He worked at the Moscow Higher Technical College from 1928 until 1930, and then from 1930 to 1939 at Azerbaijan University, where was the chair of algebra and function theory and then dean of physics and mathematics.

[1] During this period, Buchstab also did graduate studies at Moscow State under the supervision of Aleksandr Khinchin.

He defended his candidacy in 1939,[1][5] and at that time was appointed to a professorship at the Moscow State Pedagogical University.

During World War II he taught at the Azerbaijan State University and Dzerzhinskii Higher Naval Engineering College, returning to Moscow in 1943 and defending a doctorate from the Steklov Institute of Mathematics in 1944.

[1] He remained at the Moscow State Pedagogical University for the rest of his career,[1] where his students included Gregory Freiman and Ilya Piatetski-Shapiro.