BERNAYS, PAUL

born Oct. 17, 1888, London, Eng. died 1977, Zrich, Switz. in full Paul Isaak Bernays Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. After obtaining his doctorate from the University of Gttingen (1912), Bernays taught at the University of Zrich (191217), the University of Gttingen (191733), and the Swiss Federal Institute of Technology in Zrich (193459). It was at Gttingen that he formed his association with the prominent mathematician David Hilbert, who was his teacher, mentor, and collaborator. They wrote what is regarded as a classic work on mathematics, Grundlagen der Mathematik, 2 vol. (193439; reissued 196870; Foundations of Mathematics), based on Hilbert's earlier version. In 1956 Bernays revised a work of Hilbert's, Grundlagen der Geometrie (1899; The Foundations of Geometry), which went through several editions. Influenced by Hilbert's belief that the entire underlying structure of mathematics could be brought together into a single coherent entity, Bernays delved into the realm of set theory, trying to develop a set of axioms on which such a unifying system could be based. He wrote a series of articles under the title A System of Axiomatic Set Theory (published in the Journal of Symbolic Logic, 193754), from which the principal theses were published as Axiomatic Set Theory (1958). Here he simplified and organized the work of the logician John von Neumann on logic and set theory; these modifications would be further developed by the mathematician Kurt Gdel.