1970 Solomon Lefschetz
... for his paper "A page of mathematical autobiography".
1971 James B Carrell
... for his paper written jointly with Jean A Dieudonne "Invariant theory, old and new".
1971 Jean A Dieudonné
... for his paper "Algebraic geometry", and for his paper, written jointly with James B Carrell "Invariant theory, old and new".
1971 Phillip A Griffiths
... for his paper "Periods of integrals on algebraic manifolds".
1972 Edward B Curtis
... for his paper "Simplicial homotopy theory".
1972 William J Ellison
... for his paper "Waring's problem".
1972 Lawrence F Payne
... for his paper "Isoperimetric inequalities and their applications".
1972 Dana S Scott
... for his paper "A proof of the independence of the continuum hypothesis".
1975 Lipman Bers
... for his paper "Uniformization, moduli, and Kleinian groups".
1975 Martin D Davis
... for his paper "Hilbert's tenth problem is unsolvable".
1975 Joseph L Taylor
... for his paper "Measure algebras".
1975 George W Mackey
... for his paper "Ergodic theory and its significance for statistical mechanics and probability theory".
1975 H Blaine Lawson
... for his paper "Foliations".
1979 Salomon Bochner
... for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry.
1979 Hans Lewy
... for three fundamental papers: "On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables", "An example of a smooth linear partial differential equation without solution", and "On hulls of holomorphy".
1979 Antoni Zygmund
... for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis.
1979 Robin Hartshorne
... for his expository research article "Equivalence relations on algebraic cycles and subvarieties of small codimension", and his book "Algebraic geometry".
1979 Joseph J Kohn
... for his fundamental paper "Harmonic integrals on strongly convex domains. I, II".
1980 André Weil
... for the total effect of his work on the general course of twentieth century mathematics, especially in the many areas in which he has made fundamental contributions.
1980 Harold M Edwards
... for mathematical exposition in his books "Riemann's zeta function", and Fermat's last theorem".
1980 Gerhard P Hochschild
... for his significant work in homological algebra and its applications.
1981 Oscar Zariski
... for his work in algebraic geometry, especially his fundamental contributions to the algebraic foundations of this subject.
1981 Eberhard Hopf
... for three papers of fundamental and lasting importance "Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential systems", "A mathematical example displaying features of turbulence", and "The partial differential equation ut + uux = uxx".
1981 Nelson Dunford and Jacob T Schwartz
... for their expository book "Linear operators", Part I, "General theory", Part II, "Spectral theory", 1963, and Part III, "Spectral operators".
1982 Lars V Ahlfors
... for his expository work in "Complex analysis", and in "Lectures on quasiconformal mappings", and "Conformal invariants".
1982 Tsit-Yuen Lam
... for his expository work in his book "Algebraic theory of quadratic forms", and four of his papers "K0 and K1-an introduction to algebraic K-theory", "Ten lectures on quadratic forms over fields", "Serre's conjecture", and "The theory of ordered fields".
1982 John W Milnor
... for a paper of fundamental and lasting importance "On manifolds homeomorphic to the 7-sphere".
1982 Fritz John
... for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students.
1983 Paul R Halmos
... for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.
1983 Steven C Kleene
... for three important papers which formed the basis for later developments in generalized recursion theory and descriptive set theory "Arithmetical predicates and function quantifiers", "On the forms of the predicates in the theory of constructive ordinals (second paper)", and "Hierarchies of number-theoretic predicates".
1983 Shiing-Shen Chern
... for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of the field of differential geometry, and influence on mathematics through Ph.D. students.
1984 Elias M Stein
... for his book "Singular integrals and the differentiability properties of functions".
1984 Lennart Carleson
... for his papers "An interpolation problem for bounded analytic functions", "Interpolation by bounded analytic functions and the Corona problem", and "On convergence and growth of partial sums of Fourier series".
1984 Joseph L Doob
... for his fundamental work in establishing probability as a branch of mathematics and for his continuing profound influence on its development.
1985 Michael Spivak
... for his five-volume set "A Comprehensive Introduction to Differential Geometry".
1985 Robert Steinberg
... for three papers on various aspects of the theory of algebraic groups "Representations of algebraic groups", "Regular elements of semisimple algebraic groups", and "Endomorphisms of linear algebraic groups".
1985 Hassler Whitney
... for his fundamental work on geometric problems, particularly in the general theory of manifolds, in the study of differentiable functions on closed sets, in geometric integration theory, and in the geometry of the tangents to a singular analytic space.
1986 Donald E Knuth
... for his expository 3-volume work "The Art of Computer Programming".
1986 Rudolf E Kalman
... for his two fundamental papers "A new approach to linear filtering and prediction problems", and "Mathematical description of linear dynamical systems", and for his contribution to a third paper (with R S Bucy) "New results in linear filtering and prediction theory".
1986 Saunders Mac Lane
... for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.
1987 Martin Gardner
... for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American.
1987 Herbert Federer and Wendell Fleming
... for their pioneering paper "Normal and integral currents".
1987 Samuel Eilenberg
... for his fundamental contributions to topology and algebra, in particular for his classic papers on singular homology and his work on axiomatic homology theory which had a profound influence on the development of algebraic topology.
1988 Sigurdur Helgason
... for his books "Differential Geometry and Symmetric Spaces", "Differential Geometry, Lie Groups, and Symmetric Spaces", and "Groups and Geometric Analysis".
1988 Gian-Carlo Rota
... for his paper "On the foundations of combinatorial theory, I. Theory of Möbius functions".
1988 Deane Montgomery
... for his lasting impact on mathematics, particularly mathematics in America. He is one of the founders of the modern theory of transformation groups and is particularly known for his contributions to the solution of Hilbert's fifth problem.
1989 Daniel Gorenstein
... for his book "Finite Simple Groups, An Introduction to their Classification", and his two survey articles "The Classification of Finite Simple Groups" and "Classifying the Finite Simple Groups".
1989 Alberto P Calderón
... for his paper "Uniqueness in the Cauchy Problem for Partial Differential Equation".
1989 Irving Kaplansky
... for his lasting impact on mathematics, particularly mathematics in America. By his energetic example, his enthusiastic exposition, and his overall generosity, he has made striking changes in mathematics and has inspired generations of younger mathematicians.
1990 R D Richtmyer
... for his book "Difference Methods for Initial-Value Problems".
1990 Bertram Kostant
... for his paper "On the existence and irreducibility of certain series of representations".
1990 Raoul Bott
... for having been instrumental in changing the face of geometry and topology, with his incisive contributions to characteristic classes, K-theory, index theory, and many other tools of modern mathematics.
1991 Jean-François Treves
... for "Pseudodifferential and Fourier Integral Operators", Volumes 1 and 2.
1991 Eugenio Calabi
... for his fundamental work on global differential geometry, especially complex differential geometry.
1991 Armand Borel
... for his extensive contributions in geometry and topology, the theory of Lie groups, their lattices and representations and the theory of automorphic forms, the theory of algebraic groups and their representations and extensive organizational and educational efforts to develop and disseminate modern mathematics.
1993 Jacques Dixmier
... for his books "von Neumann Algebras (Algèbres de von Neumann)", "C*-Algebras (Les C*-Algèbres et leurs Representations)", and "Enveloping Algebras (Algèbres Enveloppantes)".
1993 James Glimm
... for his paper "Solution in the large for nonlinear hyperboic systems of conservation laws".
1993 Peter D Lax
... for his numerous and fundamental contributions to the theory and applications of linear and nonlinear partial differential equations and functional analysis, for his leadership in the development of computational and applied mathematics, and for his extraordinary impact as a teacher.
1993 (For Mathematical Exposition) Walter Rudin
... for his books "Principles of Mathematical Analysis", and "Real and Complex Analysis".
1993 (For Seminal Contribution to Research) George Daniel Mostow
... for his paper "Strong rigidity of locally symmetric spaces".
1993 (For Lifetime Achievement) Eugene B Dynkin
... for his foundational contributions to Lie algebras and probability theory over a long period and his production of outstanding research students in both Russia and the United States, countries to whose mathematical life he has contributed so richly.
1994 (For Mathematical Exposition) Ingrid Daubechies
... for her book "Ten Lectures on Wavelets".
1994 (For Seminal Contribution to Research) Louis de Branges
... for his proof of the Bieberbach Conjecture.
1994 (For Lifetime Achievement) Louis Nirenberg
... for his numerous basic contributions to linear and nonlinear partial differential equations and their application to complex analysis and differential geometry.
1995 (For Mathematical Exposition) Jean-Pierre Serre
... for his 1970 book "Cours d'Arithmétique", with its English translation "A Course in Arithmetic".
1995 (For Seminal Contribution to Research) Edward Nelson
... for the following two papers in mathematical physics characterized by leaders of the field as extremely innovative "A quartic interaction in two dimensions in Mathematical Theory of Elementary Particles", and "Construction of quantum fields from Markoff fields in Journal of Functional Analysis". In these papers he showed for the first time how to use the powerful tools of probability theory to attack the hard analytic questions of constructive quantum field theory, controlling renormalizations with Lp estimates in the first paper, and in the second turning Euclidean quantum field theory into a subset of the theory of stochastic processes.
1995 (For Lifetime Achievement) John T Tate
... for scientific accomplishments spanning four and a half decades. He has been deeply influential in many of the important developments in algebra, algebraic geometry, and number theory during this time.
1996 (For Mathematical Exposition) Bruce C Berndt
... for the four volumes "Ramanujan's Notebooks, Parts I, II, III, and IV".
1996 (For Mathematical Exposition) William Fulton
... for his book "Intersection Theory".
1996 (For Seminal Contribution to Research) Daniel Stroock and S R S Varadhan
... for their four papers "Diffusion processes with continuous coefficients I and II", "On the support of diffusion processes with applications to the strong maximum principle", "Diffusion processes with boundary conditions", and "Multidimensional diffusion processes".
1996 (For Lifetime Achievement) Goro Shimura
... for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.
1997 (For Mathematical Exposition) Anthony W Knapp
... for his book "Representation Theory of Semisimple Groups (An overview based on examples)", a beautifully written book which starts from scratch but takes the reader far into a highly developed subject.
1997 (For Seminal Contribution to Research) Mikhael Gromov
... for his paper "Pseudo-holomorphic curves in symplectic manifolds", which revolutionized the subject of symplectic geometry and topology and is central to much current research activity, including quantum cohomology and mirror symmetry.
1997 (For Lifetime Achievement) Ralph S Phillips
... for being one of the outstanding analysts of our time. His early work was in functional analysis: his beautiful theorem on the relation between the spectrum of a semigroup and its infinitesimal generator is striking as well as very useful in the study of PDEs. His extension theory for dissipative linear operators predated the interpolation approach to operator theory and robust control. He made major contributions to acoustical scattering theory in his joint work with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. He later extended this work to a spectral theory for the automorphic Laplace operator, relying on the Radon transform on horospheres to avoid Eisenstein series. In the last fifteen years, Ralph Phillips has done brilliant work, in collaboration with others, on spectral theory for the Laplacian on symmetric spaces, on the existence and stability of cusp forms for general noncompact quotients of the hyperbolic plane, on the explicit construction of sparse optimal expander graphs, and on the structure of families of isospectral sets in two dimensions (the collection of drums that sound the same).
1998 (For Lifetime Achievement) Nathan Jacobson
... for his many contributions to research, teaching, exposition, and the mathematical profession. Few mathematicians have been as productive over such a long career or have had as much influence on the profession as has Professor Jacobson.
1998 (For Seminal Contribution to Research) Herbert Wilf and Doron Zeilberger
... for their joint paper "Rational functions certify combinatorial identities".
1998 (For Mathematical Exposition) Joseph Silverman
... for his books "The Arithmetic of Elliptic Curves", and "Advanced Topics in the Arithmetic of Elliptic Curves".
1999 (For Lifetime Achievement) Richard V Kadison
... For almost half a century, Professor Kadison has been one of the world leaders in the subject of operator algebras, and the tremendous flourishing of this subject in the last thirty years is largely due to his efforts.
1999 (For Seminal Contribution to Research) Michael G Crandall
... for two seminal papers "Viscosity solutions of Hamilton-Jacobi equations" (joint with P-L Lions), and "Generation of semi-groups of nonlinear transformations on general Banach spaces" (joint with T M Liggett).
1999 (For Seminal Contribution to Research) John F Nash
... for his remarkable paper "The embedding problem for Riemannian manifolds".
1999 (For Mathematical Exposition) Serge Lang
... for his many mathematics books. Among Lang's most famous texts are "Algebra" and "Algebraic Number Theory".
2000 (For Lifetime Achievement) Isadore M Singer
... Singer's series of five papers with Michael F Atiyah on the Index Theorem for elliptic operators (which appeared in 1968-71) and his three papers with Atiyah and V K Patodi on the Index Theorem for manifolds with boundary (which appeared in 1975-76) are among the great classics of global analysis.
2000 (For Seminal Contribution to Research) Barry Mazur
... for his paper "Modular curves and the Eisenstein ideal".
2000 (For Mathematical Exposition) John H Conway
... in recognition of his many expository contributions in automata, the theory of games, lattices, coding theory, group theory, and quadratic forms.
2001 (For Lifetime Achievement) Harry Kesten
... for his many and deep contributions to probability theory and its applications.
2001 (For Seminal Contribution to Research) Leslie F Greengard and Vladimir Rokhlin
... for the paper "A fast algorithm for particle simulations".
2001 (For Mathematical Exposition) Richard P Stanley
... in recognition of the completion of his two-volume work "Enumerative Combinatorics".
2002 (For Lifetime Achievement) Michael Artin
... for helping to weave the fabric of modern algebraic geometry, and to Elias Stein for making fundamental contributions to different branches of analysis.
2002 (For Seminal Contribution to Research) Mark Goresky and Robert MacPherson
... for the papers "Intersection homology theory", and "Intersection homology. II".
2002 (For Mathematical Exposition) Yitzhak Katznelson
... for his book on harmonic analysis.
2003 (For Lifetime Achievement) Ron Graham
... for being one of the principal architects of the rapid development worldwide of discrete mathematics in recent years; and to Victor Guillemin for playing a critical role in the development of a number of important areas in analysis and geometry.
2003 (For Seminal Contribution to Research) Ronald Jensen
... for his paper "The fine structure of the constructible hierarchy".
2003 (For Seminal Contribution to Research) Michael Morley
... for his paper "Categoricity in power".
2003 (For Mathematical Exposition) John B Garnett
... for his book "Bounded Analytic Functions".
2004 (For Lifetime Achievement) To Cathleen Synge Morawetz
... for greatly influencing mathematics in the broad sense throughout her long and distinguished career.
2004 (For Seminal Contribution to Research) To Lawrence C Evans and Nicolai V Krylov
... for the "Evans-Krylov theorem" as first established in the papers Lawrence C Evans "Classical solutions of fully nonlinear convex, second order elliptic equations", and N V Krylov "Boundedly inhomogeneous elliptic and parabolic equations".
2004 (For Mathematical Exposition) To John W Milnor
... in recognition of a lifetime of expository contributions ranging across a wide spectrum of disciplines including topology, symmetric bilinear forms, characteristic classes, Morse theory, game theory, algebraic K-theory, iterated rational mapsÉand the list goes on.
2005 (For Lifetime Achievement) To Israel M Gelfand
... for profoundly influencing many fields of research through his own work and through his interactions with other mathematicians and students.
2005 (For Seminal Contribution to Research) To Robert P Langlands
... for his paper "Problems in the theory of automorphic forms". This is the paper that introduced what are now known as the Langlands conjectures.
2005 (For Mathematical Exposition) To Branko Grünbaum
... for his book "Convex Polytopes".
2006 (For Lifetime Achievement) To Frederick W Gehring
... for being a leading figure in the theory of quasiconformal mappings for over fifty years; and to Dennis P Sullivan for his fundamental contributions to many branches of mathematics.
2006 (For Seminal Contribution to Research) To Clifford S Gardner, John M Greene, Martin D Kruskal, and Robert M Miura
... for their paper "Korteweg de Vries equation and generalizations. VI. Methods for exact solution".
2006 (For Mathematical Exposition) To Lars V Hörmander
... for his book "The Analysis of Linear Partial Differential Operators".
2007 (Lifetime Achievement) To Henry P McKean
... for his rich and magnificent mathematical career and for his work in analysis, which has a strong orientation towards probability theory.
2007 (Seminal Contribution to Research) To Karen Uhlenbeck
... for her foundational contributions in analytic aspects of mathematical gauge theory. These results appeared in the two papers: "Removable singularities in Yang-Mills fields"; and "Connections with L:P bounds on curvature".
2007 (Mathematical Exposition) To David Mumford
... for his beautiful expository accounts of a host of aspects of algebraic geometry, including "The Red Book of Varieties and Schemes" (Springer, 1988).
2008 (Lifetime Achievement) To George Lusztig
... for entirely reshaping representation theory, and, in the process, changing much of mathematics.
2008 (Seminal Contribution to Research) To Endre Szemerédi
... for his paper "On sets of integers containing no k elements in arithmetic progression".
2008 (Mathematical Exposition) To Neil Trudinger
... for his book "Elliptic Partial Differential Equations of Second Order", written with the late David Gilbarg.
2009 (Lifetime Achievement) To Luis Caffarelli
... one of the world's greatest mathematicians studying nonlinear partial differential equations.
2009 (Seminal Contribution to Research) To Richard Hamilton
... for his paper "Three-manifolds with positive Ricci curvature".
2009 (Mathematical Exposition) To I G MacDonald
... for his book "Symmetric Functions and Hall Polynomials" .
2010 (Lifetime Achievement) To William Fulton
for playing a pivotal role in shaping the direction of algebraic geometry, forging and strengthening ties between algebraic geometry and adjacent fields, and teaching and mentoring several generations of younger mathematicians.
2010 (Mathematical Exposition) To David Eisenbud
for his book, "Commutative Algebra: With a View Toward Algebraic Geometry".
2010 (Seminal Contribution to Research) To Robert L. Griess Jr.
for his construction of the "Monster" sporadic finite simple group.
2011 (Lifetime Achievement: To John W. Milnor
for standing out from the list of great mathematicians in terms of his overall achievements and his influence on mathematics in general, both through his work and through his excellent books.
2011 (Mathematical Exposition: To Henryk Iwaniec
for his long record of excellent exposition, both in books and in classroom notes.
2011 (Seminal Contribution to Research: To Ingrid Daubechies
for her paper, "Orthonormal bases of compactly supported wavelets".
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