Buchstab was born in
Stavropol; his father was a physician. He studied at the Rostov Polytechnic Institute and
Rostov University before moving to the
faculty of mechanics and mathematics at
Moscow State University, where he earned a degree in 1928. 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. 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. He remained at the Moscow State Pedagogical University for the rest of his career, where his students included
Gregory Freiman and
Ilya Piatetski-Shapiro. ==Selected publications==