Image Credit

Maxim Kontsevich

for his pioneering works in algebra, geometry and mathematical physics and in particular deformation quantization, motivic integration and mirror symmetry.


Recently, some of the most profound advances in algebra and geometry have been inspired by ideas from physics. Maxim Kontsevich has led the way in a number of these developments.

Beginning with Heisenberg’s introduction of quantum mechanics, the mathematical process of quantization – that is, of passing from classical to quantum mechanics – has been a central theme. One version, known as deformation quantization, has for its natural setting classical spaces known as Poisson manifolds. Their exact quantization had been carried out in special cases, but in general this proved to be a formidable problem. It was resolved brilliantly by Kontsevich, who used ideas from quantum field theory.

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An Essay on the Prize

Traditionally the interaction between mathematics and theoretical physics has been concerned with topics ranging from dynamical systems and partial differential equations to differential geometry to probability theory. For the last two decades, modern algebra and algebraic geometry (which is the study of the solutions of systems of polynomial equations in several variables via algebraic methods) have taken a central position in this interaction.  Physical insights and intuition, especially from string theory, have led to a number of unexpected and striking predictions in both classical and modern algebraic geometry.  Thanks to the efforts of many mathematicians new techniques and theories have been developed and some of these conjectures have been proven.

Maxim Kontsevich has led the way in a number of these developments.  Among his many achievements is his early work on Witten’s conjecture concerning the topology and geometry of the moduli (that is parameter) spaces of all algebraic curves of a given genus, his solution of the problem of deformation quantization, his work in mirror symmetry and in a different direction the theory of motivic integration.

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About the Laureates
Maxim Kontsevich

Maxim Kontsevich was born in 1964 in Khimki, Russia and became a French citizen since 1999.  He is a Permanent Professor at l’Institut des Hautes Études Scientifiques, France and a holder of the AXA-IHÉS Chair for Mathematics.  In 1992 he received his PhD from the University of Bonn, Germany and during the period 1990 to 1993, he was a visitor at various institutes, including the Max Planck Institute, Harvard University and the Institute for Advanced Study, Princeton. He was appointed Professor at the University of California, Berkeley from 1993 to 1995 and has received many awards including the Henri Poincaré Prize in 1997, the Fields Medal in 1998 and the Crafoord Prize in 2008.  He is a member of the Academia Europaea and l’Institut de France.

Feature Story
The Shaw Prize Lecture in Mathematical Sciences 2012