Paul Bernays

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Paul Bernays (left) in conversation

Paul Bernays ([ ˈbɛɐˌnaɪs ]; born October 17, 1888 in London , † September 18, 1977 in Zurich ) was a mathematician and logician .


Paul Bernays, 1914

He came from a German-Jewish family of scholars and was a citizen of the city of Zurich . From London via Paris , Paul Bernays came to Berlin at the age of seven , where he passed the Abitur in 1907 at the Kölln Gymnasium and, in the conflict between his strong musical inclination and his interest in mathematics, decided to study the latter: first in Berlin at the TH , then at the university and from 1909 in Göttingen . In addition to his studies, which he completed in 1912 with a dissertation with Edmund Landau , he was intensely involved in the circle of the philosopher Leonard Nelson , the New Fries School , to which he - also as a member of the Jakob-Friedrich, founded by Nelson in 1912/13 Fries Society and the Society of Friends of the Philosophical-Political Academy , which was established after the First World War , remained connected throughout life.

From 1912 to 1917 he was a private lecturer in Zurich , returned to Göttingen in 1919 at the request of David Hilbert , where he became a private lecturer and in 1922 an associate professor. As a Jew, he lost his job in Göttingen in 1933 and then returned to Zurich.

From 1945 to 1958 he was a professor at the ETH Zurich . In 1947 he founded the philosophical journal Dialectica together with Gaston Bachelard and Ferdinand Gonseth .


Bernays developed David Hilbert's theory of proof further, with whom he published the work on the fundamentals of mathematics , which he wrote for the most part alone . After that he presented work on axiomatic set theory for years. His set theory with classes formed an essential basis for the later Neumann-Bernays-Gödel set theory .

He edited the Collected Writings of Leonard Nelson .


  • David Hilbert and Paul Bernays: Fundamentals of Mathematics I – II, Basic Teachings of Mathematical Sciences 40, 50, Berlin: Springer, 1934/1939
  • Paul Bernays: A System of Axiomatic Set Theory I-VII , in: Journal of Symbolic Logic, Part I in Volume 2 (1937), pp. 65-77; Part II in Volume 6 (1941), pp. 1-17, Part III in Volume 7 (1942), pp. 65ff, Part IV in Volume 7 (1942), pp. 133ff, Part V in Volume 8 (1943), p 89ff, Part VI in Volume 13 (1948), p. 65ff, Part VII in Volume 19 (1954), p. 81ff. Complete edition in: Sets and classes, on the work of Paul Bernays , editor Gert H. Müller, Amsterdam, New York, Oxford, 1976. pp. 1–119
  • Paul Bernays: Axiomatic Set Theory , Amsterdam 1958
  • Treatises on the Philosophy of Mathematics. , Darmstadt 1976


  • Gert H. Müller (editor): Sets and Classes. On the Work of Paul Bernays , North Holland, Amsterdam 1976 (with a short biography of GH Müller and a list of publications)
  • GH Müller Paul Bernays . In: Mathematical Intelligencer 1 (1978), pp. 27-28
  • H. Lauener Paul Bernays . In: Zeitschrift für Allgemeine Wissenschaftstheorie 9 (1978), pp. 13-20
  • E. Engeler On the logical work of Paul Bernays . In: Dialectica 32 (1978), pp. 191-200
  • Ernst Specker Paul Bernays . In: Logic Colloquium '78. Proceedings of the Colloquium held in Mons, August 1978 , edited by M. Boffa, D. van Dalen, K. McAloon, Amsterdam: North Holland 1979 (Studies in Logic and the Foundations of Mathematics; 97), pp.381-389
  • Akihiro Kanamori Paul Bernays and Set Theory . In: Bulletin of Symbolic Logic 15 (2009), 1 (March), pp.43-69
  • Thomas Fuchs: Bernays, Paul. In: Historical Lexicon of Switzerland .

Web links

Individual evidence

  1. ^ Leonard Nelson: Collected writings. Edited by Paul Bernays, Willi Eichler , Arnold Gysin, Gustav Heckmann , Grete Henry-Hermann , Fritz von Hippel, Stephan Körner, Gerhard Weisser, Werner Kroebel . Felix Meiner Verlag, Hamburg 1970–1977