N. N. Luzin at the Crossroads of the Events in European History of the First Half of the 20th Century

 
PIIS020596060018958-5-1
DOI10.31857/S020596060018958-5
Publication type Article
Status Published
Authors
Affiliation: M. V. Lomonosov Moscow State University
Address: Russian Federation, Moscow, Leninskie gory, 1
Journal nameVoprosy istorii estestvoznaniia i tekhniki
EditionVolume 43 Issue 1
Pages101-130
Abstract

A prominent Russian mathematician Nikolai Nikolaevich Luzin (1883– 1950) lived in a very difficult period of Russian history: two world wars, two 1917 revolutions in Russia, the Bolsheviks’ coming to power, the Civil War of 1917–1922, and the construction of a new type of state, accompanied by mass terror that impacted all the strata of Soviet society. It was against the backdrop of these dramatic events that the process of Luzin’s formation and flourishing as a scientist and founder of one of the leading mathematical schools of the 20th century, the Moscow school of function theory that became one of the cornerstones in the foundation of the Soviet mathematical school, took place. Two periods can be distinguished in Luzin’s work: the first period was devoted to the problems of the metric theory of functions and culminated in his famous dissertation “The Integral and the Trigonometric Series” (1915), and the second period was mainly devoted to the development of problems in the theory of analytic sets. The implication of Luzin’s research was the problem of the structure of the arithmetic continuum that became the ultimate purpose of his work. Fortune favored the scientist: the complicated turns of history he happened to be involved in did not hinder, and sometimes even facilitated, the successful development of his studies. Even the catastrophe that descended upon him in 1936, “the case of Academician Luzin,” even though it had put an end to the normal development of his creative thought, ended with a smoothest possible outcome for him.

KeywordsN. N. Luzin, D. F. Egorov, set theory, theory of functions of a real variable, Moscow school of function theory, axiom of choice, continuum hypothesis, M. Ya. Suslin, effectivism, Borel set, analytic set
Received23.10.2021
Publication date28.03.2022
Number of characters75134
Cite  
100 rub.
When subscribing to an article or issue, the user can download PDF, evaluate the publication or contact the author. Need to register.

Number of purchasers: 0, views: 381

Readers community rating: votes 0

1. [Khinchin, A. Ia.] (1927) Matematika [Mathematics], in: Petrov, F. N. (ed.) Desiat’ let sovetskoi nauke. Sbornik statei [Ten Years of Soviet Science. A Collection of Articles]. Moskva and Leningrad: Gosudarstvennoe izdatel’stvo, pp. 39–51.

2. Bari, N. K., and Liusternik, L. A. (1951) Raboty N. N. Luzina po metricheskoi teorii funktsii [N. N. Luzin’s Works on the Metric Theory of Functions], Uspekhi matematicheskikh nauk, vol. 6, no. 6 (46), pp. 28–46.

3. Bogachev, V. I. (2009) K istorii otkrytiia teorem Egorova i Luzina [Towards the History of the Discovery of the Theorems of Egorov and Luzin], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 13 (48), pp. 54–67.

4. Bogachev, V. I. (2013) Luzinskie motivy v sovremennykh issledovaniiakh [Luzin’s Motives in Modern Research], Sovremennye problemy matematiki i mekhaniki, vol. 8, no. 2, pp. 4–24.

5. Demidov, S. S. (1999) Professor Moskovskogo universiteta Dmitrii Fedorovich Egorov i imiaslavie v Rossii v pervoi treti XX stoletiia [Moscow University Professor Dmitry Fedorovich Egorov and Onomatodoxy in Russia at the First Third of the 20th Century], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 4 (39), pp. 123–156.

6. Demidov, S. S., and Levshin, B. V. (eds.) (2019) Delo akademika Nikolaia Nikolaevicha Luzina [The Case of Academician Nikolai Nikolaevich Luzin]. Moskva: Izdatel’stvo MTsNMO.

7. Demidov, S. S., and Tokareva, T. A. (2005) Formirovanie sovetskoi matematicheskoi shkoly [Formation of the Soviet Mathematical School], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 10 (45), pp. 142–159.

8. Diugak, P. (Dugac, P.) (2000) “Delo” Luzina i frantsuzskie matematiki [The Luzin “Case” and French Mathematicians], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 5 (40), pp. 119–142.

9. Dobretsov, N. L., and Marchuk, G. I. (eds.) (2000) Vek Lavrent’eva (kniga vospominanii) [The Century of Lavrentiev: A Book of Memoirs]. Novosibirsk: Izdatel’stvo SO RAN, filial “Geo”. Egorov, D. F. (1980) Pis’ma k N. N. Luzinu [Letters to N. N. Luzin], Istoriko-matematicheskie issledovaniia, vol. 30, pp. 335–361.

10. Ermolaeva, N. S. (2001) Tsentrobezhnye sily sud’by V. A. Kostitsyna [The Centrifugal Forces of V. A. Kostitsyn’s Fate], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 6 (41), pp. 127–163.

11. Gao, S. (2009) Invariant Descriptive Set Theory. Boca Raton, FL: CRC Press.

12. Golubev, V. V., and Bari, N. K. (1951) Biografiia N. N. Luzina [N. N. Luzin’s Biography], in: Luzin, N. N. Integral i trigonometricheskii riad [Integral and Trigonometric Series]. Moskva and Leningrad: GITTL, pp. 11–31.

13. Igoshin, V. I. (1996) Mikhail Iakovlevich Suslin. 1894–1919 [Mikhail Yakovlevich Suslin. 1894–1919]. Moskva: Nauka and Fizmatlit.

14. Iushkevich, A. P. (1968) Istoriia matematiki v Rossii do 1917 goda [History of Mathematics in Russia until 1917]. Moskva: Nauka.

15. Kanovei, V. (2008) Borel Equivalence Relations; Structure and Classification. New York: American Mathematical Society, 2008.

16. Kanovei, V. G. (1985) Razvitie deskriptivnoi teorii mnozhestv pod vliianiem trudov N. N. Luzina [The Development of Descriptive Set Theory, Influenced by N. N. Luzin’s Works], Uspekhi matematicheskikh nauk, vol. 40, no. 3 (243), pp. 117–155.

17. Kanovei, V. G., and Liubetskii, V. A. (2007) Sovremennaia teoriia mnozhestv: nachala descriptivnoi dinamiki [Modern Set Theory: Basics of Descriptive Dynamics]. Moskva: Nauka.

18. Kanovei, V. G., and Liubetskii, V. A. (2010) Sovremennaia teoriia mnozhestv: borelevskie i proektivnye mnozhestva [Modern Set Theory: Borel and Projective Sets]. Moskva: Izdatel’stvo MTsNMO.

19. Kanovei, V. G., and Liubetskii, V. A. (2013) Sovremennaia teoriia mnozhestv: absoliutno nerazreshimye klassicheskie problemy [Modern Set Theory: Absolutely Unsolvable Classical Problems]. Moskva: Izdatel’stvo MTsNMO.

20. Keldysh, L. V. (1974) Idei N. N. Luzina v deskriptivnoi teorii mnozhestv [N. N. Luzin’s Ideas in Descriptive Set Theory], Uspekhi matematicheskikh nauk, vol. 29, no. 5 (179), pp. 183–196.

21. Keldysh, L. V., and Novikov, P. S. (1953) Raboty N. N. Luzina v oblasti deskriptivnoi teorii mnozhestv [Works by N. N. Luzin in the Field of Descriptive Set Theory], Uspekhi matematicheskikh nauk, vol. 8, no. 2 (54), pp. 93–104.

22. Kostitsyn, V. A. (2017) “Moe utrachennoe schast’e…”: vospominaniia, dnevniki [“My Lost Happiness...”: Memoirs, Diaries]. Moskva: Novoe literaturnoe obozrenie, vol. 1–2.

23. Lebeg, A. (Lebesgue, H.) (1985) Predislovie k knige N. N. Luzina “Lektsii ob analiticheskikh mnozhestvakh i ikh prilozheniiakh” [Foreword to N. N. Luzin’s Book “Lectures on Analytic Sets and Their Applications”], Uspekhi matematicheskikh nauk, vol. 40, no. 3 (243), pp. 9–14.

24. Lusin, N. (1911) Über eine Potenzreihe, Rendiconti del Circolo matematico di Palermo, vol. 32, pp. 386–390.

25. Lusin, N. (1912) Sur l’absolue convergence des séries trigonométriques, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 155, pp. 580–582.

26. Lusin, N. (1912) Sur les propriétés de l’intégrale de M. Denjoy, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 155, pp. 1475–1477.

27. Lusin, N. (1912) Sur les propriétés des fonctions mesurables, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 154, pp. 1688–1690.

28. Lusin, N. (1913) Sur la convergence des series trigonometriques de Fourier, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 156, pp. 1655–1658.

29. Lusin, N. (1914) Sur un problème de M. Baire, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 158, pp. 1258–1261.

30. Lusin, N. (1930) Leçons sur les ensembles analytiques et leurs applications. Préface de M. Henri Lebesgue; une note de M. Waclaw Sierpinski. Paris: Gauthier-Villars.

31. Luzin, N. N. (1912) Dobavlenie k stat’e “K osnovnoi teoreme integral’nogo ischisleniia” [Addition to the Paper “On the Fundamental Theorem of Integral Calculus”], Matematicheskii sbornik, vol. 28, no. 2, p. 544.

32. Luzin, N. N. (1912) K absoliutnoi skhodimosti trigonometricheskikh riadov [On the Absolute Convergence of Trigonometric Series], Matematicheskii sbornik, vol. 28, no. 3, pp. 461–472.

33. Luzin, N. N. (1912) K osnovnoi teoreme integral’nogo ischisleniia [On the Fundamental Theorem of Integral Calculus], Matematicheskii sbornik, vol. 28, no. 2, pp. 266–294.

34. Luzin, N. N. (1912) Ob odnom sluchae riada Tylor’a [On One Case of the Taylor Series], Matematicheskii sbornik, vol. 28, no. 3, p. 295–302.

35. Luzin, N. N. (1915) Integral i trigonometricheskii riad [Integral and Trigonometric Series]. Мoskva: Tipografiia Lissnera i Sobko.

36. Luzin, N. N. (1958) Sobranie sochinenii [Collected Works]. Moskva: Izdatel’stvo AN SSSR, vol. 2.

37. Luzin, N. N. (1997) Dva pis’ma M. Ia. Vygodskomu [Two Letters to M. Ya. Vygodsky], Istorikomatematicheskie issledovaniia, vtoraia seriia, vol. 11 (46), pp. 267–306.

38. Luzin, N. N., and Florenskii, P. A. (1989) Perepiska [Correspondence], Istoriko-matematicheskie issledovaniia, vol. 31, pp. 125–191.

39. Moschovakis, Y. (1980) Descriptive Set Theory. Amsterdam: North Holland.

40. Polovinkin, S. M. (1986) O studencheskom matematicheskom kruzhke pri Moskovskom matematicheskom obshchestve v 1902–1903 gg. [On the Student Mathematical Circle at the Moscow Mathematical Society in 1902–1903], Istoriko-matematicheskie issledovaniia, vol. 30, pp. 148–158.

41. Protasova, L. A., and Tiulina, I. A. (1995) Vladimir Vasil’evich Golubev. 1884–1954 [Vladimir Vasil’evich Golubev. 1884–1954]. Moskva: Nauka.

42. Stechkin, S. B. (1951) O skhodimosti i raskhodimosti trigonometricheskikh riadov [On the Convergence and Divergence of Trigonometric Series], Uspekhi matematicheskikh nauk, vol. 6, no. 2 (42), pp. 148–149.

43. Tiulina, A. K. (2006) Ob odnoi rukopisi neizvestnogo avtora (k biografii N. N. Luzina) [On a Manuscript by an Unknown Author (Towards N. N. Luzin’s Biography)], Istorikomatematicheskie issledovaniia, vtoraia seriia, vol. 11 (46), pp. 267–306.

44. Ul’ianov, P. L. (1985) O rabotakh N. N. Luzina po metricheskoi teorii funktsii [On N. N. Luzin’s Works on the Metric Theory of Functions], Uspekhi matematicheskikh nauk, vol. 40, no. 3 (243), pp. 15–70.

45. Uspenskii, V. A. (1985) Vklad N. N. Luzina v deskriptivnuiu teoriiu mnozhestv i funktsii: poniatiia, problemy, predskazaniia [N. N. Luzin’s Contribution to the Descriptive Theory of Sets and Functions: Concepts, Problems, Predictions], Uspekhi matematicheskikh nauk, vol. 40, no. 3 (243), pp. 85–116.

46. Volkov, V. A. (2005) D. F. Egorov: novye arkhivnye dokumenty (k istorii moskovskoi matematicheskoi shkoly) [D. F. Egorov: New Archival Documents (Towards the History of the Moscow Mathematical School)], Istoriko-matematicheskie issledovaniia, vtoraia seriia, vol. 10 (45), pp. 13–19.

Система Orphus

Loading...
Up