Paul Bernays Swiss mathematician Date of Birth: 17.10.1888 Country: Switzerland

1. Paul Bernays
2. Early Life and Education
3. Academic Career
4. Nazi Persecution and Relocation
5. Collaboration with Hilbert
6. Axiomatization of Set Theory

Paul Bernays

Paul Bernays, a Swiss mathematician, made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. As a close friend and long-time collaborator of David Hilbert, Bernays played a crucial role in shaping the foundations of mathematics.

Early Life and Education

Bernays was born into a Swiss Jewish family in London, but his family soon relocated to Berlin and later Cologne, where he attended gymnasium from 1895 to 1907. Initially torn between music and mathematics, Bernays ultimately chose mathematics and pursued his studies at the University of Berlin. There, he studied under renowned mathematicians such as Edmund Landau, Issai Schur, and Ferdinand Frobenius. After two years in Berlin, Bernays moved to Göttingen, where he attended lectures by David Hilbert, Felix Klein, and Hermann Weyl.

Academic Career

In 1912, Bernays returned to Berlin University, completing his dissertation in analytic number theory under the supervision of Edmund Landau. He completed his Habilitation (qualification to teach) at the University of Zurich under Ernst Zermelo in the same year and became a lecturer at the university.

In 1917, Bernays accepted an invitation from David Hilbert to become his assistant in Göttingen. Together, they delved into the foundations of mathematics, which became the focus of Bernays' doctoral dissertation (1919). He subsequently became an extraordinary professor at the University of Göttingen.

Nazi Persecution and Relocation

With the rise of the Nazis in Germany, Bernays was dismissed from his position and returned to Switzerland. He worked at the Polytechnic Institute in Zurich, becoming a professor in 1945. Between 1935 and 1936, Bernays also worked at the Institute for Advanced Study in Princeton, USA.

Collaboration with Hilbert

Bernays' collaboration with Hilbert continued, and together they published the monumental two-volume monograph "Grundlagen der Mathematik" ("Foundations of Mathematics") from 1934 to 1939. After Hilbert's death, Bernays published a second edition of the work in 1968, incorporating his own findings.

Axiomatization of Set Theory

Bernays also made significant contributions to the axiomatization of set theory, co-authoring the "von Neumann–Bernays–Gödel axiomatization." Additionally, he co-founded the philosophical journal "Dialectica" in 1947.