Paul Bernays


Paul Bernays
Paul Bernays
Born 17 October 1888(1888-10-17)
London
Died 18 September 1977(1977-09-18) (aged 88)
Zurich
Nationality Swiss
Fields mathematics
Alma mater University of Berlin
Doctoral advisor Edmund Landau
Doctoral students Haskell Curry
Known for mathematical logic
axiomatic set theory
philosophy of mathematics
Influences Issai Schur, Edmund Landau

Paul Isaac Bernays (17 October 1888 London – 18 September 1977 Zurich) was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.

Contents

Biography

Bernays spent his childhood in Berlin. Bernays attended the Köllner Gymnasium, 1895-1907. At the University of Berlin, he studied mathematics under Issai Schur, Edmund Landau, Ferdinand Georg Frobenius, and Friedrich Schottky; philosophy under Alois Riehl, Carl Stumpf and Ernst Cassirer; and physics under Max Planck. At the University of Göttingen, he studied mathematics under David Hilbert, Edmund Landau, Hermann Weyl, and Felix Klein; physics under Voigt and Max Born; and philosophy under Leonard Nelson.

In 1912, the University of Berlin awarded him a Ph.D. in mathematics, for a thesis, supervised by Landau, on the analytic number theory of binary quadratic forms. That same year, the University of Zurich awarded him the Habilitation for a thesis on function theory and Picard's theorem. The examiner was Ernst Zermelo. Bernays was Privatdozent at the University of Zurich, 1912-17, where he came to know George Pólya.

Starting in 1917, David Hilbert employed Bernays to assist him with his investigations of the foundations of arithmetic. Bernays also lectured on other areas of mathematics at the University of Göttingen. In 1919, that university awarded him a second Habilitation, for a thesis on the axiomatics of the propositional calculus of Principia Mathematica.

In 1922, Göttingen appointed Bernays extraordinary professor without tenure. His most successful student there was Gerhard Gentzen. In 1933, he was dismissed from this post because of his Jewish ancestry. After working privately for Hilbert for six months, Bernays and his family moved to Switzerland, whose nationality he had inherited from his father, and where the ETH employed him on occasion. He also visited the Institute for Advanced Study in Princeton, USA, and the University of Pennsylvania.

Mathematical work

Bernays's collaboration with Hilbert culminated in the two volume work Grundlagen der Mathematik by Hilbert and Bernays (1934, 1939), discussed in Sieg and Ravaglia (2005). In seven papers, published between 1937 and 1954 in the Journal of Symbolic Logic, republished in (Müller 1976), Bernays set out an axiomatic set theory whose starting point was a related theory John von Neumann had set out in the 1920s. Von Neumann's theory took the notion of function as primitive; Bernays recast Von Neumann's theory so that sets and proper classes were primitive. Bernays's theory, with some modifications by Kurt Gödel, is now known as the Von Neumann–Bernays–Gödel set theory.

Publications

References

External links


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Paul Bernays — (* 17. Oktober 1888 in London; † 18. September 1977 in Zürich) war ein Mathematiker und Logiker. Paul Bernays (links) im Gespräch Inhaltsverzeichnis …   Deutsch Wikipedia

  • Paul Bernays — (à gauche) Paul Bernays né le 17 octobre 1888 à Londres et mort le 18 septembre 1977 à Zurich, est un mathématicien suisse qui a joué un rôle crucial dans le développement de la logique mathématique …   Wikipédia en Français

  • BERNAYS — BERNAYS, family originating in Germany with branches elsewhere in Central Europe and the U.S. ISAAC BEN JACOB BERNAYS (1792–1849), rabbi of Hamburg, Germany, was born in Mainz, studied at Wuerzburg University and at the yeshivah of Abraham Bing… …   Encyclopedia of Judaism

  • Bernays — ist der Familienname folgender Personen: Chacham Isaak Bernays, (1792–1849) Oberrabbiner der Deutsch Israelitischen Gemeinde in Hamburg, Vorreiter der modernen Orthodoxie Edward Bernays (1891–1995), Public Relations Forscher, Urenkel von Isaak… …   Deutsch Wikipedia

  • Bernays — is a surname and may refer to:* Isaac Bernays (1792 1840), a German rabbi, and father of: ** Jakob Bernays (1824 1881), a German classical linguist ** Michael Bernays (1834 1897), a German literature historian * Edward Bernays (1891 1995), the… …   Wikipedia

  • Paul Lorenzen — 1967 Paul Lorenzen[1] (* 24. März 1915 in Kiel; † 1. Oktober 1994 in Göttingen) war ein deutscher Philosoph, Wissenschaftstheoretiker, Mathematiker und …   Deutsch Wikipedia

  • Paul F. Linke — Paul Ferdinand Linke (* 15. März 1876 in Magdeburg; † 19. Juni 1955 in Brannenburg am Inn[1]) war ein deutscher Phänomenologe, welcher in der Strömung der Gegenstandsphänomenologie[2] und am Übergang von Phänomenologie und analytischer… …   Deutsch Wikipedia

  • Bernays —  Cette page d’homonymie répertorie des personnes (réelles ou fictives) partageant un même patronyme. Paul Bernays (17 octobre 1888 – 18 septembre 1977), mathématicien suisse ; Edward Bernays (22 novembre 1891 – 9 mars 1995), considéré… …   Wikipédia en Français

  • Bernays–Schönfinkel class — The Bernays–Schönfinkel class of formulas, named after Paul Bernays and Moses Schönfinkel, is a decidable fragment of first order logic formulas.It corresponds to formulas which, when written in prenex normal form, have an exists^*forall^*… …   Wikipedia

  • Paul Heyse — Paul Heyse, ca. 1860 Heyse Portrait von …   Deutsch Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.