Wac{\l}aw Franciszek Sierpi\'nski (1882 -- 1969) and the phenomenon of Polish set theory school

G. I. Sinkevich

Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 304-319.

Résumé

This year marks the 140th anniversary of the birth of the Polish mathematician Wacław Sierpiński, founder of the Warsaw School of Set Theory. The main directions of his research are number theory, set theory, measure theory, topology. Some years spent by him in Moscow, in the atmosphere of a young school of function theory, and collaboration with N.N. Luzin, left an imprint on his further research. Upon returning to his homeland, he managed to captivate and rally colleagues on the basis of the study and use of set theory, measure theory and topology. Set theory did not require prior specialization, it united mathematicians of various directions, and its methods made it possible to obtain results at a much lower cost than the methods of special sections of mathematics. Polish journal "Fundamenta Mathematicae" was founded in 1920, was entirely devoted to set theory, had a "Problems" section, and was published in the main European languages, thanks to which a fruitful international scientific dialogue arose. Numerous studies of Sierpinski himself served as the basis for the studies of his students.

Détail

Keywords: Wacław Sierpiński, polish set theory school.

Bibliographie

[1] Demidov, S. S., “From the Early History of the Moscow School of Function Theory”, Istoriko-matematicheskie issledovaniya, 1986, 124–130 | MR | Zbl

[2] Demidov, S. S., Esakov V. D., “Introduction”, Case of Academician Nikolai Nikolaevich Luzin, eds. S.S. Demidov, B.V. Lyovshin, Russkij hristianskij gumanitarnyj institut, Sankt-Peterburg, 1999, 9–50 | MR

[3] Luzin N. N., Collected works in three volumes, v. 2, M., 1958

[4] Mel'nikov I.G., “Waclaw Sierpinski”, Istoriko-matematicheskie issledovaniya, M., 1979, 361–365 | Zbl

[5] “N.N. Luzin's letters to A. Danjoy”, Publikaciya, vvedenie i prim. P. Dugac, Istoriko-matematicheskie issledovaniya, M., 1978, 314–348

[6] “W. Sierpiński's letters to N.N. Luzin”, Publikaciya V.A. Volkova i F.A. Medvedeva, Istoriko-matematicheskie issledovaniya, M., 1979, 366–373

[7] Saks S., Theory of the integral, IL, M., 1949

[8] Sierpiński W., “The Zermelo axiom and its role in the development of set theory and in analysis (Chitano na zasedanii Mosk. mat. o-va 21 fevralya 1917 g.)”, Matematicheskij sbornik, 31 (1924), 94–128

[9] Sierpiński W., Pythagorean Triangles, Per. pod red i s primechaniyami S.I. Zetelya, Uchpedgiz, M., 1959

[10] Sierpiński W., On solving equations in integers, Per. I.G. Mel'nikova, Fizmatgiz, M., 1961

[11] Sierpiński W., One Hundred Elementary but Difficult Problems in Arithmetic, Per., predislovie i primech. V.A. Golubeva, Uchpedgiz, M., 1961

[12] Sierpiński W., What We Know and What We Do Not. Know of Prime Numbers, Per. I.G. Mel'nikova, Fizmatgiz, M.–L., 1963

[13] Sierpiński W., On the set theory, Per. Z.Z. Rochinskogo, Prosveshchenie, M., 1966 | MR

[14] Sierpiński W., Problems in Elementary Number Theory, Per. s pol'skogo i predislovie I.G. Mel'nikova, Prosveshchenie, M., 1968, 250 pp. | MR

[15] Sinkevich G. I., Georg Cantor Polish set theory school, Izd-vo SPbGASU, SPb., 2012 | MR

[16] “Materialy Wacława Sierpińskiego (1882-1969)”, Biuletyn Archiwum Polskiej Akademii nauk, 43, Warszawa, 2002, 6–65

[17] Janiszewski Z., “O potrzebach matematyki w Polsce”, Nauka Polska, 1919, no. 1, 15–18

[18] Kuratowski K., “50 tomów “Fundamenta Mathematicae””, Wiadomości Matematyczne, 1962, no. 6, 12

[19] Kuratowski K., “Wacław Sierpiński 1882–1969”, Nauka Polska, 17:6 (1969), 163–172 | MR

[20] Landau E., Vorlesungen über Zahlentheorie, in 3 Bd, v. 2, Aus der analytischen und geometrischen Zahlentheorie, S. Hurzel, Leipzig, 1927, 183–188

[21] Lebesgue H., “À propos d'une nouvelle revue mathématique: “Fundamenta mathematicae””, Bulletin des Sciences Mathématiques. Ser. 2, 46:1 (1922), 35–48

[22] Marczewski E., “O pracach Wacława Sierpińskiego”, Wiadomości Matematyczne, 14 (1972), 65–72 | MR | Zbl

[23] Schinzel A., “Życiorys Wacława Sierpińskiego”, Wiadomości Matematyczne, 12 (1971), 303–308 | Zbl

[24] Schinzel A., “Wacław Sierpiński's papers on the theory of numbers”, Acta Arithmetica, 21:1 (1972), 7–13 | DOI | MR | Zbl

[25] Sierpiński W., Oeuvres choisies, 1–3, v. 1, PWN, Warszawa, 1975 ; v. 2, 1975; v. 3, 1976 | MR | Zbl | Zbl

[26] Sierpiński W., Teoria mnogości, Kółko matem.-fiz. Uczniów Uniw. Jana Kazimierza, Lwów, 1910

[27] Sierpiński W., “Sur une série de polynomes qui, ordonnée convenablement, peut représenter une fonction continue quelconque”, Biuletyn Polskiej Akademii Umiejȩtnosci. Kraków, 1912, 33–43

[28] Sierpiński W., “Sur une série de polynomes qui, ordonnée convenablement, peut représenter une fonction continue quelconque”, Biuletyn Polskiej Akademii Umiejȩtnosci. Kraków, 1912, 33–43

[29] Sierpiński W., “O powierzchni, na której każdy łuk jest nieskończenie długi”, Sprawozdania z posiedzen Towarzystva Naukowego Warszawskiego, 6:3 (1913), 353–356

[30] Sierpiński W., “O krzywych wypełniających kwadrat”, Prace Matematyczno-Fizyczne, 25 (1912), 193–219

[31] Sierpiński W., “Sur une courbe non quarrable”, Biuletyn Polskiej Akademii Umiejȩtnosci, Kraków, 1913, 254–265

[32] Sierpiński W., Teoria miary Lebesgue'a, Kółko matem.-fiz. uczniow Uniw. Jana Kazimierza, Lwów, 1914

[33] Sierpiński W., “Sur deux problèmes de la théorie des fonctions non dérivables”, Biuletyn Polskiej Akademii Umiejȩtności. Kraków, 1914, 162–182

[34] Sierpiński W., “Démonstration élémentaire d'un théorème de M. Borel sur les nombres absolument normaux et détermination effective d'un tel nombre”, Bulletin de la Societe Mathematique de France, 45 (1917), 125–132 | DOI | MR

[35] Sierpiński W., “Sur quelques problèmes qui impliquent des fonctions non mesurables”, Comptes rendus hebdomadaires des seances de l'Academie des sciences, 164 (1917), 882–884

[36] Sierpiński W., “Sur une extension de la notion de densité des ensembles”, Comptes rendus hebdomadaires des seances de l'Academie des sciences, 164 (1917), 995–994

[37] Sierpiński W., “Pewne twierdzenie o kontynuach”, Wiadomości Matematyczne, 23 (1919), 181–186

[38] Sierpiński W., “Sur une conséquence du petit théorème de Fermat”, Bull. Int. Acad. Polon. Sci. Cracovie. A, 1920, 103–104

[39] Sierpiński W., “Sur un ensemble fermé conduisant à un ensemble non mesurable V”, Fundamenta Mathematicae, 7 (1925), 198–202 | DOI

[40] Sierpiński W., Hypothése du continu, Monografie matematyczne, 4, z subwencji Funduszu Kultury Narodowey, Warszawa–Lwów, 1934

[41] Sierpiński W., Cardinal and ordinal numbers, PWN, Warszawa, 1958 | MR

[42] Sierpiński W., “Sur un problème concernant les nombres $k2^n+1$”, Elem. Math., 15 (1960), 73–74 ; Corrigendum, 17 (1962), 85 | MR | Zbl

[43] Solovay R. M., A model of set theory in which every set is Lebesgue measurable, Annals of Mathematics Studies, Princeton University, New Jersey | MR