Sweedler received his Ph.D. from the
Massachusetts Institute of Technology in 1965. His thesis,
Commutative Hopf Algebras with Antipode, was written under the direction of thesis advisor
Bertram Kostant. Sweedler wrote
Hopf Algebras (1969), which became the standard reference book on
Hopf algebras. He, with Harry P. Allen, used Hopf algebras to prove in 1969 a famous 25-year-old conjecture of Jacobson about the forms of generalized Witt algebras over algebraically closed fields of finite characteristic. From 1965 to the mid 1980s Sweeder worked on commutative algebra and related disciplines. Since the mid 1980s Sweedler has worked primarily on
computer algebra. His research resulted in his position as director of the
Army Center of Excellence for computer algebra. He was a Guggenheim Fellow for the academic year 1980–1981. With his wife Kristin, he helped establish the Sweedler Nature Preserve. ==Selected publications==