Browse Prizes and Awards

The 2023 Bôcher Memorial Prize is awarded to Frank Merle, Pierre Raphaël, Igor Rodnianski, and Jérémie Szeftel for their groundbreaking work establishing the existence of blow-up solutions to the defocusing NLS equation in some supercritical regimes and to the compressible Euler and Navier-Stokes equations.

The 2020 Bôcher Memorial Prize is awarded to Camillo De Lellis for his innovative point of view on the construction of continuous dissipative solutions of the Euler equations, which ultimately led to Isett's full solution of the Onsager conjecture, and his spectacular work in the regularity theory of minimal surfaces, where he completed and improved Almgren's program. The Prize is also awarded to Lawrence Guth for his deep and influential development of algebraic and topological methods for partitioning the Euclidean space and multi-scale organization of data, and his powerful applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations. The third recipient of the 2020 Bôcher Memorial Prize is Laure Saint-Raymond for her transformative contributions to kinetic theory, fluid dynamics, and Hilbert's sixth problem on "developing mathematically the limiting processes...which lead from the atomistic view to the laws of motion of continua."

Prize announcement as seen in the news release.

Twenty-fourth award: to András Vasy "for his fundamental paper 'Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces,' Inventiones Mathematicae, 194 (2013), 381­513."

Prize announcement as seen in Notices of the AMS and in the news release.

Twenty-third award: to Simon Brendle for his outstanding solutions of long standing problems in geometric analysis including the solution with R. Schoen of the differentiable sphere theorem (JAMS 22 2009) and the solution of the Lawson conjecture (to appear Acta Mathematica 2013). Brendle is also recognized for his deep contributions to the study of the Yamabe equation.

Prize announcement as seen in Notices of the AMS.

Twenty-second award: to Gunther Uhlmann for his fundamental work on inverse problems; and to Assaf Naor for introducing new invariants of metric spaces and for applying his new understanding of the distortion between various metric structures to theoretical computer science.

Prize announcement as seen in Notices of the AMS.

Twenty-first award: to Alberto Bressan for his fundamental works on hyperbolic conservation laws; and to Charles Fefferman for his many fundamental contributions to different areas of analysis; and to Carlos Kenig for his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE.

Prize announcement as seen in Notices of the AMS.

Twentieth award: to Frank Merle for his fundamental work in the analysis of nonlinear dispersive equations.

Prize announcement as seen in Notices of the AMS.

Nineteenth award: to Daniel Tataru for his fundamental paper "On global existence and scattering for the wave maps equations," Amer. Jour. of Math. 123 (2001) no. 1, 37-77; and to Terence Tao for his recent fundamental breakthrough on the problem of critical regularity in Sobolev spaces of the wave maps equations, "Global regularity of wave maps I. Small critical Sobolev norm in high dimensions", Int. Math. Res. Notices (2001), no.6, 299-328 and "Global regularity of wave maps II. Small energy in two dimensions", to appear in Comm. Math. Phys. (2001 or early 2002); and to Fanghua Lin for his fundamental contributions to our understanding of the Ginzburg-Landau (GL) equations with a small parameter.

Prize announcement as seen in Notices of the AMS.

Eighteenth award: to Demetrios Christodoulou for his contributions to the mathematical theory of general relativity, and to Sergiu Klainerman for his contributions to nonlinear hyperbolic equations, and to Thomas Wolff for his work in harmonic analysis.

Prize announcement as seen in Notices of the AMS.

Seventeenth award: to Leon Simon for his profound contributions toward understanding the structure of singular sets for solutions of variational problems.

Prize announcement as seen in Notices of the AMS and in the news release.

Sixteenth award: to Richard M. Schoen for his work on the application of partial differential equations to differential geometry, in particular his completion of the solution to the Yamabe Problem in Conformal deformation of a Riemannian metric to constant scalar curvature, Journal of Differential Geometry, volume 20 (1984), pp. 479-495.

Fourteenth award: to Luis A. Caffarelli for his deep and fundamental work in nonlinear partial differential equations, in particular his work on free boundary problems, vortex theory and regularity theory.

Thirteenth award: to Alberto P. Calderón in recognition of his fundamental work on the theory of singular integrals and partial differential equations, and in particular for his paper Cauchy integrals on Lipschitz curves and related operators, Proceedings of the National Academy of Sciences, USA, volume 74 (1977), pp. 1324-1327.

Twelfth award: to Donald S. Ornstein in recognition of his paper, Bernoulli shifts with the same entropy are isomorphic, Advances in Mathematics, volume 4 (1970), pp. 337-352.

Eleventh award: to I. M. Singer in recognition of his work on the index problem, especially his share in two joint papers with Michael F. Atiyah, The index of elliptic operators. I, III, Annals of Mathematics, Series 2, volume 87 (1968), pp. 484-530, 546-604.

Tenth award: to Paul J. Cohen for his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics, volume 82 (1960), pp. 191-212.

Ninth award: to Louis Nirenberg for his work in partial differential equations.

Eighth award: to Norman Levinson for his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years.

Seventh award: to A. C. Schaeffer and D. C. Spencer for their memoir, Coefficients of schlicht functions. I, II, III, IV, Duke Mathematical Journal, volume 10 (1943), pp. 611-635, volume 12 (1945), pp. 107-125, and the Proceedings of the National Academy of Sciences, volume 32 (1946), pp. 111-116, volume 35 (1949), pp. 143-150.

Sixth award: to Jesse Douglas for his memoirs, Green's function and the problem of Plateau, American Journal of Mathematics, volume 61 (1939), pp. 545-589; The most general form of the problem of Plateau, American Journal of Mathematics, volume 61(1939), pp. 590-608; and Solution of the inverse problem of the calculus of variations, Proceedings of the National Academy of Sciences, volume 25 (1939), pp. 631-637.

Fifth award: to John von Neumann for his memoir, Almost periodic functions and groups. I, II, Transactions of the American Mathematical Society, volume 36 (1934), pp. 445-492, and volume 37 (1935), pp. 21-50.

Fourth award: to Marston Morse for his memoir, The foundations of a theory of the calculus of variations in the large in m-space, Transactions of the American Mathematical Society, volume 31 (1929), pp. 379-404; and to Norbert Wiener for his memoir, Tauberian theorems, Annals of Mathematics, Series 2, volume 33 (1932), pp. 1-100.

Third award: to J. W. Alexander for his memoir, Combinatorial analysis situs, Transactions of the American Mathematical Society, volume 28 (1926), pp. 301-329.

Second award: to E. T. Bell for his memoir, Arithmetical paraphrases. I, II, Transactions of the American Mathematical Society, volume 22 (1921), pp. 1-30, 198-219; and to Solomon Lefschetz for his memoir, On certain numerical invariants with applications to Abelian varieties, Transactions of the American Mathematical Society, volume 22 (1921), pp. 407-482.

First award: to G. D. Birkhoff for his memoir, Dynamical systems with two degrees of freedom. Transactions of the American Mathematical Society, volume 18 (1917), pp. 199-300.