- Statements of variational principles
- Foundations of probability and analytic geometry
- Number theory.
The spirit of the prize is focused on rewarding the results of researches 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 (2011).
Previous prize winners
- 1989 Awarded jointly to Abbas Bahri for the introduction of new methods in the calculus of variations and to Kenneth Ribet for his contribution to number theory and Fermat's Last Theorem.
- 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.
- 1993 Awarded to Jean-Michel Coron for his contributions to the study of variational problems and control theory.
- 1995 Awarded to Andrew Wiles for his works on the Shimura–Taniyama–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.
- 2003 Awarded to Luigi Ambrosio for his impressive contributions to the calculus of variations and geometric measure theory, and their link with partial differential equations.
- 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.
- 2007 Awarded to Chandrashekhar Khare for his proof (with Jean-Pierre Wintenberger) of the Serre modularity conjecture in number theory.
- 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 of optimal 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 (with Arul Shankar) 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 (in collaboration with Mihalis Dafermos, Sergiu Klainerman, and Hans Lindblad).
- 2013 Awarded jointly to Camillo De Lellis for his fundamental contributions (in collaboration with László Székelyhidi) 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.
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.