James Ax
Encyclopedia
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 Ph.D.
from the University of California, Berkeley
in 1961 under the direction of Gerhard Hochschild
, with a dissertation on The Intersection of Norm Groups. After one year at Stanford University, he joined the mathematics faculty at Cornell University
. In 1969, he moved to the mathematics department at Stony Brook University and remained on the faculty until 1977. In the 1980s, he and James Simons
founded a quantitative finance firm, Axcom Trading Advisors
, which was later acquired by Renaissance Technologies
and renamed the Medallion Fund. The latter fund was named after the Cole Prize
won by James Ax and the Veblen Prize
won by James Simons
.
The Ax Library in the Department of Mathematics at the University of California, San Diego
houses his mathematical books.
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and 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...
by using model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
. He shared 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...
with Simon B. Kochen
Simon B. Kochen
Simon Bernhard Kochen is an American mathematician, working in the fields of model theory, number theory and quantum mechanics....
, which was awarded 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...
.
James Ax earned his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
in 1961 under the direction of Gerhard Hochschild
Gerhard Hochschild
Gerhard Paul Hochschild was an American mathematician who worked on Lie groups, algebraic groups, homological algebra and algebraic number theory....
, with a dissertation on The Intersection of Norm Groups. After one year at Stanford University, he joined the mathematics faculty at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
. In 1969, he moved to the mathematics department at Stony Brook University and remained on the faculty until 1977. In the 1980s, he and James Simons
James Harris Simons
James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over $15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...
founded a quantitative finance firm, Axcom Trading Advisors
Axcom Trading Advisors
Axcom Trading Advisors was an early alternative investment management company founded by Elwyn Berlekamp and based in Berkeley, CA. It was acquired by Renaissance Technologies Corp in 1992, whereafter its investment instruments were either subsumed into Renaissance's flagship Medallion Fund. The...
, which was later acquired by Renaissance Technologies
Renaissance Technologies
Renaissance Technologies is a hedge fund management company of about 275 employees and more than $ billion in assets under management in three funds...
and renamed the Medallion Fund. The latter fund was named after the Cole Prize
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...
won by James Ax and the Veblen Prize
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
won by James Simons
James Harris Simons
James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over $15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...
.
The Ax Library in the Department of Mathematics at the University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
houses his mathematical books.
See also
- Ax-Grothendieck theoremAx-Grothendieck theoremIn mathematics, the Ax–Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck....
- Ax-Kochen theorem
- Leopoldt's conjectureLeopoldt's conjectureIn algebraic number theory, Leopoldt's conjecture, introduced by , states that p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual...
- Schanuel's conjectureSchanuel's conjectureIn mathematics, specifically transcendence theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions of the rational numbers.-Statement:The conjecture is as follows:...
External links
- James B. Ax Library - at UCSDUniversity of California, San DiegoThe University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
.