1978

IZRAIL M. GELFAND, Moscow State University, for work in functional analysis, group representation, and seminal contributions to many areas of mathematics.  And; CARL L. SIEGEL , Georg-August University, Gottingen, W. Germany, for contributions to the theories of numbers, several complex variables, and celestial mechanics.

1979

JEAN LERAY, College de France, Paris, France, for pioneering work on development and application of topological methods to the study of differential equations. And; ANDRE WEIL, Institute for Advanced Study, Princeton, U.S.A., for inspired introduction of algebro-geometry methods to the theory of numbers.

1980

HENRI CARTAN, Universite de Paris, for pioneering work in algebraic topology, complex variables, homological algebra and inspired leadership of a generation of mathematicians. And; ANDREI N. KOLMOGOROV, Moscow State University, for deep and original discoveries in Fourier analysis, probability theory, ergodic theory and dynamical systems.

1981

LARS V. AHLFORS, Harvard University, for seminal discoveries and creation of powerful new methods in geometric function theory. And; OSCAR ZARISKI, Harvard University, creator of the modern approach to algebraic geometry, by its fusion with commutative algebra.

1982

HASSLER WHITNEY, Institute for Advanced Study, Princeton, for his fundamental work in algebraic topology, differential geometry and differential topology. And; MARK GRIGOR'EVICH KREIN, Ukrainian S.S.R. Academy of Sciences, Odessa, U.S.S.R., for his fundamental contributions to functional analysis and its applications.

1983/4

SHIING S. CHERN, University of California, Berkeley, for outstanding contributions to global differential geometry, which have profoundly influenced all mathematics. And; PAUL ERDOS, Hungarian Academy of Sciences, Budapest, for numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for stimulating mathematicians the world over.

1984/5

KUNIHIKO KODAIRA, The Japan Academy, Tokyo, Japan, for his outstanding contributions to the study of complex manifolds and algebraic varieties, And; HANS LEWY, University of California, Berkeley, U.S.A., for initiating many, now classic and essential, developments in partial differential equations.

1986

SAMUEL EILENBERG, Columbia University, N.Y., for his fundamental work in algebraic topology and homological algebra. And; ATLE SELBERG, Institute for Advanced Study, Princeton, U.S.A., for his profound and original work on number theory and on discrete groups and automorphic forms.

1987

KIYOSHI ITO, Kyoto University, Kyoto, Japan, for fundamental contributions to pure and applied probability theory, especially creation of stochastic differential & integral calculus. And; PETER D. LAX, New York University, N.Y., U.S.A., for his outstanding contributions to many areas of analysis and applied mathematics.

1988

FRIEDRICH HIRZEBRUCH,Max-Planck-Institut and University of Bonn, W.Germany for outstanding work combining topology, algebraic and differential geometry, and algebraic number theory; and his stimulation of mathematical cooperation and research. And; LARS HORMANDER, University of Lund, Lund, Sweden, for fundamental work in modern analysis, in particular, application of pseudo-differential and Fourier integral operators to linear partial differential equations.

1989

ALBERTO P. CALDERON, University of Chicago, for groundbreaking work on singular integral operators & their application to important partial differential equations problems. And; JOHN W. MILNOR, Institute for Advanced Study, Princeton, for ingenious and highly original discoveries in geometry, which have opened important new vistas in topology from the algebraic, combinatorial, and differentiable viewpoint.

1990

ENNIO DE GIORGI, Scuola Normale Superiore, Pisa, Italy, for his innovating ideas and fundamental achievements in partial differential equations and calculus of variations. And ILYA PIATETSKI-SHAPIRO, Tel-Aviv University, for fundamental contributions in homogeneous complex domains, discrete groups, representation theory & automorphic forms.

1991

Not awarded.

1992

LENNART A.E. CARLESON, University of Uppsala, Uppsala, Sweden, and U.C.L.A, Los Angeles, U.S.A, for his fundamental contributions to Fourier analysis, complex analysis, quasi-conformal mappings and dynamical systems. And JOHN G. THOMPSON, University of Cambridge, Cambridge, U.K., for his profound contributions to all aspects of finite group theory and connections with other branches of mathematics.

1993

MIKHAEL GROMOV, Institut des Hautes Etudes Scientifiques, France , for  revolutionary contributions to global Riemmanian and symplectic geometry, algebraic topology, geometric group theory and the theory of partial differential equations. And;  JACQUES TITS, College de France, Paris, for pioneering, fundamental contributions to theory of the structure of algebraic & other classes of groups & in particular for theory of buildings.

1994/5

JURGEN K. MOSER, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, for his fundamental work on stability in Hamiltonian mechanics and his profound and influential contributions to nonlinear differential equations.

1995/6

ROBERT LANGLANDS, Institute for Advanced Study, Princeton, for path-blazing work & extraordinary insight in number thory, automorphic forms and group representation. And ANDREW J. WILES, Princeton University, for spectacular contributions to number theory & related fields, major advances on fundamental conjectures, & settling Fermat's last theorem.

1996/7

JOSEPH B. KELLER, Stanford University, for profound, innovative contributions to: optical electromagnetic, acoustic wave propagation & fluid, solid, quantum & statistical mechanics. And; YAKOV G. SINAI, Princeton University, and Landau Institute of Theoretical Physics, Moscow, for fundamental contributions to mathematically rigorous methods in statistical mechanics and the ergodic theory of dynamical systems and their applications in physics.

1998

Not awarded

1999

LASZLO LOVASZ, Yale University, and Eotvos University, Budapest, for outstanding contributions to combinatorics, theoretical computer science & combinatorial optimization. And,  ELIAS M. STEIN, Princeton University, for contributions to classical & "Euclidean" Fourier analysis and for exceptional impact on a new analysts through eloquent teaching and writing.

2000

RAOUL BOTT, Harvard University, for his deep discoveries in topology and differential geometry and their applications to Lie groups, differential operators and mathematical physics. And, JEAN-PIERRE SERRE, College de France, Paris, for fundamental contributions to topology, algebraic geometry, algebra, & number theory and his inspirational lectures & writing.

2001

VLADIMIR I. ARNOLD, Steklov Mathematical Institute, Moscow, and University Paris-Dauphine, for deep, influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory. And, SAHARON SHELAH, Hebrew University of Jerusalem, for his many fundamental contributions to mathematical logic and set theory, and their applications within other parts of mathematics.

2002/3

MIKIO SATO, Research Institute for Mathematical Sciences, Kyoto University, for creation of ‘algebraic analysis', including hyperfunction & microfunction theory, holonomic quantum field theory, and a unified theory of soliton equations. And, JOHN T. TATE,Department of Mathematics, University of Texas, Austin, Texas, USA, for his creation of fundamental concepts in algebraic number theory.

2004

Not Awarded

2005

GREGORY A. MARGULIS, for monumental contributions to algebra and SERGEI P. NOVIKOV, for his contributions to algebraic topology, differential topology and mathematical physics