The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have been given since 1970, from a bequest of Leroy P. Steele, and were set up in honor of George David Birkhoff, William Fogg Osgood and William Caspar Graustein. The way the prizes are awarded was changed in 1976 and 1993, but the initial aim of honoring expository writing as well as research has been retained. The prizes of $5,000 are not given on a strict national basis, but relate to mathematical activity in the USA, and writing in English (originally, or in translation).
for his book Partial Differential Equations, published by the American Mathematical Society, Providence, RI, 1998 (first edition) and 2010 (second edition).
for their book Analytic Combinatorics, an authoritative and highly accessible compendium of its subject, which demonstrates the deep interface between combinatorial mathematics and classical analysis.
for their book Ideals, Varieties, and Algorithms, which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers in many fields.
for his books Positivity in Algebraic Geometry I and II, published in 2004. These books were instant classics that have profoundly influenced and shaped research in algebraic geometry over the past decade.
awarded to Yuri Burago, Dmitri Burago, and Sergei Ivanov for their book A Course in Metric Geometry, in recognition of excellence in exposition and promotion of fruitful ideas in geometry.
in recognition of their book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences, 42, Springer-Verlag, New York, 1983; reprinted with revisions and corrections, 1990).
for their work The classification of finite simple groups: groups of characteristic 2 type, Mathematical Surveys and Monographs, 172, American Mathematical Society, Providence, RI, 2011.
for his book Commutative Algebra: With a View Toward Algebraic Geometry (Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995. xvi+785 pp.)
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.
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.)
for his many mathematics books. Among Lang's most famous texts are Algebra [Addison-Wesley, Reading, MA, 1965; Second edition, 1984; Third edition, 1993, ISBN0-201-55540-9] and Algebraic Number Theory [Addison-Wesley, Reading, MA, 1970; Second edition, Graduate Texts in Mathematics, 110, Springer-Verlag, New York, 1994, ISBN0-387-94225-4].
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.
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.
for his books Principles of Mathematical Analysis, McGraw-Hill (1953, 1964, and 1976) and Real and Complex Analysis, McGraw-Hill (1966, 1974, and 1976).
for their paper "Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming," (published in 1995 in the Journal of the ACM).
for two papers: “The cohomology structure of an associative ring,” Ann. Math. 78 (1963), 267-288 and “On the deformation of rings and algebras,” Ann. Math. 79 (1964), 59-103.
for his highly original paper "Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms," published in 1986 in Inventiones Mathematicae.
for his fundamental contributions to Geometric Analysis and in particular for his paper Simon, Leon (1983). "Asymptotics for a Class of Non-Linear Evolution Equations, with Applications to Geometric Problems". The Annals of Mathematics. 118 (3): 525. doi:10.2307/2006981.
for his books "The existence of multidimensional shock fronts," Vol 43, Number 281, and "The stability of multidimensional shock fronts," Vol 41, Number 275. Both books appeared in the Memoirs of the AMS in 1983.
for his influential paper "Degrees of growth of finitely generated groups and the theory of invariant means," which appeared in Russian in 1984 in Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya and in English translation a year later. The paper stands as a landmark in the development of the now-burgeoning area of geometric group theory.
for their paper, "Partial regularity of suitable weak solutions of the Navier-Stokes equations." Communications Pure and Applied Math, vol 35 no 6, 771-831 (1982).
for his book, Classification Theory and the Number of Nonisomorphic Models (Studies in Logic and the Foundations of Mathematics, 92, North-Holland Publishing Co., Amsterdam–New York, 1978; 2nd edition, 1990).
for his contributions to low dimensional topology, and in particular for a series of highly original papers, starting with "Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds" (Ann. of Math. (2) 124 (1986), no. 2, 203–246), that revolutionized 3-manifold theory.
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. Natl. 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).
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.
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.
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 on 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.
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 American Mathematical Society 114 (1965) 514–538).
for his paper "Modular curves and the Eisenstein ideal" in Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, no. 47 (1978), 33-186.
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.
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.
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.
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.
for his paper Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, number 78, Princeton University Press (1973).
Leroy P. Steele Prizes awarded prior to 1993
1992 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).
1992 James Glimm for his paper, Solution in the large for nonlinear hyperbolic systems of conservation laws, Communications on Pure and Applied Mathematics, XVIII (1965), pp.697–715.
1992: 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.
1991: Jean-François Treves for Pseudodifferential and Fourier Integral Operators, Volumes 1 and 2 (Plenum Press, 1980).
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
1990 R. D. Richtmyer for his book Difference Methods for Initial-Value Problems (Interscience, 1st Edition 1957 and 2nd Edition, with K. Morton, 1967).
1990 Bertram Kostant for his paper, On the existence and irreducibility of certain series of representations, Lie Groups and their Representations (1975), pp.231–329.
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.
1989 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.
1989 Alberto Calderón for his paper Uniqueness in the Cauchy Problem for Partial Differential Equations, American Journal ofMathematics, volume 80 (1958), pp.16–36.
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.
1988 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).
1988 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.
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.
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, Annals of Mathematics, volume 72 (1960), pp.458–520.
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.
1986 Rudolf E. Kálmán 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.
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.
1985 Michael Spivak for his five-volume set, "A Comprehensive Introduction to Differential Geometry" (second edition, Publish or Perish, 1979).
1985 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).
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.
1984 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.
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.
1983 Paul R. Halmos for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.
1983 Stephen Cole 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.
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.
1982 Lars 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).
1982 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).
1982 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.
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.
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, 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.
1981 Nelson Dunford, 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.
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, 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.
1980 Gerhard Hochschild for his significant work in homological algebra and its applications.
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, 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.
1979 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.
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, 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 on Pure and Applied Mathematics, volume 13 (1960), pp.587–591.
1976, 1977, 1978: No awards were made.
1975 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.
1975 H. Blaine Lawson for his paper, Foliations, Bulletin of the American Mathematical Society, volume 80 (1974), pp.369–418.
1975 Lipman Bers for his paper, Uniformization, moduli, and Kleinian groups, Bulletin of the London Mathematical Society, volume 4 (1972), pp.257–300.
1971 Jean 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.
1971 Phillip A. Griffiths for his paper, Periods of integrals on algebraic manifolds, Bulletin of the American Mathematical Society, volume 76 (1970), pp.228–296.
1970 Solomon Lefschetz for his paper, A page of mathematical autobiography, Bulletin of the American Mathematical Society, volume 74 (1968), pp.854–879.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Topology is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Vladimir Igorevich Arnold was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem.
John Willard Milnor is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize and all three Steele prizes.
Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
Raoul Bott was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
Solomon Lefschetz was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
Élie Joseph Cartan was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems, and differential geometry. He also made significant contributions to general relativity and indirectly to quantum mechanics. He is widely regarded as one of the greatest mathematicians of the twentieth century.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists.
André Lichnerowicz was a French differential geometer and mathematical physicist. He is considered the founder of modern Poisson geometry.
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. The MSC is used by many mathematics journals, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The current version is MSC2020.
Bertram Kostant was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.
Alexander A. Beilinson is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017, he was elected to the National Academy of Sciences. In 2018, he received the Wolf Prize in Mathematics and in 2020 the Shaw Prize in Mathematics.
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Mikhail Mikhailovich Postnikov was a Soviet mathematician, known for his work in algebraic and differential topology.
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
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