[4] He had over the years more than 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Mikhail Kapranov, Vyacheslav Shokurov, Ralph Kaufmann, Victor Kolyvagin, Alexander A. Voronov, and Hà Huy Khoái.

[2] Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations.

[8][9] Manin pioneered the field of arithmetic topology (along with John Tate, David Mumford, Michael Artin, and Barry Mazur).

[10] He also formulated the Manin conjecture, which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties.

[11] In mathematical physics, Manin wrote on Yang–Mills theory, quantum information, and mirror symmetry.