The Bôcher Memorial Prize was founded by the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
in 1923 in memory of
Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in
analysis
Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
There have been forty-one prize recipients. The first woman to win the award,
Laure Saint-Raymond, did so in 2020. About eighty percent of the journal articles recognized since 2000 have been from ''
Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...
'', the ''
Journal of the American Mathematical Society
The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988.
Abstracting and indexing
This journal is abs ...
'', ''
Inventiones Mathematicae'', and ''
Acta Mathematica''.
Past winners
Source:
* 1923
George David Birkhoff
George David Birkhoff (March21, 1884November12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-body ...
for
::''Dynamical systems with two degrees of freedom.''
Trans. Amer. Math. Soc. 18 (1917), 119-300.
* 1924
Eric Temple Bell for
::''Arithmetical paraphrases. I, II.'' Trans. Amer. Math. Soc. 22 (1921), 1-30, 198-219.
* 1924
Solomon Lefschetz for
::''On certain numerical invariants with applications to Abelian varieties.'' Trans. Amer. Math. Soc. 22 (1921), 407-482.
* 1928
James W. Alexander II for
::''Combinatorial analysis situs.'' Trans. Amer. Math. Soc. 28 (1926), 301-329.
* 1933
Marston Morse for
::''The foundations of a theory of the calculus of variations in the large in m-space.'' Trans. Amer. Math. Soc. 31 (1929), 379-404.
* 1933
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology ( MIT). A child prodigy, Wiener late ...
for
::''Tauberian theorems.''
Ann. Math. 33 (1932), 1-100.
* 1938
John von Neumann
John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
for
::''Almost periodic functions. I.'' Trans. Amer. Math. Soc. 36 (1934), 445-294
::''Almost periodic functions. II.'' Trans. Amer. Math. Soc. 37 (1935), 21-50
* 1943
Jesse Douglas for
::''Green's function and the problem of Plateau.''
Amer. J. Math. 61 (1939), 545-589
::''The most general form of the problem of Plateau.'' Amer. J. Math. 61 (1939), 590-608
::''Solution of the inverse problem of the calculus of variations.'' Proc. Natl. Acad. Sci. U.S.A. 25 (1939), 631-637.
* 1948
Albert Schaeffer and
Donald Spencer for
::''Coefficients of schlicht functions. I.''
Duke Math. J. 10 (1943), 611-635
::''Coefficients of schlicht functions. II.'' Duke Math. J. 12 (1945), 107-125
::''Coefficients of schlicht functions. III.'' Proc. Natl. Acad. Sci. U.S.A. 32 (!946), 111-116
::''Coefficients of schlicht functions. IV.'' Proc. Natl. Acad. Sci. U.S.A. 35 (1949), 143-150.
* 1953
Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, ...
for "his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years"
* 1959
Louis Nirenberg for "his work in partial differential equations"
* 1964
Paul Cohen for
::''On a conjecture of Littlewood and idempotent measures.'' Amer. J. Math. 82 (1960), 191-212.
* 1969
Isadore Singer for "his work on the index problem" and especially
::''The index of elliptic operators. I.'' Ann. of Math. (2) 87 (1968), 484-530
::''The index of elliptic operators. III.'' Ann. of Math. (2) 87 (1968), 546-604
: both written with
Michael Atiyah.
* 1974
Donald Samuel Ornstein for
::''Bernoulli shifts with the same entropy are isomorphic.''
Adv. Math. 4 (1970), 337-352.
* 1979
Alberto Calderón for "his fundamental work on the theory of singular integrals and partial differential equations" and in particular
:: ''Cauchy integrals on Lipschitz curves and related operators.'' Proc. Natl. Acad. Sci. U.S.A. 74 (1977), 1324-1327.
* 1984
Luis 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"
* 1984
Richard Melrose for "his solution of several outstanding problems in diffraction theory and scattering theory and for developing the analytical tools needed for their resolution"
* 1989
Richard Schoen for "his work on the application of partial differential equations to differential geometry," in particular
::''Conformal deformation of a Riemannian metric to constant scalar curvature.''
J. Diff. Geom. 20 (1984), 479-495.
* 1994
Leon Simon for:
::''Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems.'' Ann. of Math. (2) 118 (1983), no. 3, 525–571.
::''Cylindrical tangent cones and the singular set of minimal submanifolds.'' J. Diff. Geom. 38 (1993), no. 3, 585–652.
::''Rectifiability of the singular set of energy minimizing maps.'' Calc. Var. Partial Differential Equations 3 (1995), no. 1, 1–65.
* 1999
Demetrios Christodoulou for:
::''The global nonlinear stability of the Minkowski space.'' Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp.
ritten with Sergiu Klainerman">Sergiu_Klainerman.html" ;"title="ritten with Sergiu Klainerman">ritten with Sergiu Klainerman::''Examples of naked singularity formation in the gravitational collapse of a scalar field.'' Ann. of Math. (2) 140 (1994), no. 3, 607–653.
::''The instability of naked singularities in the gravitational collapse of a scalar field.'' Ann. of Math. (2) 149 (1999), no. 1, 183–217
* 1999 Sergiu Klainerman for:
::''The global nonlinear stability of the Minkowski space.'' Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp. [written with
Demetrios Christodoulou]
::''Space-time estimates for null forms and the local existence theorem.''
Communications on Pure and Applied Mathematics, Comm. Pure Appl. Math. 46 (1993), no. 9, 1221–1268
ith Matei Machedon">Matei_Machedon.html" ;"title="ith Matei Machedon">ith Matei Machedon::''Smoothing estimates for null forms and applications.'' Duke Math. J. 81 (1995), no. 1, 99–133
ith Matei Machedon">Matei_Machedon.html" ;"title="ith Matei Machedon">ith Matei Machedon* 1999 Thomas Wolff for "his work in harmonic analysis," "harmonic measure, and unique continuation," including
::''Counterexamples with harmonic gradients in .'' Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), 321–384, Princeton Math. Ser., 42, Princeton Univ. Press, Princeton, NJ, 1995
::''An improved bound for Kakeya type maximal functions.'' Rev. Mat. Iberoamericana 11 (1995), no. 3, 651–674.
::''A Kakeya-type problem for circles.'' Amer. J. Math. 119 (1997), no. 5, 985–1026
* 2002
Daniel Tătaru for
::''On global existence and scattering for the wave maps equations.'' Amer. J. Math. 123 (2001) no. 1, 37–77
: in addition to his "important work on Strichartz estimates for wave equations with rough coefficients and applications to quasilinear wave equations, as well as his many deep contributions to unique continuation problems"
* 2002
Terence Tao for
::''Global regularity of wave maps I. Small critical Sobolev norm in high dimensions.'' Internat. Math. Res. Notices (2001), no. 6, 299–328
::''Global regularity of wave maps II. Small energy in two dimensions.'' Comm. Math. Phys. 2244 (2001), no. 2, 443–544.
: in addition to "his remarkable series of papers, written in collaboration with J. Colliander, M. Keel, G. Staffilani, and H. Takaoka, on global regularity in optimal Sobolev spaces for KdV and other equations, as well as his many deep contributions to Strichartz and bilinear estimates."
* 2002
Lin Fanghua for
::''Some dynamical properties of Ginzburg-Landau vortices.'' Comm. Pure Appl. Math. 49 (1996), no. 4, 323–359.
::''Gradient estimates and blow-up analysis for stationary harmonic maps.'' Ann. of Math. (2) 149 (1999), no. 3, 785–829.
:in addition to other "fundamental contributions to our understanding of the Ginzburg-Landau (GL) equations with a small parameter" and "many deep contributions to harmonic maps and liquid crystals."
* 2005
Frank Merle for "his fundamental work in the analysis of nonlinear dispersive equations" including:
::''Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation.'' Ann. of Math. (2) 155 (2002), no. 1, 235–280
ritten with Yvan Martel">Yvan_Martel.html" ;"title="ritten with Yvan Martel">ritten with Yvan Martel::''Blow up in finite time and dynamics of blow up solutions for the -critical generalized KdV equation.'' Journal of the American Mathematical Society">J. Amer. Math. Soc. 15 (2002), no. 3, 617–664
ritten with Yvan Martel">Yvan_Martel.html" ;"title="ritten with Yvan Martel">ritten with Yvan Martel::''On universality of blow-up profile for critical nonlinear Schrödinger equation.''
Invent. Math. 156 (2004), no. 3, 565–672 [with Pierre Raphael">Inventiones Mathematicae">Invent. Math. 156 (2004), no. 3, 565–672 [with Pierre Raphael]
* 2008 Alberto Bressan for:
::''Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem.'' Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford, 2000. xii+250 pp.
::''Vanishing viscosity solutions of nonlinear hyperbolic systems.'' Ann. of Math. (2) 161 (2005), no. 1, 223–342
ritten with Stefano Bianchini">Stefano_Bianchini.html" ;"title="ritten with Stefano Bianchini">ritten with Stefano Bianchini* 2008 Charles Fefferman for "his many fundamental contributions to different areas of analysis" including
::''A sharp form of Whitney's extension theorem.'' Ann. of Math. (2) 161 (2005), no. 1, 509–577
::''Whitney's extension problem for .'' Ann. of Math. (2) 164 (2006), no. 1, 313–359.
* 2008
Carlos Kenig for "his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE" including:
::''Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle.'' Comm. Pure Appl. Math. 46 (1993), no. 4, 527–620
ritten with Gustavo Ponce and Luis Vega (mathematician)">Luis Vega">Gusta.html" ;"title="Gustavo_Ponce.html" ;"title="ritten with Gustavo Ponce">ritten with Gustavo Ponce and Luis Vega (mathematician)">Luis Vega::''Global well-posedness of the Benjamin-Ono equation in low-regularity spaces.'' J. Amer. Math. Soc. 20 (2007), no. 3, 753–798 [written with
Alexandru Ionescu">Alexandru Ionescu (mathematician)">Alexandru Ionescu::''Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation.''
Acta Math. 201 (2008), no. 2, 147–212
Frank Merle">ritten with
Frank Merle* 2011
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" and his "remarkable work
..on a lower bound in the sparsest cut problem" including
:: ''On metric Ramsey-type phenomena.'' Ann. of Math. (2) 162 (2005), no. 2, 643–709
ritten with Yair Bartal, Nathan Linial">Yair_Bartal.html" ;"title="ritten with Yair Bartal">ritten with Yair Bartal, Nathan Linial, and Manor Mendel]
::''Metric cotype.'' Ann. of Math. (2) 168 (2008), no. 1, 247–298 [written with Manor Mendel]
::''Euclidean distortion and the sparsest cut.'' J. Amer. Math. Soc. 21 (2008), no. 1, 1–21 [written with
Sanjeev Arora and
James R. Lee]
::''Compression bounds for Lipschitz maps from the Heisenberg group to .'' Acta Math. 207 (2011), no. 2, 291–373
ritten with Jeff Cheeger and Bruce Kleiner">Jeff_Cheeger.html" ;"title="ritten with Jeff Cheeger">ritten with Jeff Cheeger and Bruce Kleiner]
* 2011 Gunther Uhlmann for "his fundamental work on inverse problems" including
::''The Calderón problem with partial data.'' Ann. of Math. (2) 165 (2007), no. 2, 567–591 [written with
Carlos Kenig and
Johannes Sjöstrand]
::''The Calderón problem with partial data in two dimensions.'' J. Amer. Math. Soc. 23 (2010), no. 3, 655–691
ritten with Oleg Imanuvilov and Masahiro Yamamoto (mathematician)">Masahiro Yamamoto">Oleg Imanuvilov">ritten with Oleg Imanuvilov and Masahiro Yamamoto (mathematician)">Masahiro Yamamoto: as well as "incisive work on boundary rigidity with L. Pestov and with P. Stepanov and on nonuniqueness (also known as cloaking) with A. Greenleaf, Y. Kurylev, and M. Lassas."
* 2014 Simon Brendle for "his outstanding solutions of long standing problems in geometric analysis", including
::''Manifolds with 1/4-pinched curvature are space forms.'' J. Amer. Math. Soc. 22 (2009), no. 1, 287–307.
Richard Schoen">ritten with
Richard Schoen::''Embedded minimal tori in and the Lawson conjecture.'' Acta Math. 211 (2013), no. 2, 177–190.
: in addition to "his deep contributions to the study of the Yamabe equation."
* 2017
András Vasy for
::''Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces.'' Invent. Math. 194 (2013), 381-513.
* 2020
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" including:
:: ''Dissipative continuous Euler flows.'' Invent. Math. 193 (2013), no. 2, 377–407
ritten with László Székelyhidi">László_Székelyhidi.html" ;"title="ritten with László Székelyhidi">ritten with László Székelyhidi:: ''Regularity of area minimizing currents III: blow-up.'' Ann. of Math. (2) 183 (2016), no. 2, 577–617 [written with Emanuele Spadaro]
* 2020 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" including:
:: ''A restriction estimate using polynomial partitioning.'' J. Amer. Math. Soc. 29 (2016), no. 2, 371–413
:: ''A sharp Schrödinger maximal estimate in .'' Ann. of Math. (2) 186 (2017), no. 2, 607–640
ritten with Xiumin Du and Xiaochun Li">Xiumin_Du.html" ;"title="ritten with Xiumin Du">ritten with Xiumin Du and Xiaochun Li]
* 2020
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,'" including:
::''The Brownian motion as the limit of a deterministic system of hard-spheres.'' Invent. Math. 203 (2016), no. 2, 493–553
ritten with Thierry Bodineau and Isabelle Gallagher">Thierry_Bodineau.html" ;"title="ritten with Thierry Bodineau">ritten with Thierry Bodineau and Isabelle Gallagher]
::''Mathematical study of degenerate boundary layers: a large scale ocean circulation problem.'' Mem. Amer. Math. Soc. 253 (2018), no. 1206, vi+105 pp. [written with Anne-Laure Dalibard]
* 2023
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" including
::''On the implosion of a compressible fluid I: smooth self-similar inviscid profiles.'' Annals of Mathematics 196 (2022);
::''On the implosion of a compressible fluid II: singularity formation.'' Annals of Mathematics 196 (2022); and
::''On blow up for the energy super critical defocusing nonlinear Schrödinger equations.'' Inventiones Mathematicae 227 (2022).
See also
*
List of mathematics awards
References
External links
AMS Prize - Bôcher Memorial Prize
{{DEFAULTSORT:Bocher Memorial Prize
Awards of the American Mathematical Society
Awards established in 1923
Triennial events
1923 establishments in the United States
Mathematical analysis