Simon B. Kochen
Encyclopedia
Simon Bernhard Kochen is an American
mathematician
, working in the fields of model theory
, number theory
and quantum mechanics
.
Kochen received his Ph.D. (Ultrafiltered Products and Arithmetical Extensions) from Princeton University
in 1958 under the direction of Alonzo Church
. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department 1989-92 and became the Henry Burchard Fine Professor in mathematics in 1994. During 1966-7 and 1978-9, Kochen was at the Institute for Advanced Study
.
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
from involving p-adic techniques.
In 1967 Kochen and Ernst Specker
proved the Kochen–Specker theorem in quantum mechanics. In 2004 Kochen and John Horton Conway
proved the free will theorem
. The theorem states that if we have a certain amount of free will
, then, subject to certain assumptions, so must some elementary particles.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working in the fields of model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
Kochen received his Ph.D. (Ultrafiltered Products and Arithmetical Extensions) from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1958 under the direction of Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department 1989-92 and became the Henry Burchard Fine Professor in mathematics in 1994. During 1966-7 and 1978-9, Kochen was at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
.
In 1967 he was awarded, together with James Ax
James Ax
James Burton Ax was a mathematician who proved several results in algebra and number theory by using model theory. He shared the seventh Frank Nelson Cole Prize in Number Theory with Simon B. Kochen, which was awarded for a series of three joint papers on Diophantine problems.James Ax earned his...
, the seventh Frank Nelson Cole Prize in Number Theory
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
for a series of three joint papers on Diophantine problems
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
from involving p-adic techniques.
In 1967 Kochen and Ernst Specker
Ernst Specker
Ernst P. Specker is a Swiss mathematician. Much of his most influential work has been on Quine’s New Foundations, a set theory with a universal set, but he is most famous for the Kochen–Specker theorem in quantum mechanics, showing that certain types of hidden variable theories are impossible...
proved the Kochen–Specker theorem in quantum mechanics. In 2004 Kochen and John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
proved the free will theorem
Free will theorem
The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.-Axioms:The proof of the theorem...
. The theorem states that if we have a certain amount of free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
, then, subject to certain assumptions, so must some elementary particles.