From 1969 until 1974, he was a student in the Faculty of Mechanics and Mathematics at Moscow State University (MSU) under joint supervision of Dmitry Fuchs and Israel Gelfand.
Feigin was not accepted to the graduate school of MSU due to increasingly anti-semitic policies at that institution at that time.
After working as a computer programmer in industry for some time, he was accepted in 1976 to the graduate school of Yaroslavl State University and defended his thesis "Cohomology of current Lie algebras on smooth manifolds" in 1981 at Steklov Institute in Leningrad.
Boris Feigin is a professor at the Independent University of Moscow and a senior research fellow at Landau Institute for Theoretical Physics since 1992.
[4] In 2023, Feigin immigrated to Israel and joined the faculty of the Hebrew University of Jerusalem.