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G. Sinkevich. Some clarifications on the history of Russian mathematics of the 20th century // Handbook of Teichmüller Theory/ ed. A.Papadopoulos. Series: IRMA Lectures in Mathematics & Theoretical Physics European Mathematical Society, 2019. – P. 340-347.

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In this note, I would like to bring a few additions that clarify some points in A. Papadopoulos's article related to the biographies of P. Florensky and N. Luzin. My additions may shed a different light on this complicated period of the history of mathematics in the Soviet Union.
SOME CLARIFICATIONS ON THE HISTORY OF RUSSIAN
MATHEMATICS OF THE 20TH CENTURY
(APPENDIX TO A. PAPADOPOULOS’ ARTICLE)
GALINA SINKEVICH
In this note, I would like to bring a few additions that clarify some points in
A. Papadopoulos’s article related to the biographies of P. Florensky and N. Luzin.
My additions may shed a different light on this complicated period of the history
of mathematics in the Soviet Union.
According to B. Mlodzeevsky, it was characteristic for Moscow mathematicians
of the turn of the 19th and 20th centuries, “to explain mathematics through the
worldview, and worldview through the mathematics” [8, p.185]. The leading role
in this orientation of the Moscow school belonged to N. V. Bugaev, whose theory
of discontinuous functions was considered in a philosophical context and had a
wide resonance among Moscow mathematicians [4], although his colleagues did not
appreciate his mathematical results and lectures [12, p. 165–185].
In 1897, at the First Congress of Mathematicians in Zurich Bugaev made a
report On the influence of mathematics on the worldview [1]. According to him,
world laws are explained in the language of the theory of continuous functions.
This gave rise to determinism, while in the natural and human sciences many
phenomena cannot be subordinate to the laws of mathematical analysis. Using
continuity, only part of the world events can be explained. At the same time,
a new science emerges from number theory, a theory of discontinuous functions,
called arhythmology. In the realm of philosophy proper, arhythmology is refracted
into monadology. The arhythmological point of view complements the analytical
worldview. Combining both worldview approaches, analytic (using mathematical
analysis) and arhythmological (using the theory of discontinuous functions), and
adding probability theory in necessary cases, Bugaev obtains a scientific world
view that allows us to explain mechanically world phenomena. Finally, whenever
phenomena do not obey the correct laws, probability theory applies. From the
cumulative application of all these departments of mathematics, a true scientific
and philosophical outlook was formed.
N. Luzin and P. Florensky entered Moscow University with a difference of one
year (1901 and 1900 respectively). They soon became friends. First a mathematics
student and then a priest, Florensky was a very ambiguous figure. No doubt he was
very talented. In his student years, he was fascinated by Bugaev’s ideas. He then
became interested in Cantor’s set theory. Florensky was the first to publish a com-
petent statement of Cantor’s ideas in Russian (On the symbols of Infinity, 1904).
But then his interests shifted towards theology. After graduating from university
he entered as a student the Moscow Theological Academy. He needed mathemat-
ics only as a basis for building the philosophical foundation of the universe. His
philosophical and religious works, The pillar and foundation of truth (1914), Re-
verse perspective (1919), Imaginaries (imaginary numbers) in geometry (1922) are
widely known. In particular, in his last work, Florensky interprets the complex
Date: May 3, 2019.
1
2 GALINA SINKEVICH
plane as a two-sided object for the rehabilitation of the Ptolemaic model of the
Universe.
The statement that Florensky was extremely talented in mathematics is debat-
able. Luzin and his teacher D. Egorov estimated the mathematical success of the
student Florensky low. In 1908, Luzin wrote to his wife about Florensky: “As
soon as he showed his work in mathematics, again the old opinion began to stir
in me: all his works have no value in the field of mathematics. Hints, beautiful
comparisons are something that revels and promises, is tantalizing, alluring and
ineffectual. And in the end I stopped understanding what Florensky is. Or is it
a precursor of the new, the petrel, or a capable person with subconscious hellish
self-love, who, because of the desire to be the best of all, has retired here? [7, p.
150].
In 1904–1907, Luzin experienced spiritual crisis which was so severe that he
wanted to stop practicing mathematics, and even wanted to take his own life. One
reason for the crisis was the dramatic atmosphere that preceded the first revolution.
His teacher Egorov hastily sent Luzin from Russia to France to prepare him for
professorship. At this time, Luzin was under the strong influence of Florensky. On
the ambiguity of Florensky’s personality and his negative charisma, L. Sabaneev
wrote in his memoirs (1915): “Very black and very thin, for some reason he always
looked down and slightly sideways, he did not like to show his eyes. He never smiled.
It was a strange thing—he had many students, apparently, he taught them not only
classical theological subjects common to the spiritual sciences, but also gave them
esoteric knowledge and habits. Three of his students committed suicide—powerful
vibes emanated from him, and I myself felt it, felt that not all fluids were good,
there were very demonic among them. I don’t remember exactly who, but speaking
of him, one of the Russian ‘neo-Christian’ group called him ‘a clever and cruel
Lavra priest’. In any case, he was an absolutely extraordinary person, and I am
very grateful to the fate that brought him together with me, although not for long”
[11].
The relations between Luzin and Florensky were uneven and the influence of
Florensky on the mathematical search for Luzin is problematic.
In 1915, Luzin presented his master’s thesis Integral and trigonometric series,
with so strong results that it was qualified as a doctor’s thesis. Starting in 1917,
Luzin began to teach at Moscow University, a group of talented students gath-
ered around him. This circle was named Luzitania. It was a happy period of the
relationship between a teacher and equally talented students. Years passed, the
students themselves became leaders of scientific schools, and in the meantime, the
Stalinist terror gained momentum in the Soviet Union. Trials began, the search for
“enemies of the people” was going on. Under the blow was the intelligentsia, the old
professorship. Much has been written about this in Russian literature. The Soviet
government sought to subjugate the Academy of Sciences, to “domesticate” the old
scientists, orienting them to the tasks of communist construction, re-educate Soviet
scientists in the spirit of communist ideology. For this, any contradiction among
scientists was used. The conflict between Luzin and his former disciples in 1936
served as a convenient pretext. About this tragic story, see above all [2].
Despite this fact, it is impossible to perceive the persecution of Luzin as a direct
manifestation of Stalin’s terror. It was part of a more general process. Stalin did
not set himself the goal of punishing Luzin and did not even know about the begin-
ning of the persecution. The reason was different: the happy period of Lusitania
ended, the former disciples became independent scientific leaders, and rivalry be-
gan. A tangle of very complex contradictions both in the mathematical community
and in society as a whole, multiplied by the difficult character of Luzin, who in his
A NOTE ABOUT MIKHA¨
IL LAVRENTIEFF 3
own way understood his role in the students’ successes; denunciations written on
Luzin by the pro-Communists E. Kolman and V. Molodshij; the clash of traditional
ethics of old scientists with the new ethics of the younger scientific generation; the
atmosphere of fear cultivated among the intelligentsia by the Stalinist search for
“enemies of the people”: all this inspired this persecution. The case was accom-
panied by violent attacks on Luzin in the newspapers. Nevertheless, it did not go
beyond the academic environment, and a month later it was completed by the De-
cree of the Presidium of the Academy of Sciences of 08/05/1936 on Academician
Luzin with the following wording: “Given the importance of N. N. Luzin as a major
mathematician, and weighing the full force of social impact, what had revealed in
such a broad, unanimous and fair condemnation of the behavior of N. N. Luzin,
and based on the desire to give Luzin the opportunity to restructure his whole be-
havior and work, we consider it possible to limit the warning to N.N. Luzin that in
the absence of a decisive change in his future behavior, the Presidium will have to
urgently raise the question of expelling N.N. Luzin from the academic ranks” [3].
Luzin escaped the terrible machine of Stalin’s repression, which many well-known
scientists got into, including Florensky who was shot in 1937. See also (in Russian)
S. Novikov (Jr.) [10], a very deep study of Yu. Neretin [9], and (in English) A.E.
Levin [5]. Luzin recovered with difficulty after the persecution, he was ill for a long
time, then continued his scientific work, but he no longer made major discoveries.
References
[1] N. V. Bugaev. Mathematics and the scientific and philosophical outlook (in Russian). Matem-
aticheskij sbornik, 25 (1905) 2. p. 349–369.
[2] The case of Academician Nikolai Nikolaevich Luzin, eds. Sergei S. Demidov, Boris V. Levshin;
trans. Roger Cooke. American Mathematical Society. 2016. (History of Mathematics, 43).
[3] The Decree of the Presidium of the Academy of Sciences of 08/05/1936 about Academician
N.N. Lusin. http://www.math.nsc.ru/LBRT/g2/english/ssk/ARTICLES/2012-1-11.pdf
[4] S .S. Demidov. N. V. Bugaev and the origin of Moscow school of real variable function theory.
Istoriko-matematicheskie issledovaniya. Moscow:Nauka, 29 (1985) p. 113–124.
[5] A. E. Levin. Anatomy of a public campaign “Academician Luzin’s case” in Soviet political
history. Slavic Review, V, 49 (1990), 1. p. 90–108.
[6] M. M. Lavrentieff, Father did not foresee such turns (in Russian). Open
Archive of the Siberian Branch of the Russian Academy of Sciences.
http://odasib.ru/openarchive/DocumentImage.cshtml?id=Xu kray 634993802507080078 5064&eid=Oh 0001 0047
[7] [N. N. Luzin] Correspondence between N. N. Luzin with PA Florensky (1904-1922) (in Rus-
sian). Publication and notes by S. S. Demidov, A. N. Parshin, S. M. Polovinkin and P. V.
Florensky. Istoriko-matematicheskie issledovaniya. Moscow: Nauka, 31 (1989) p. 116–191.
[8] E. Mioduszewski. Mathematicians and philosophers (in Russian) / Transl. from Polish and
comments by G. Sinkevich. Al’manah “Russkij mir”. Prostranstvo i vremya russkoj kul’tury.
Saint-Petersburg: Russkaya kultura, 7 (2012) p. 179-199.
[9] Yu. Neretin. Nikolay Luzin, his students, adversaries, and defenders (notes on the history of
Moscow mathematics, 1914-1936). https://arxiv.org/pdf/1710.10688.pdf
[10] S. Novikov (Jr.), My stories. http://www.mi.ras.ru/ snovikov/Mem.pdf
[11] L. L. Sabaneev, Memories of Russia (in Russian). Moscow: Classica. 2005. ?XI.
http://www.belousenko.com/books/memoirs/sabaneev vosp o rossii.htm
[12] M. Ya. Vygodskij. Mathematics and its leaders at Moscow University in the second half of the
19 century (in Russian). Istoriko-matematicheskie issledovaniya. Moscow: Nauka. 1 (1948),
p. 141–181.
G. Sinkevich, Saint Petersburg State University of Architecture and Civil Engi-
neering, Vtoraja Krasnoarmejskaja ul. 4, St. Petersburg, 190005, Russia, Department
of Mathematics, galina.sinkevich@gmail.com
ResearchGate has not been able to resolve any citations for this publication.
Article
In October 1985, when I first began research on the case of Academician Luzin, rumors had surfaced in the Soviet Union that new official regulations would require scientific articles containing no classified information to be published in Soviet journals before they could be cleared for publication abroad. The rumors were true. The effect of these new regulations clearly resembled the campaign against the mathematician Nikolai Nikolaevich Luzin, which had taken place fifty years before. Luzin was the victim of the first Soviet mass media campaign against such publication. The case against him appears to be an insignificant moment in the witch-hunting mania of the 1930s, since the propaganda was apparently aimed only at one full member of the Soviet Academy of Sciences and his alleged misconduct.
Mathematics and the scientific and philosophical outlook (in Russian). Matematicheskij sbornik
  • N V Bugaev
N. V. Bugaev. Mathematics and the scientific and philosophical outlook (in Russian). Matematicheskij sbornik, 25 (1905) 2. p. 349-369.
Bugaev and the origin of Moscow school of real variable function theory. Istoriko-matematicheskie issledovaniya
  • S S N Demidov
S.S. Demidov. N. V. Bugaev and the origin of Moscow school of real variable function theory. Istoriko-matematicheskie issledovaniya. Moscow:Nauka, 29 (1985) p. 113-124.
Open Archive of the Siberian Branch of the Russian Academy of Sciences
  • M M Lavrentieff
M. M. Lavrentieff, Father did not foresee such turns (in Russian). Open Archive of the Siberian Branch of the Russian Academy of Sciences. http://odasib.ru/openarchive/DocumentImage.cshtml?id=Xu kray 634993802507080078 5064&eid=Oh 0001 0047
Mathematicians and philosophers (in Russian) / Transl. from Polish and comments by G. Sinkevich. Al'manah "Russkij mir". Prostranstvo i vremya russkoj kul'tury
  • E Mioduszewski
E. Mioduszewski. Mathematicians and philosophers (in Russian) / Transl. from Polish and comments by G. Sinkevich. Al'manah "Russkij mir". Prostranstvo i vremya russkoj kul'tury. Saint-Petersburg: Russkaya kultura, 7 (2012) p. 179-199.
Memories of Russia (in Russian)
  • L L Sabaneev
L. L. Sabaneev, Memories of Russia (in Russian). Moscow: Classica. 2005. ?XI. http://www.belousenko.com/books/memoirs/sabaneev vosp o rossii.htm
Mathematics and its leaders at Moscow University in the second half of the 19 century (in Russian). Istoriko-matematicheskie issledovaniya
  • M Ya
  • Vygodskij
M. Ya. Vygodskij. Mathematics and its leaders at Moscow University in the second half of the 19 century (in Russian). Istoriko-matematicheskie issledovaniya. Moscow: Nauka. 1 (1948), p. 141-181.
Saint Petersburg State University of Architecture and Civil Engineering, Vtoraja Krasnoarmejskaja ul
  • G Sinkevich
G. Sinkevich, Saint Petersburg State University of Architecture and Civil Engineering, Vtoraja Krasnoarmejskaja ul. 4, St. Petersburg, 190005, Russia, Department of Mathematics, galina.sinkevich@gmail.com