the
science of quantitative relations and spatial forms of the real world." It
arose out of "the most elementary needs of economic life," such as counting
objects, surveying land, measuring time, and building structures. In later
centuries mathematics became so abstract that its origins in the real world
were sometimes forgotten by mathematicians, but Kolmogorov reminded them that
"the abstractness of mathematics does not mean its divorce from material
reality. In direct connection with the demands of technology and science the
fund of knowledge of quantitative relations and spatial forms studied by
mathematics constantly grows." Kolmogorov then went on to sketch a history of
mathematics in which its growth was intimately related to economic and
technological demands. His views were consistent with Lenin’s insistence on
the material world as the source of human knowledge, and Engels’s emphasis on
technical needs as a motivating force in the development of knowledge. [Graham
1993, p 118]

In a paper published in 2002 based on his own experiences, George Gunther
Lorentz (1910-2006) quotes the testimony and reflection of one of Kolmogorov’s
most famous students, Vladimir Igorevič Arnold (1937-2010), published in the
volume Kolmogorov in perspective in 2000 by the American Mathematical Society
and the London Mathematical Society [AA.VV. 2000]. Precisely in an attempt to
reconstruct the reasons which prompted Kolmogorov in the two-year period
1953-54 to deal with one of the mathematical questions which, after
probability, made him more famous - the one which today goes by the name of
KAM theory - he writes:

Although Andrei Nikolaevich himself regarded the hopes that appeared in
1953131313Stalin died in March 1953 as the main stimulus for his work, he
always spoke with gratitude about Stalin (following the old principle of
saying only nice things about the dead): "First, he gave each academician a
quilt in the hard year of the war, and second, he pardoned my fight in the
Academy of Sciences, saying, ’such things happen also here’." Andrei
Nikolaevich also tried to speak kindly about Lysenko, who had fallen into
disfavor, claiming that the latter had sincerely erred out of ignorance (while
Lysenko was in power, the relation of Andrei Nikolaevich to this "champion in
the struggle against chance in science" was quite different).
[…] "Some day I will explain everything to you," Andrei Nikolaevich used to
tell me after having done something contrary to his principles. Seemingly,
pressure was exerted on him by some evil genius whose influence was enormous
(the role of the group transmitting the pressure was played by well-known
mathematicians). He hardly lived to the times when it became possible to speak
of these things, and, like almost all people of his generation who lived
through the 1930’s and 40’s, he was afraid of "them" to his last day. One
should not forget that for a professor of that time not to tell the proper
authorities about seditious remarks made by an undergraduate or graduate
student not infrequently meant being accused the next day of having sympathy
with the seditious ideas (in a denouncement by the very same student-
provocateur). [Arnold 2000, p. 92]

In the same year that the great purge of Soviet astronomers began, there was
an event involving mathematicians and the research group of which Kolmogorov
was a part.
The Luzin affair 141414[Levin 1990], [Lorentz 2002],[Katuteladze 2012],
[Katuteladze 2013], [Demidov, Lëvshin 2016], started with anonymous accusation
by the newspaper Pravda in eight long articles from July 2 to 16, 1936, as
"Enemy under the guise of a Soviet citizen" [Kutateladze 2013, p.A86]. A
commission was immediately appointed by the Academy of Sciences and the first
session of the process began on July 7, 1936, which was followed by others in
a few days. A sentence was reached, which proved to be less drastic than the
tones of the articles and the trial, and the Soviet mathematician was
acquitted of practically all charges. In this affair was involved Enrst
Ko’lman, a Cezch emigrée of Jewish ascendence and Marxist convictions. Aleksey
E. Levin writes in [Levin 1990]:

Kol’man’s formal position inside the party hierarchy was head of the
mathematical section of the Communist Academy during the first half of the
1930s; he was subsequently promoted early in 1936 to head of the science
department of the party’s Moscow City Committee (he held this office until
1938 when he apparently lost some powerful protection and was sent to a
teaching position). During the 1930s, Kol’man regularly published on the
philosophy of mathematics and had many personal connections in mathematical
circles, especially among politically active youth.
Kol’man’s status makes it unlikely that any public attack on Luzin would have
been launched without his approval. [Levin 1990, pp 98-99]

A rift opened between Luzin and most of his students, including Kolmogorov and
Aleksandrov, who played an active role in the commission set up for the trial.
After the denouement of the matter, the split continued to manifest itself:
ten years after the Luzin affair, he voted against the election of Alexandrov
to become a full member of the Academy of Sciences:

Lusin died in 1950, but not before a final violent collision with Aleksandrov
and Kolmogorov. In 1946, the Academy had to elect a new group of members, this
time with preference to the applied sciences. This allowed Lusin to vote
against the topologist Aleksandrov. To everybody’s consternation, as a
reaction, Kolmogorov slapped Lusin’s face on the floor of the Academy. The
president of the Academy, S. I. Vavilov, was at a loss of what to do. Finally
the incident was reported to the Kremlin. It was said that Stalin was not
astonished. "This happens even among us," was his reply. In other words,
Stalin recommended to do nothing.151515This was the fight to which Kolmogorov
referred in the words reported by Arnold [Lorentz 2002, p 207]

##  3 On a new confimation of Mendel’s Laws: Kolmogorov participates in the
polemic on genetics in the USSR 1940

The so-called Lysenko affair is one vexed question on science and ideology in
the Soviet Union. A violent campaign against genetics, not considered to
conform to dialectical materialism was one of the most devastating political
intrusions into Soviet intellectual life under the Stalin regime.161616To name
a few, see [Joravsky 1970], [Graham 1993], [Graham 2016], [Ptushenko 2021]
Trochym Denysovych Lysenko (September 29, 1898 Karlivka (Ukraine) - November
20, 1976, Moscow) exerted a growing influence on Russian biology from the
mid-1930s onwards, until it reached the vertex of an ascending parabola in the
late 1940s, with the approval of Joseph Stalin171717At the Congress of the
Communist Party of the Soviet Union in 1935, Lysenko delivered a speech which
ended with the applause of the audience and the emblematic exclamation of
Joseph Stalin, present at the congress: ”Bravo, comrade Lysenko, bravo!”
himself, only to hit rock bottom after more than thirty years, in 1965, when
geneticists called him an impostor and attributed to him all the damage caused
to Soviet agriculture - just think that in the thirty years 1935-65 Russia,
from Europe’s granary became an importing country, after a series of failed
crops.
Among the tenets of what will be termed Lysenkonism are the critique of
Mendelism, the denial of the applicability of chemistry, physics and
mathematics to the solution of any biological problem [Lysenko 1940], as well
as the promise to quickly solve all agricultural tasks set by the party.

###  3.1 The Lysenko affair

I his book The Lysenko affair (1970), the American historian of science David
Joravsky wrote:

Thus the Lysenko affair has been pictured as a latter-day version of Galileo
versus the Church, or Darwin versus the churches: new science denounced to
save old theology. The historical reality was far less high-minded, far more
serious. Lysenko’s school did not derive from a moribund tradition in science;
it rebelled against science altogether. Farming was the basic problem, not
theoretical ideology. Not only genetics but all the sciences that impinge on
agriculture were tyranically abused by quacks and time-servers for about
thirty-five years. The basic motivation was not a dream of human
perfectibility but a selfdeceiving arrogance among political bosses, a
conviction that they knew better than scientists how to increase farm yields.
The Lysenko affair, in short, was thirty-five years of brutal irrationality in
the campaign for improved farming, with severe convulsions resulting in the
academic disciplines that touch on agriculture. [Joravky 1970, p. vii]

Graham devoted chapter 6 of his book Science in Russia and the Soviet Union: A
Short History [Graham 1993] to this topic:

The roots of Lysenkoism lie not in Marxist ideology, but in the social and
political context of Soviet Russia in the 1930s. Lysenko originated his ideas
outside the circles of Marxist philosophers and outside the community of
established geneticists. He was a simple agronomist who developed ideas about
plants not very different from those of many practical selectionists of the
late nineteenth and early twentieth centuries, but who was able to promote
those ideas to an unheralded prominence because of the political and social
situation in which he found himself. An extremely shrewd but basically
uneducated man, he learned how to capitalize on the opportunities that the
centralized bureaucracy and ideologically charged intellectual atmosphere
presented. Seeing that his ideas would fare better if they were dressed in the
garb of dialectical materialism, with the help of a young ideologist he recast
his arguments in Marxist terms.
[…] Alarmed that the science of genetics itself might be eclipsed,
Vavilov181818It refers to Nikolai Vavilov (November 25, 1887 - January 26,
1943), a Russian agronomist, botanist and geneticist, famous for his
expeditions around the world in search of varieties of agricultural plants. He
was an exemplary researcher with encyclopedic knowledge: he contributed to
genetics, botany, plant physiology, plant breeding, plant systematics and
evolution and biochemistry. abandoned the effort to compromise with Lysenko
and pointed out the errors in his biological views.
[…] A few other brave people continued to speak up against Lysenko. At a
conference on genetics in December 1936, A.S. Serebrovskii, an outstanding
geneticist and sincere Marxist, called Lysenko’s campaign "a fierce attack on
the greatest achievements of the twentieth century…an attempt to throw us
backward a half-century." [Graham 1993, p. 124, 129-130]

Lysenko’s most famous opponent, Nikolai Vavilov, paid with his life for a
heroic attempt to publicly defend the achievements of biology hitherto
achieved in the Soviet Union, and to oppose Lysenko’s scientifically
unsubstantiated ideas. As early as 1935 Lysenko began to attack his colleague,
accusing him of having hindered the development of agricultural production in
Russia. And, although in 1939 Vavilov was elected president of the VII
International Congress of Genetics, it was not enough to maintain his
prestige. Accused Vavilov of defending classical Mendelian genetics,
considered by party ideologues a "bourgeois pseudoscience", he was imprisoned
in 1940 and a year later sentenced to death. He died of starvation in 1943 in
the Russian prison of Saratov. He was on of the many biologists arrested,
exiled and repressed.
In a recent book, Lysenko’s ghost (2016) considering recent genetical
research, has developed a synthetic but thorough examination of genuine
scientifc aspects of the discussion on epigenetics together with the evolution
of repression and terror under Stalinism. In the conclusion he writes (pp.
139-140):

With the realization that the inheritance of acquired characteristics might
happen after all, was Lysenko right? No, he was not. Some people may think so
because they mistakenly link Lysenko uniquely to the doctrine of acquired
characteristics, a belief that has been around for serveral thousand years.
Lysenko was a very poor scientist, and the inheritance of acquired
characteristics was actually a small part of what he claimed.
The fathers and mothers of epigenetics did not use Lysenko’s results but
developed their views on the basis of molecular biology. […] Lysenko
disregarded the action of genes […].
Does this mean that Lysenko was totally worthless as a practical plant
breeder, especially in his early years? No. Lysenko had talents in the field
[…]. If Lysenko had lived in a normal democratic country, he would be
remembered, if at all, as a talented farmer working away in his fields,
employing idiosincratic methods but never garnering much support. None of his
methods are employed in Russia today. But in the Soviet Union in the 1930s, a
country suffering from famine (caused in large part by the disastrous
collectivization effort), the need for quick agricultural remedies was acute,
and Lysenko offered them.

###  3.2 Kolmogorov against Lysenko and Kol’man

In 1939, the scholar N.I. Ermolaeva published an article entitled (translated
into English), Once again about pea laws191919In Russian: Yeshche raz o
gorokhovikh zakonakh, which went against the validity of Mendel’s principle
and where, in particular, it ended that Mendel’s principle that self-
pollination of hybrid plants resulted in 3: 1202020Mendel’s principle, based
on the 3:1 ratio, states that the dominant trait is present three times as
often as the recessive trait segregation ratios was false.
At that time, Kolmogorov had already long been interested in biology, one of
his passions since childhood. The article was brought to Kolmogorov’s
attention by geneticist Aleksandr Sergeevich Serebrovskii 212121[Kolmogorov
1940, p 222]. Serebrovskii (Kusrk, February 18, 1892 - Bolshevo, June 26,
1948) was a prominent Russian geneticist, the founder of the Department of
Genetics of Moscow University. His major contributions are due to the genetic
study of chicken breeds and the development of poultry farming.. In a paper
published in 1940 222222the episode took place at the turn of the world war -
after the sanctioning of the Russo-German pact of August 1939 and a few months
before the entry into the war of the USSR after the German invasion of June
1941 in the reports of the USSR Academy of Sciences, he discussed Ermolaeva
data as well as T. K. Enin data as discussed by Kol’Man:

In the discussion on genetics that took place in the autumn of 1939 much
attention was paid to checking whether or not Mendel’s laws were really true.
In the basic discussion on the validity of the entire concept of Mendel, it
was quite reasonable and natural to concentrate on the simplest case, which,
according to Mendel, results in splitting in the ratio 3:1. For this simplest
case of crossing $Aa\times Aa$, with the feature A dominating over the feature
$a$, it is well known that Mendel’s concept leads to the conclusion that in a
sufficiently numerous progeny (no matter whether it consists of one family or
involves many separate families resulting from various pairs of heterozygous
parents of type $Aa$) the ratio between the number of individuals with the
feature A (that is, the individuals of the type $AA$ or $Aa$) to the number of
individuals with the feature a ($aa$ type) should be dose to the ratio 3:1.
T.K. Enin, N.I. Ermolaeva and E. Kol’man have concentrated on checking this
simplest consequence of Mendel’s concept. However, Mendel’s concept not only
results in this simplest conclusion on the approximate ratio $3:1$ but also
makes it possible to predict the average deviations from this ratio. Owing to
this it is the statistical analysis of deviations from the ratio $3:1$ that
gives a new, more subtle and exhaustive way of proving Mendel’s ideas on
feature splitting. In this paper we will try to indicate what we think to be
the most rational methods of such checking and to illustrate these methods on
the material of the paper by N.I. Ermolaeva.

And he adds in conclusion a strong attack against Kol’man’s contribution:

Kol’man’s paper referred to in the beginning of this note does not contain any
new facts; it only analyses Enin’s data and is based on a complete
misunderstanding of the circumstances set forth in this paper. [Kolmogorov
1940, p. 227].

Kolmogorov applied a statistic test, now called the Kolmogorov or Kolmogorov-
Smirnov test in order to analyze in this more polished way the validity of
Mendel’s ratio. Kolmogorov’s paper prompted a reaction by Kol’man and by
Lysenko himself.
Mathematicians Alan Stark and Eugene Seneta, in the article A.N. Kolmogorov’s
defense of Mendelism published in 2011 [Stark, Seneta 2011], examined
Kolmogorov’s paper and reused the test used by the Russian mathematician in
the data collected by Ermolaeva. They have shown that there were errors not
only in Ermolaeva’s obviously incorrect calculations - and in the consequent
deduction of the inadequacy of Mendel’s law - but also in the experiment
itself performed by Kolmogorov:

In the above brief $\chi^{2}$ analysis we have attempted to use an essentially
equivalent test to Kolmogorov’s inasmuch as it relies on the approximate
standard normality of the $\Delta$’s, after “cleaning” the data appropriately.
So while the conclusion drawn by Kolmogoroff (1940) confirms what is now
totally accepted, the evidence in support of this conclusion is not as strong
as his paper presents. Of course his statistical technology was well beyond
the understanding of Lyssenko (1940) and Kolman (1940), who could hardly argue
on the grounds of its incompletely justified application and possible
arithmetic error, to data which may have been poorly prepared. Seneta (2004)
describes Kolman’s leading role in the attacks on mathematicians and
traditional pure mathematics in the Soviet Union during the Stalinist era.

Futhermore, at the end of the article they write:

In his defense of Mendelism, Kolmogorov […] relied simply on data. As we have
seen, he ignored the fact that, strictly speaking, his test of him assumed
continuous data while the actual data was discrete and in some cases based on
inappropriately small numbers [Stark, Seneta 2011, p. 185]

Kolmogorov had not only corrected the results obtained by Ermolaeva, but his
defense against Mendelism first involved Kol’man and Lysenko (even if he was
not directly mentioned), as Ermolaeva was a student of him. In fact, Lysenko
responded in a comment published in the reports of the Academy:, in In
Response to the Article by A. N. Kolmogorov, [Lysenko 1940]:

In "Doklady Akademii Nauk SSSR", Volume XXVII, N 1 of 1940, an article by
academician A.N. Kolmogorov "On a new confirmation of Mendel’s laws". In this
article, the author, wanting to prove the "correctness" and inviolability of
Mendel’s statistical law, gives a number of mathematical arguments, formulas
and even curves. I don’t feel competent enough to understand this system of
mathematical evidence. Besides, I, as a biologist, don’t care whether Mendel
was a good or a bad mathematician. I have already published my assessment of
Mendel’s statistical work several times, stating that he had nothing to do
with biology. In this note I would just like to note that even the above-
mentioned article by the famous mathematician A.N. Kolmogorov has nothing to
do with biological science.
[…] That is why we biologists do not take the slightest interest in
mathematical calculations that confirm the useless statistical formulas of the
Mendelists. [Lysenko 1940, p 834-835]

Also Kol’man also supported the agronomist’s point of view.232323As stated in
the note 84 in [Joravsky 1970], p. 414.
It could have ended much worse for the Russian mathematician, but he was
spared from the great purge. There is no doubt that at that time Kolmogorov’s
fame in the field of probability theory - a field with a strong Russian
tradition for more than a century - was undisputed, and this may have favored
him over the fates of other academics; moreover the cautious and submissive
behavior maintained by Kolmogorov and his friend Aleksandrov242424Kolmogorov
and Aleksandrov had lived together since 1935, (ref [Kolmogorov 1986]). during
the period of the Stalinist regime - the same behavior which has led some to
believe that they were "friends of the regime" - has to be taken into account.
Consider also in [Levin 1990], the description of Kol’man previous attitude to
the two mathematical friends:

When the campaign was over252525He refers to the campaign against Luzin
Kol’man’s monograph, Predmet i metod sovremennoi matematiki, was
published262626Year 1936. The scholarly qualities of this very primitive and
inaccurate book are of no relevance here, although it is worth noting that the
author expressed his gratitude to A. N. Kolmogorov and P. S. Aleksandrov for
reading a draft manuscript.

Therefore, only hypotheses, but no certainty about the reasons for his
salvation. Nevertheless, quoting Lorentz’s words in [Lorentz 2002, p 183] The
voice of Kolmogorov raised in defense of Mendel’s laws was ignored.

##  4 Final remarks

What prompted the reaction of Kolmogorov to a paper by a student of Lysenko,
who was in those years reaching a great influence? No doubt he was encouraged
to do so by a fellow Academician, the genetist Serebrovskii, who could thought
that the mathematical authority of Kolmogorov regarding numbers in Mendel’s
laws of heredity could help their defense of Mendelism and maintain USSR
biolgoy in connection with the international accepted ideas. Moreover, the
role of mathematical studies in the discussions on evolution was growing in
the late 1930s272727See [Kingsland 1985]; [Israel 1993]; [Israel, Millán Gasca
2002]. At Moscow, the biologist Georgii Frantsevich Gause (1910-1989) has
intensely worked on the mathematical analysis of the struggle for life and
published two monographies on it in the USA and in France (respectively in
1934 and 1935) . Kolmogorov was sympathetic with this research trend, and this
can be linked to his vision of Mathematics as present in the Soviet
Encyclopedia. The reaction of Lysenko’s against mathematics in biology can be
understood as an underlying aspect of the harsh exchange in the Stalinst
Russia of 1940.

## Acknowledgement

I thank Luca Biasco and Ana Millán Gasca for insights and comments on this
preprint, which is subject to further improvements.

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