James Ax

James Burton Ax (born January 10, 1937 , † June 11, 2006 ) was an American mathematician who studied number theory , logic , algebra , mathematical physics and financial mathematics and founded a hedge fund .

Ax went to Peter Stuyvesant High School in New York City and Brooklyn Polytechnic University . In 1961 he received his doctorate in Berkeley with Gerhard Hochschild ( The intersection of norm groups ). After a year as an instructor at Stanford University , he became an assistant professor at Cornell University . In 1965/66 he was a Guggenheim Fellow at Harvard . In 1967 he became a Sloan Research Fellow and Associate Professor at Cornell and in 1969 a professor (at the time the youngest in the university's history). In the same year he was lured away by James Simons to the State University of New York at Stony Brook , where he stayed until his retirement in 1977. Most recently he lived in Marina del Rey .

In 1967 he received the Cole Prize for Number Theory for the Ax-Cooking Theorem on the solvability of polynomials in -adic numbers ( Diophantine Problems over local fields 1-3, American Journal of Mathematics Vol. 87, 1965 ) together with Simon Koch (Princeton University) , Pp. 605, 631, Annals of Mathematics, Vol. 83, 1966, p. 437). The unusual thing about the proof was the use of methods from mathematical logic and model theory ( ultra products ). The theorem says that every non-constant homogeneous polynomial of degree has at least one zero in the -adic numbers in at least variables , apart from a finite number of “exceptional prime numbers” . The theorem was conjectured by Emil Artin ( Guy Terjanian found a first counterexample for one of the exceptional prime numbers in 1966). Before Ax and Cooking, Serge Lang , among others, dealt with Artin's conjecture. 1968 proved Ax the decidability of the elementary theory of finite fields ( The elementary theory of finite fields , Annals of Mathematics Vol. 88). ${\ displaystyle p}$ ${\ displaystyle d}$ ${\ displaystyle d ^ {2} +1}$ ${\ displaystyle p}$ ${\ displaystyle p}$

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 the hedge fund company Axcom . This was later bought by Renaissance Technologies , a company founded by James Simons, and called the Medallion Fund (in memory of the Cole Prize for Ax and the Oswald Veblen Prize for Simons). The fund is now one of the most profitable in the world thanks to the mathematical modeling of trading in financial products.

In the early 1990s, Ax retired and went to San Diego , California , where he continued researching the fundamentals of quantum mechanics and also attended writing courses at university (in 2005 he completed a thriller screenplay "Bots").

Web links

Individual evidence

↑ Notices AMS, January 2008, p. 67

personal data
SURNAME	Ax, James
ALTERNATIVE NAMES	Ax, James Burton (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	January 10, 1937
DATE OF DEATH	June 11, 2006

[1] Notices AMS, January 2008, p. 67