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Yuri Ivanovich Manin (; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
He received a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He became a professor at the Max-Planck-Institut für Mathematik in Bonn, where he was director from 1992 to 2005 and then director emeritus. He was also a Trustee Chair Professor at Northwestern University from 2002 to 2011.
He had over the years more than 50 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Mikhail Kapranov, Vyacheslav Shokurov, Ralph Kaufmann, Victor Kolyvagin, Alexander L. Rosenberg, Alexander A. Voronov, and Hà Huy Khoái.
Manin died on 7 January 2023 in Bonn.
He developed the Manin obstruction, indicating the role of the Brauer group in accounting for obstructions to the Hasse principle via Grothendieck's theory of global , setting off a generation of further work.
Manin pioneered the field of arithmetic topology (along with John Tate, David Mumford, Michael Artin, and Barry Mazur). He also formulated the Manin conjecture, which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties.
In mathematical physics, Manin wrote on Yang–Mills theory, quantum information, and mirror symmetry. He was one of the first to propose the idea of a quantum computer in 1980 with his book Computable and Uncomputable.
He wrote a book on and , showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra.Manin: Cubic forms – algebra, geometry, arithmetics, North Holland 1986
In 1990, he became a foreign member of the Royal Netherlands Academy of Arts and Sciences. He was a member of eight other academies of science and was also an honorary member of the London Mathematical Society.
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