Paul Bernays

Paul Bernays was of the Jewish faith and a citizen of Switzerland. He remained unmarried throughout his life and lived in Zürich with his mother and two unmarried sisters.

By nature, he was friendly and benevolent, helping several authors with their papers. He never passed judgement on others and always tried to see everything with positivity.

Even in his 80s, he remained active in research. He died of a heart condition on 18 September 1977, at the age of 88, in Zurich, Switzerland.

Paul Bernays was born on October 17, 1888 in London. He was the son of Julius Bernays, a Swiss businessman, and Sarah Brecher. He had a happy childhood growing up with a younger brother and three younger sisters.

From 1895 to 1907, he studied at the K¨ollnisches Gymnasium. He demonstrated a keen interest in music and became an immensely talented pianist. He later explored his talent in composing music as well.

He also studied at the Technische Hochschule Charlottenburg for about half a year. During his school life, he also enjoyed studying ancient languages and mathematics.

After school, he joined the University of Berlin where he studied for four semesters primarily under Issai Schtur, Landau, Frobenius, and Schottky in mathematics; Riehl, Stumpf, and Cassirer in philosophy, and Max Planck in physics.

Subsequently, he studied at Gottingen for six semesters, majoring in mathematics and studying philosophy and theoretical physics as additional subjects. He attended lectures on mathematics mainly by Hilbert, Landau, Weyl and Klein; on physics by Voigt and Born, and on philosophy chiefly by Leonard Nelson.

In 1912, Paul Bernays received his Ph.D. in mathematics from the University of Berlin. His doctoral dissertation on the analytic number theory of binary quadratic forms was completed under Landau.

Later that year, he obtained his Habilitation from the University of Zurich for a dissertation on complex analysis and Picard's theorem, completed under professor Zermelo.

He was a Privatdozent at the University of Z¨urich from 1912 to 1917. During this period, he became acquainted with Georg P´olya, Einstein, and Hermann Weyl.

In 1917, he was invited by Hilbert to assist him in his research of the foundations of arithmetic. The job took him back to Gottingen and he helped Hilbert in preparing lectures and notes.

Alongside, he also gave lectures on mathematics at the University of Gottingen, where he obtained the Venia Legendi in 1919.

Paul Bernays' partnership with Hilbert resulted in a two volume work, ‘Grundlagen der Mathematik’ (1934–1939). The work attempted to build mathematics from symbolic logic and a proof from it is now known as the Hilbert–Bernays paradox.

In seven papers published in the Journal of Symbolic Logic between 1937 and 1954, he embarked on the axiomatic set theory whose foundation was laid by John von Neumann in the 1920s. Bernays’ theory, with some alterations by Kurt Gödel later, came to be known as the Von Neumann–Bernays–Gödel set theory.

In 1956, he revised Hilbert’s ‘Grundlagen der Geometrie’ (1899) on the foundations of geometry. He believed that the whole structure of mathematics could be combined as a single logical entity.

Bernays research in proof theory and axiomatic set theory helped to produce a new discipline of mathematical logic. His axiomatic set theory was further developed by Kurt Gödel and is presently known as the Von Neumann–Bernays–Gödel set theory.