Simon Bernhard Kochen (; born 14 August 1934, Antwerp) is a

Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, working in the fields of model theory,

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

and

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...

Biography

Kochen received his Ph.D. (''Ultrafiltered Products and Arithmetical Extensions'') from

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

in 1958 under the direction of

Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...

. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department from 1989 to 1992 and became the Henry Burchard Fine Professor in mathematics in 1994.Princeton Philosophy Department bio
/ref> During 1966–1967 and 1978–1979, Kochen was at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

. In 1967 he was awarded, together with James Ax, the seventh Frank Nelson Cole Prize in Number Theory for a series of three joint papers on Diophantine problems involving p-adic techniques. Kochen and Ax also co-authored the

Ax–Kochen theorem The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer ''d'' there is a finite set ''Yd'' of prime numbers, such that if ''p'' is any prime not in ''Yd'' then every homogeneous polynomial of degree ...

, an application of model theory to

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

. In 1967 Kochen and

Ernst Specker Ernst Paul Specker (11 February 1920, Zurich – 10 December 2011, Zurich) was a Swiss mathematician. Much of his most influential work was on Quine's New Foundations, a set theory with a universal set, but he is most famous for the Kochen ...

proved the

Kochen–Specker theorem In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on th ...

in quantum mechanics and quantum contextuality.Kochen, Specker: ''The problem of hidden variables in quantum mechanics.'' Journal of Mathematics and Mechanics, volume 17, 1967, pages 59–88 In 2004 Kochen and

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...

proved the

free will theorem The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen ...

. The theorem states that if we have a certain amount of

free will Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to ac ...

, then, subject to certain assumptions, so must some

elementary particles In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, anti ...

References

External links

* {{DEFAULTSORT:Kochen, Simon B. Living people Model theorists 1934 births Scientists from Antwerp Institute for Advanced Study visiting scholars

Biography

See also

References

External links