He completed his
Ph.D. in mathematics at the
Massachusetts Institute of Technology in 1954. His doctoral supervisor was
George W. Whitehead, and his doctoral dissertation was on
Finite Computability of the Homotopy Groups of Finite Groups. In 1962–63, he visited the
Institute for Advanced Study in
Princeton, New Jersey, and in 1964 he received the
Guggenheim Fellowship. He was elected a Fellow of the
American Academy of Arts and Sciences in 1974 and a Fellow of the
American Mathematical Society in 2012. He died on December 22, 2021, just before his 95th birthday, as a Professor Emeritus of Mathematics at Brandeis University. ==Contributions to mathematics==