In 1939 he graduated from secondary school in the city of Aleysk of the Altai Territory and in the same year entered Tomsk University.
After the first year, he transferred to the correspondence ("distance education" or "learning by mail") department and worked as a mathematics teacher in Aleysk.
Beginning in 1946 A. I. Shirshov worked at the Stanichno-Luhansk secondary school in the Luhansk Oblast and studied in the correspondence department of Voroshilovgrad Pedagogical Institute, graduating there in 1949.
[5] From 1960 until his death A. I. Shirshov worked at the Sobolev Institute of Mathematics, while being a professor at Novosibirsk State University.
Anatoly Shirshov was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groups and projective planes.