# James Ax

James Burton Ax ( * 1937, † 2006) was an American mathematician who worked on number theory, logic, algebra, mathematical physics and financial mathematics and was the founder of a hedge fund.

Ax went to the Peter Stuyvesant High School in New York City and the Brooklyn Polytechnic University. In 1961 he received his doctorate at Berkeley to Gerhard Hochschild (The intersection of norm groups). After a year as an instructor at Stanford University, he became an Assistant Professor at Cornell University. 1965/66 he was a Guggenheim Fellow at Harvard. In 1967 he was associate professor at Cornell and in 1969 Professor (as at that time the youngest in the history of the university). In the same year he was recruited by James Simons at the State University of New York at Stony Brook, where he remained until his retirement in 1977.

In 1967 he was awarded with Simon Cook ( Princeton University), the Cole Prize for number theory for the Ax -Cooking- theorem on the solvability of polynomials in the p-adic numbers ( Diophantine problem over local fields 1-3, American Journal of Mathematics Bd.87, 1965, S.605, 631, Annals of Mathematics, Vol 83, 1966, S.437 ). The unusual proof was on the use of methods from mathematical logic and model theory (Ultra Products ). The theorem states that the degree in at least variables at least one zero in the - adic numbers, each non-constant homogeneous polynomial, except for a finite number " of exceptional primes ". 1968 proved Ax the decidability of the elementary theory of finite fields (The elementary theory of finite fields, Annals of Mathematics Bd.88 ).

In the 1970s he devoted himself to the fundamentals of physics, including an axiomatization of space-time and the group-theoretical properties of the axioms of quantum mechanics. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Transcendence and differential algebraic geometry ).

In the 1980s, he developed financial mathematical algorithms and founded a hedge fund company Axcom. Later it was acquired by Renaissance Technologies Corporation by James Simons and called Medallion Fund ( in memory of the Cole Prize for Ax and the Oswald Veblen Prize for Simons), who was his time leader in the mathematical modeling of trade in financial products.

In the early 1990s Ax withdrew and went to San Diego in California, where he studied further on the foundations of quantum mechanics and also attended writing classes at the University (2005, he completed a thriller screenplay "bots").