Just before the end of his time there, he attended a five-day international meeting, the Arbeitstagung, where he sketched a proof of the Witten conjecture to the amazement of Michael Atiyah and other mathematicians and his invitation to the institute was subsequently extended to three years.

In 1992, Kontsevich was appointed to a full professorship in mathematics at the University of California, Berkeley, before moving in 1995 to France, where he joined the Institut des Hautes Études Scientifiques in Bures-sur-Yvette as a permanent member.

His work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry.

In 1998, he won the Fields Medal "for his contributions to algebraic geometry, topology, and mathematical physics, including the proof of Witten's conjecture of intersection numbers in moduli spaces of stable curves, construction of the universal Vassiliev invariant of knots, and formal quantization of Poisson manifolds.

"[5] In July 2012, he was an inaugural awardee of the Breakthrough Prize in Fundamental Physics, the creation of physicist and internet entrepreneur, Yuri Milner.