Paul Bernays Biography
Paul Isaac Bernays was a famous Swiss mathematician who made noteworthy contributions to the philosophy of mathematics and developed a new discipline of mathematical logic. Foremost among his work was the proof theory and the axiomatic set theory. Born in London, he grew up in Paris and Berlin. As a child, he showed a keen interest in music as well as ancient languages and mathematics. In college, he majored in mathematics and also studied philosophy and theoretical physics as additional subjects. At the age of 24, he received his doctoral degree in mathematics from the University of Berlin. He also obtained his Habilitation from the University of Zurich and became a Privatdozent there. Soon, he joined David Hilbert as his research assistant in investigating the foundations of arithmetic. Eventually, he was awarded the Venia Legendi at the University of G¨ottingen but lost the post during Second World War due to his Jewish ancestry. He finally moved to Switzerland where he taught at the Eidgen¨ossische Technische Hochschule, Z¨urich. He is best remembered for his joint two volume work ‘Grundlagen der Mathematik’ (1934-39) with Hilbert, and his Axiomatic Set Theory which was published in 1958.
- 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.
- 1922 onwards, he became extraordinary professor without tenure at Gottingen. He also attended the lectures of, among others, Emmy Noether, van der Waerden and Herglotz, preferring to learn by listening rather than reading.
- In 1933, he lost the Venia Legendi post at the University of Gottingen because of his Jewish ancestry. Hilbert hired him privately as his assistant for six months. Later, the family shifted to Switzerland.
- In 1934, and several times later, he was employed at Eidgen¨ossische Technische Hochschule (ETH), Z¨urich in a provisional teaching position. In 1935-36, he gave lectures on mathematical logic and axiomatic set theory at the Institute for Advanced Study, Princeton.
- In 1939, he received the Venia Legendi at the ETH and in 1945, he became extraordinary professor. He gave lectures on algebraic number fields, set theory, elliptic functions, geometrical constructions, the concept of number, elements of analysis, mathematical logic, the introduction of proof theory, lattice theory, the constitution of the continuum, etc.
- He also continued to attend lectures and seminars given by intellectual colleagues and friends like Michel Plancheret, Beno Eckmann, Eduard Stiefel and Heinz Hopf.
- He became acquainted with Ferdinand Gonseth and realized a similarity in viewpoint with him. Hence, he participated in several of Gonseth’s conferences and joined the editorial board of ‘Dialectica’.
- He later became a member of the International Society for the Philosophy of Science, founded by Pere S. Dockx. He became its President for two years. From 1956t o 1965, he was invited thrice as visiting professor to the University of Pennsylvania, Philadelphia.
- 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.
- 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.
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