The spirit of the prize is focused on rewarding the results of research accessible to the greatest number of professional mathematicians within these fields. The Fermat prize was created in 1989 and is awarded once every two years in Toulouse by the Institut de Mathématiques de Toulouse. The amount of the Fermat prize has been fixed at 20,000 Euros for the twelfth edition.
1991 Awarded to Jean-Louis Colliot-Thélène for his work on number theory and rational manifolds the research for which was undertaken to a large extent with Jean-Jacques Sansuc.
1995 Awarded to Andrew Wiles for his works on the Taniyama–Shimura–Weil conjecture which resulted in the demonstration of the proof of Fermat's Last Theorem.
1997 Awarded to Michel Talagrand for his fundamental contributions in various domains of probability.
1999 Awarded jointly to Fabrice Béthuel and Frédéric Hélein for several important contributions to the theory of variational calculus, which have consequences in Physics and Geometry.
2001 Awarded jointly to Richard Taylor for his various contributions to the study of links between Galois representations and automorphic forms and to Wendelin Werner for his works on the intersection exponents of Brownian motion and their impact in theoretical Physics.
2005 Awarded jointly to Pierre Colmez for his contributions to the study of L-functions and p-adic Galois representations and to Jean-François Le Gall for his contributions to the fine analysis of planar Brownian motions, his invention of the Brownian snake and its applications to the study of non-linear partial differential equations.
2009 Awarded jointly to Elon Lindenstrauss for his contributions to ergodic theory and their applications in number theory; and to Cédric Villani for his contributions to the theory ofoptimal transport and his studies of non-linear evolution equations.
2011 Awarded jointly to Manjul Bhargava for his work on various generalizations of the Davenport-Heilbronn estimates and for his recent startling results on the average rank of elliptic curves; and to Igor Rodnianski for his fundamental contributions to the studies of the equations of general relativity and to the propagation of the light on the space-time curves.
2013 Awarded jointly to Camillo De Lellis for his fundamental contributions to the conjecture of Onsager about dissipative solutions of the Euler-equations and for his work to the regularity of minimal surfaces; and to Martin Hairer for his contributions to the analysis of stochastic partial differential equations, especially for the regularity of their solutions and convergence to the equilibrium.
2015 Awarded jointly to Laure Saint-Raymond for the development of asymptotic theories of partial differential equations, including the fluid limits of rarefied flows, multiscale analysis in plasma physics equations and ocean modeling, and the derivation of the Boltzmann equation from interacting particle systems; and to Peter Scholze for his invention of perfectoid spaces and their application to fundamental problems in algebraic geometry and in the theory of automorphic forms.
2017 Awarded jointly to Simon Brendle for his numerous and profound results in geometric analysis, involving partial differential equations of elliptic, parabolic and hyperbolic type; in particular for his elegant proof of Lawson's conjecture, for his characterization of soliton solutions of Ricci flows and mean curvature in dimension 3 as well as for his remarkable contributions, in collaboration with Gerhard Huisken, to the analysis of mean curvature flow of mean convex surfaces in manifolds of dimension 3; and to for his remarkable work of depth and creativity in the analysis of nonlinear partial differential equations and in particular for his recent contributions to the rigorous and complete resolution of hydrodynamic stability problems raised at the end of the 19th century by the founding fathers of modern fluid mechanics.
2019 Awarded jointly to Alexei Borodin for the invention of integrable probability theory, a new area at the interface of representation theory, combinatorics and statistical physics; and to Maryna Viazovska for her original solution of the famous sphere packing problem in dimensions 8 and 24.
There has also been a Pierre Fermat medal, which has been awarded for example to Linus Pauling and Ernst Peschl.
Junior Fermat Prize
The Junior Fermat Prize is a mathematical prize, awarded every two years to a student in the first four years of university for a contribution to mathematics. The amount of the prize is 2000 Euros.
