At
Moscow State University he received his undergraduate degree and in 1967 his Russian
Candidate of Sciences degree (PhD). His dissertation К проблеме тождества в конечно-определённых группах и полугруппах (On the identity problem in finitely-presented groups and semigroups) was supervised by
Andrey Markov Jr. and
Sergei Adian. Makanin spent his career (since 1966) working at the Steklov Institute of Mathematics (since 2013 as a freelance employee). From the Steklov Institute of Mathematics he received in 1977 his Russian
Doctor of Sciences degree (similar to
habilitation) with dissertation Проблема разрешимости уравнений в свободной полугруппе (The problem of solvability of equations in a free semigroup). On the basis of his 1977 dissertation he was an invited speaker at the 1978
International Congress of Mathematicians in Helsinki. He gained international recognition for his research on combinatorial group theory and algorithmic problems in the theory of semigroups.
Zlil Sela,
Eliyahu Rips, and others have made important applications of Makanin-Razborov diagrams to
geometric group theory. In 1982 Makanin published a complete solution (an algorithm with proof of validity) to the problem of recognizing the solvability of equations in a free group. An English translation was published in 1983. In 1984 (followed by English translation in 1985) he published a proof, using techniques similar to those in his 1982 paper, of the decidability, for any free group, of two different formal theories generated by that free group. ==Remarks on Makanin's research==