He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers[2][3][4] on Diophantine problems.
He 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.
In 1969, he was recruited by his Berkeley classmate Jim Simons to move from Cornell to the mathematics department at Stony Brook University.
[7] In the 1970s, he worked on the fundamentals of physics, including an axiomatization of space-time and the group theoretical properties of the axioms of quantum mechanics.
In the 1980s, he and Simons founded the quantitative finance firm Axcom Trading Advisors,[8][9] which was later acquired by Renaissance Technologies and renamed the Medallion Fund.