Leroy P. Steele Prizes
Leroy P. Steele Prize for Lifetime Achievement
Leroy P. Steele Prize for Mathematical Exposition
Leroy P. Steele Prize for Seminal Contribution to Research
These prizes were established in 1970 in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein, and are endowed under the terms of a bequest from Leroy P. Steele. From 1970 to 1976 one or more prizes were awarded each year for outstanding published mathematical research; most favorable consideration was given to papers distinguished for their exposition and covering broad areas of mathematics. In 1977 the Council of the AMS modified the terms under which the prizes are awarded. Since then, up to three prizes have been awarded each year in the following categories: (1) for the cumulative influence of the total mathematical work of the recipient, 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; (2) for a book or substantial survey or expository-research paper; (3) for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research. In 1993, the Council formalized the three categories of the prize by naming each of them: (1) The Leroy P. Steele Prize for Lifetime Achievement; (2) The Leroy P. Steele Prize for Mathematical Exposition; and (3) The Leroy P. Steele Prize for Seminal Contribution to Research. Each of these three US$5,000 prizes is awarded annually.
Special Note: beginning with the 1994 prize, there has been a five-year cycle of fields for the Seminal Contribution to Research Award. That cycle would have the 2008 prize awarded in discrete mathematics (discrete mathematics alternates with logic every five years), then analysis in 2009, algebra in 2010, applied mathematics in 2011, geometry/topology in 2012 and then logic in 2013, renewing the cycle.
Next awards: January 2011. Call for nominations.
January 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.
January 2010 - Mathematical Exposition: To David Eisenbud for his book, Commutative Algebra: With a View Toward Algebraic Geometry (Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995. xvi+785 pp.)
January 2010 - Seminal Contribution to Research: To Robert L. Griess Jr. for his construction of the “Monster” sporadic finite simple group, which he first announced in “A construction of F1 as automorphisms of a 196,883-dimensional algebra” (Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 2, part 1, 686–691) with details published in “The friendly giant” (Invent. Math. 69 (1982), no. 1, 1–102).
January 2009 - Lifetime Achievement: To Luis Caffarelli, one of the world's greatest mathematicians studying nonlinear partial differential equations (PDE).
January 2009 - Mathematical Exposition: To I.G. MacDonald for his book Symmetric Functions and Hall Polynomials (second edition, Clarendon Press, Oxford University Press, 1995).
January 2009 - Seminal Contribution to Research: To Richard Hamilton for his paper "Three-manifolds with positive Ricci curvature," J. Differential Geom. 17 (1982), 255-306.
January 2008 - Lifetime Achievement: To George Lusztig for entirely reshaping representation theory, and, in the process, changing much of mathematics.
January 2008 - Mathematical Exposition: To Neil Trudinger for his book Elliptic Partial Differential Equations of Second Order, written with the late David Gilbarg.
January 2008 - Seminal Contribution to Research: To Endre Szemerédi for his paper "On sets of integers containing no k elements in arithmetic progression", Acta Arithmetica XXVII (1975), 199-245.
January 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.
January 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).
January 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", Communications in Mathematical Physics, 83 (1982), 11-29 and "Connections with L:P bounds on curvature", Communications in Mathematical Physics, 83 (1982), 31-42.
January 2006 - 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.
January 2006 - Mathematical Exposition : To Lars V. Hörmander for his book, The Analysis of Linear Partial Differential Operators.
January 2006 - Seminal Contribution to Research : To Clifford S. Gardner, John M. Greene, Martin D. Kruskal, and Robert M. Miura for their paper “KortewegdeVries equation and generalizations. VI. Methods for exact solution”, Comm. Pure Appl. Math. 27 (1974), 97–133.
January 2005 - 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.
January 2005 - Mathematical Exposition : To Branko Grünbaum for his book, Convex Polytopes.
January 2005 - Seminal Contribution to Research : To Robert P. Langlands for his paper "Problems in the theory of automorphic forms," (Springer Lecture Notes in Math. 170 (1970), 18-86). This is the paper that introduced what are now known as the Langlands conjectures.
January 2004 - Lifetime Achievement : To Cathleen Synge Morawetz for greatly influencing mathematics in the broad sense throughout her long and distinguished career.
January 2004 - 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 maps…and the list goes on.
January 2004 - 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”, Communications in Pure and Applied Mathematics 35 (1982), no. 3, 333–363; and N. V. Krylov, “Boundedly inhomogeneous elliptic and parabolic equations”, Izvestiya Akad. Nauk SSSR, ser. mat. 46 (1982), no. 3, 487–523; and translated in Mathematics of the USSR, Izvestiya 20 (1983), no. 3, 459–492.
January 2003 - Lifetime Achievement : To 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.
January 2003 - Mathematical Exposition : To John B. Garnett for his book, Bounded Analytic Functions (Pure and Applied Mathematics, 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981, xvi + 467 pp.)
January 2003 - Seminal Contribution to Research : To Ronald Jensen for his paper “The fine structure of the constructible hierarchy” (Annals of Mathematical Logic 4 (1972) 229–308); and to Michael Morley for his paper “Categoricity in power” (Transactions of the AMS 114 (1965) 514–538).
January 2002 - Lifetime Achievement : To 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.
January 2002 - Mathematical Exposition : To Yitzhak Katznelson for his book on harmonic analysis.
January 2002 - Seminal Contribution to Research : To Mark Goresky and Robert MacPherson for the papers, “Intersection
homology theory”, Topology 19 (1980), no. 2, 135–62 (IH1) and “Intersection homology. II”, Invent. Math. 72 (1983), no. 1, 77–129 (IH2).
January 2001 - Lifetime Achievement : To Harry Kesten for his many and deep contributions to probability theory and its applications.
January 2001 - Mathematical Exposition : To Richard P. Stanley in recognition of the completion of his two-volume work Enumerative Combinatorics.
January 2001 - Seminal Contribution to Research : To Leslie F. Greengard and Vladimir Rokhlin for the paper "A fast algorithm for particle simulations", J. Comput. Phys. 73, no. 2 (1987), 325-348.
January 2000 - Lifetime Achievement : To 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.
January 2000 - Mathematical Exposition : To John H. Conway in recognition of his many expository contributions in automata, the theory of games, lattices, coding theory, group theory, and quadratic forms.
January 2000 - Seminal Contribution to Research : To Barry Mazur for his paper "Modular curves and the Eisenstein ideal" in Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, no. 47 (1978), 33-186.
January 1999 - Lifetime Achievement : To 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.
January 1999 - Mathematical Exposition : To Serge Lang for his many mathematics books. Among Lang's most famous texts are Algebra [Addison-Wesley, Reading, MA, 1965; Second edition, 1984; Third edition, 1993, ISBN 0-201-55540-9] and Algebraic Number Theory [Addison-Wesley, Reading, MA, 1970; Second edition, Graduate Texts in Mathematics, 110, Springer-Verlag, New York, 1994, ISBN: 0-387-94225-4].
January 1999 - Seminal Contribution to Research : To Michael G. Crandall for two seminal papers: "Viscosity solutions of Hamilton-Jacobi equations" (joint with P.-L. Lions), Trans. Amer. Math. Soc. 277 (1983), 1-42, and "Generation of semi-groups of nonlinear transformations on general Banach spaces" (joint with T.M. Liggett), Amer. J. Math. 93 (1971), 265-298.
January 1999 - Seminal Contribution to Research : To John F. Nash for his remarkable paper: "The embedding problem for Riemannian manifolds," Ann. of Math. (2) 63 (1956) 20-63.
January 1998 - Lifetime Achievement : To 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.
January 1998 - Mathematical Exposition : To Joseph Silverman for his books, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106, Springer-Verlag, New; York-Berlin, 1986; and Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 151, Springer-Verlag, New York, 1994.
January 1998 - Seminal Contribution to Research : To Herbert Wilf and Doron Zeilberger for their joint paper, "Rational functions certify combinatorial identities," Journal of the American Mathematical Society, 3 (1990) 147-158.
January 1997 - Lifetime Achievement : To 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).
January 1997 - Mathematical Exposition : To Anthony W. Knapp for his book, Representation Theory of Semisimple Groups (An overview based on examples), Princeton University Press, 1986, a beautifully written book which starts from scratch but takes the reader far into a highly developed subject.
January 1997 - Seminal Contribution to Research : To Mikhael Gromov for his paper, Pseudo-holomorphic curves in symplectic manifolds, Inventiones Math. 82 (1985), 307-347, which revolutionized the subject of symplectic geometry and topology and is central to much current research activity, including quantum cohomology and mirror symmetry.
August 1996 - Lifetime Achievement : To 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.
August 1996 - Mathematical Exposition : To Bruce C. Berndt for the four volumes, Ramanujan's Notebooks, Parts I, II, III, and IV (Springer, 1985, 1989, 1991, and 1994).
August 1996 - Mathematical Exposition : To William Fulton for his book, Intersection Theory, Springer-Verlag, "Ergebnisse series," 1984.
August 1996 - Seminal Contribution to Research : To Daniel Stroock and S.R.S. Varadhan for their four papers: Diffusion processes with continuous coefficients I and II, Comm. Pure Appl. Math. 22 (1969), 345-400, 479-530; On the support of diffusion processes with applications to the strong maximum principle, Sixth Berkeley Sympos. Math. Statist. Probab., vol. III, 1970, pp. 333-360; Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 34 (1971), 147-225; Multidimensional diffusion processes, Springer-Verlag, 1979.
August 1995 - Lifetime Achievement : To 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.
August 1995 - Mathematical Exposition : To Jean-Pierre Serre for his 1970 book Cours d'Arithmétique, with its English translation, published in 1973 by Springer Verlag, A Course in Arithmetic.
August 1995 - Seminal Contribution to Research : To 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, MIT Press, 1966, pages 69-73; and Construction of quantum fields from Markoff fields in Journal of Functional Analysis, 12 (1973), 97-112. 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 L^p estimates in the first paper, and in the second turning Euclidean quantum field theory into a subset of the theory of stochastic processes.
August 1994 - Lifetime Achievement: To Louis Nirenberg for his numerous basic contributions to linear and nonlinear partial differential equations and their application to complex analysis and differential geometry.
August 1994 - Mathematical Exposition: To Ingrid Daubechies for her book, Ten Lectures on Wavelets (CBMS 61, SIAM, 1992, ISBN 0-8987-1274-2).
August 1994 - Seminal Contribution to Research: To Louis de Branges for his proof of the Bieberbach Conjecture.
August 1993 - Lifetime Achievement: To 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.
August 1993 - Mathematical Exposition: To Walter Rudin for his books Principles of Mathematical Analysis, McGraw-Hill (1953, 1964, and 1976); and Real and Complex Analysis, McGraw-Hill (1966, 1974, and1976).
August 1993 - Seminal Contribution to Research: To George Daniel Mostow for his paper Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, number 78, Princeton University Press (1973).
August 1992: To Jacques Dixmier for his books von Neumann Algebras (Algèbres de von Neumann ), Gauthier-Villars, Paris (1957); C*-Algebras (Les C*-Algèbres et leurs Representations ), Gauthier-Villars, Paris (1964); and Enveloping Algebras (Algèbres Enveloppantes ), Gauthier-Villars, Paris (1974). [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]
August 1992: To James Glimm for his paper, Solution in the large for nonlinear hyperboic systems of conservation laws, Communications on Pure and Applied Mathematics, XVIII (1965), pp. 697-715. [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]
August 1992: To 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. [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]
August 1991: To Jean-François Treves for Pseudodifferential and Fourier Integral Operators, Volumes 1 and 2 (Plenum Press, 1980).
August 1991: To Eugenio Calabi for his fundamental work on global differential geometry, especially complex differential geometry.
August 1991: To 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
August 1990: To R. D. Richtmyer for his book Difference Methods for Initial-Value Problems (Interscience, 1st Edition 1957 and 2nd Edition, with K. Morton, 1967).
August 1990: To Bertram Kostant for his paper, On the existence and irreducibility of certain series of representations, Lie Groups and their Representations (1975), pp. 231-329.
August 1990: To 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.
August 1989: To Daniel Gorenstein for his book Finite Simple Groups, An Introduction to their Classification (Plenum Press, 1982); and his two survey articles The Classification of Finite Simple Groups and Classifying the Finite Simple Groups, Bulletin of the American Mathematical Society, volume 1 (1979) pp. 43-199, and volume 14 (1986) pp. 1-98, respectively.
August 1989: To Alberto P. Calderón for his paper Uniqueness in the Cauchy Problem for Partial Differential Equations, American Journal ofMathematics, volume 80 (1958), pp. 16-36.
August 1989: To 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.
August 1988: To Sigurdur Helgason for his books Differential Geometry and Symmetric Spaces (Academic Press, 1962), Differential Geometry, Lie Groups, and Symmetric Spaces (Academic Press, 1978); and Groups and Geometric Analysis (Academic Press, 1984).
August 1988: To Gian-Carlo Rota for his paper On the foundations of combinatorial theory, I. Theory of Möbius functions, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, volume 2 (1964), pp. 340-368.
August 1988: To 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.
August 1987: To Martin Gardner for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American.
August 1987: To Herbert Federer and Wendell Fleming for their pioneering paper, Normal and integral currents, Annals of Mathematics, volume 72 (1960), pp. 458-520.
August 1987: To 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 toplogy.
January 1986: To Donald E. Knuth for his expository work, The Art of Computer Programming, 3 Volumes (1st Edition 1968, 2nd Edition 1973).
January 1986: To Rudolf E. Kalman for his two fundamental papers: A new approach to linear filtering and prediction problems, Journal of Basic Engineering, volume 82, (1960), pp. 35-45; and Mathematical description of linear dynamical systems, SIAM Journal on Control and Optimization, volume 1 (1963), pp. 152-192; and for his contribution to a third paper, (with R. S. Bucy) New results in linear filtering and prediction theory, Journal of Basic Engineering, volume 83D (1961), pp. 95-108.
January 1986: To Saunders Mac Lane for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.
August 1985: To Michael Spivak for his five-volume set, A Comprehensive Introduction to Differential Geometry (second edition, Publish or Perish, 1979).
August 1985: To Robert Steinberg for three papers on various aspects of the theory of algebraic groups: Representations of algebraic groups, Nagoya Mathematical Journal, volume 22 (1963), pp. 33-56; Regular elements of semisimple algebraic groups, Institut des Hautes Études Scientifiques, Publications Mathématiques, volume 25 (1965), pp. 49-80; and Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, volume 80 (1968).
August 1985: To 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.
August 1984: To Elias M. Stein for his book, Singular integrals and the differentiability properties of functions, Princeton University Press (1970).
August 1984: To Lennart Carleson for his papers: An interpolation problem for bounded analytic functions, American Journal of Mathematics, volume 80 (1958), pp. 921-930; Interpolation by bounded analytic functions and the Corona problem, Annals of Mathematics (2), volume 76 (1962), pp. 547-559; and On convergence and growth of partial sums of Fourier series, Acta Mathematica volume 116 (1966), pp. 135-157.
August 1984: To Joseph L. Doob for his fundamental work in establishing probability as a branch of mathematics and for his continuing profound influence on its development.
August 1983: To Paul R. Halmos for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.
August 1983: To 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, Transactions of the American Mathematical Society 79 (1955), pp. 312-340; On the forms of the predicates in the theory of constructive ordinals (second paper), American Journal of Mathematics 77 (1955), pp. 405-428; and Hierarchies of number-theoretic predicates, Bulletin of the American Mathematical Society 61 (1955), pp. 193-213.
August 1983: To 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.
August 1982: To Lars V. Ahlfors for his expository work in Complex analysis (McGraw-Hill Book Company, New York, 1953), and in Lectures on quasiconformal mappings (D. Van Nostrand Co., Inc., New York, 1966) and Conformal invariants (McGraw-Hill Book Company, New York, 1973).
August 1982: To Tsit-Yuen Lam for his expository work in his book Algebraic theory of quadratic forms (1973), and four of his papers: K_0 and K_1-an introduction to algebraic K-theory (1975), Ten lectures on quadratic forms over fields (1977), Serre's conjecture (1978), and The theory of ordered fields (1980).
August 1982: To John W. Milnor for a paper of fundamental and lasting importance, On manifolds homeomorphic to the 7-sphere, Annals of Mathematics (2) 64 (1956), pp. 399-405.
August 1982: To 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.
August 1981: To Oscar Zariski for his work in algebraic geometry, especially his fundamental contributions to the algebraic foundations of this subject.
August 1981: To Eberhard Hopf for three papers of fundamental and lasting importance: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential systems, Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Naturwissenschaftliche Klasse, volume 95 (1943), pp. 3-22; A mathematical example displaying features of turbulence, Communications on Applied Mathematics, volume 1 (1948), pp. 303-322; and The partial differential equation u_t + uu_x = u_{xx}, Communications on Pure and Applied Mathematics, volume 3 (1950), pp. 201-230.
August 1981: To Nelson Dunford and Jacob T. Schwartz for their expository book, Linear operators, Part I, General theory, 1958; Part II, Spectral theory, 1963; Part III, Spectral operators, 1971, Interscience Publishers, New York.
August 1980: To 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.
August 1980: To Harold M. Edwards for mathematical exposition in his books Riemann's zeta function, Pure and Applied Mathematics, number 58, Academic Press, New York and London, 1974; and Fermat's last theorem, Graduate Texts in Mathematics, number 50, Springer-Verlag, New York and Berlin, 1977.
August 1980: To Gerhard P. Hochschild for his significant work in homological algebra and its applications.
August 1979: To Antoni Zygmund for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis.
August 1979: To Robin Hartshorne for his expository research article Equivalence relations on algebraic cycles and subvarieties of small codimension, Proceedings of Symposia in Pure Mathematics, volume 29, American Mathematical Society, 1975, pp. 129-164; and his book Algebraic geometry, Springer-Verlag, Berlin and New York, 1977.
August 1979: To Joseph J. Kohn for his fundamental paper: Harmonic integrals on strongly convex domains. I, II, Annals of Mathematics, Series 2, volume 78 (1963), pp. 112-248 and volume 79 (1964), pp. 450-472.
January 1979: To Salomon Bochner for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry.
January 1979: To 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, Annals of Mathematics, Series 2, volume 64 (1956), pp. 514-522; An example of a smooth linear partial differential equation without solution, Annals of Mathematics, Series 2, volume 66 (1957), pp. 155-158; On hulls of holomorphy, Communications in Pure and Applied Mathematics, volume 13 (1960), pp. 587-591.
1976, 1977, 1978: No awards were made.
August 1975: To George W. Mackey for his paper, Ergodic theory and its significance for statistical mechanics and probability theory, Advances in Mathematics, volume 12 (1974), pp. 178-286.
August 1975: To H. Blaine Lawson for his paper, Foliations, Bulletin of the American Mathematical Society, volume 80 (1974), pp. 369-418.
January 1975: To Lipman Bers for his paper, Uniformization, moduli, and Kleinian groups, Bulletin of the London Mathematical Society, volume 4 (1972), pp. 257-300.
January 1975: To Martin D. Davis for his paper, Hilbert's tenth problem is unsolvable, American Mathematical Monthly, volume 80 (1973), pp. 233-269.
January 1975: To Joseph L. Taylor for his paper, Measure algebras, CBMS Regional Conference Series in Mathematics, Number 16, American Mathematical Society, 1972.
August 1972: To Edward B. Curtis for his paper, Simplicial homotopy theory, Advances in Mathematics, volume 6 (1971), pp. 107-209.
August 1972: To William J. Ellison for his paper, Waring's problem, American Mathematical Monthly, volume 78 (1971), pp. 10-36.
August 1972: To Lawrence F. Payne for his paper, Isoperimetric inequalities and their applications, SIAM Review, volume 9 (1967), pp. 453-488.
August 1972: To Dana S. Scott for his paper, A proof of the independence of the continuum hypothesis, Mathematical Systems Theory, volume 1 (1967), pp. 89-111.
August 1971: To James B. Carrell for his paper, written jointly with Jean A. Dieudonne, Invariant theory, old and new, Advances in Mathematics, volume 4 (1970), pp. 1-80.
August 1971: To Jean A. Dieudonné for his paper, Algebraic geometry, Advances in Mathematics, volume 3 (1969), pp. 223-321, and for his paper, written jointly with James B. Carrell, Invariant theory, old and new, Advances in Mathematics, volume 4 (1970), pp. 1-80.
August 1971: To Phillip A. Griffiths for his paper, Periods of integrals on algebraic manifolds, Bulletin of the American Mathematical Society, volume 76 (1970), pp. 228-296.
August 1970: To Solomon Lefschetz for his paper, A page of mathematical autobiography, Bulletin of the American Mathematical Society,volume 74 (1968), pp. 854-879.
