1994 Nemmers Prize in Mathematics Recipient

Yuri I. Manin

For fundamentally contributing to diverse branches of mathematics like algebraic geometry, number theory, and mathematical physics, solving major problems and developing techniques opening new avenues of research

Yuri I. Manin is a scientific member of the Max Planck Institute for Mathematics, Bonn, Germany, and Steklov Mathematical Institute, Moscow, Russia.

Manin is widely regarded as one of the outstanding mathematicians of the 20th century and his work spans such diverse branches of mathematics as algebraic geometry, number theory, and mathematical physics.

He enriched these fields by numerous fundamental contributions, including the solution of major problems and the development of techniques that opened new avenues of research.

In his 1963 proof of the Mordell conjecture for function fields, Manin introduced what is now known as Gauss-Manin connection, an indispensable tool in modern algebraic geometry in its own right. In 1971, Manin (with Iskovskih) found counter-examples to the longstanding problem of Luroth concerning rational uniformization of algebraic manifolds.

Manin's work in number theory, especially in p-adic analysis and theory modular forms, drew intuition from geometry and used "continuous" techniques to attack fundamental arithemetic problems. His study of Diophantine equations led to the discovery of new asymptotic properties of their solutions and a new obstruction for their solvability (Brauer-Manin obstruction).

Among Manin's many contributions to mathematical physics is the classification of instantons, the solutions of field equations describing microscopic quantum fluctuations of the vacuum. His 1978 work on this problem (with Drinfiled), besides being of fundamental importance in physics, laid the foundation for the recent progress in the purely mathematical study of 4-mainfolds. He has also done important work on Hamiltonian structure of completely integrable wave equations, construction of algebro-geometric solutions of Yang-Mills-Dirac equations, string theory, and quantum groups.

A native of Simferopol, Russia, Manin received a bachelor's degree from Moscow State University in 1958 and a Ph.D. from the Steklov V.A. Institute of Mathematics in Moscow in 1960. He held a chair in mathematics at Moscow State University from 1965-1991.

Manin was a visiting professor at several universities, including Harvard University, Massachusetts Institute of Technology, and Columbia University from 1991-1993, when he became co-director of the Max Planck Institute for Mathematics. He is also the author or co-author of ten monographs and more than 150 papers.

Manin has been the recipient of numerous awards, including the Brouwer Gold Medal in 1987 for his work in number theory and a Lenin Prize in 1967 for work in algebraic geometry. He is a corresponding member of the Russian Academy of Sciences, a foreign member of the Royal Netherlands Academy of Arts and Sciences, and a member of Academia Europaea.