Manin was until 1991 professor at the University of Moscow, and has since 1993 been at the
Max Planck Institut für Mathematik in Bonn, the last years as its director.
Manin has an extensive scientific production, with many deep and fundamental results,
and spanning a large part of mathematics, from algebraic and arithmetic geometry – diophantine equations,
p-adic analysis, modular forms – to the study of solutions of Yang–Mills equations and
their connection with 4-dimensional manifolds.
He has been central to the development of the theory of quantum groups,
quantum cohomology, and mirror symmetry that has taken place in the last decade,
and which represents a transition area between mathematics and mathematical physics.
