A bequest from Leroy P Steele endowed this prize which was first awarded in 1970. It was set up to honour George David Birkhoff, William Fogg Osgood, and William Caspar Graustein. From 1970 to 1976 the prize was given for outstanding published mathematical research, preference given to work which was broad and particularly well written. In 1976 the Council of the American Mathematical Society decided to award three categories of Leroy P Steele Prizes. These were Lifetime Achievement, Mathematical Exposition, and Seminal Contribution to Research. In 1994 the last of these three categories was put onto a five year cycle of topics: analysis, algebra, applied mathematics, geometry and topology, and discrete mathematics/logic. This last area would alternate between the two topics so that discrete mathematics would be the topic of the award once every ten years.

**1970** Solomon Lefschetz

... for his paper "A page of mathematical autobiography".

... for his paper written jointly with Jean A Dieudonne "Invariant theory, old and new".

... for his paper "Algebraic geometry", and for his paper, written jointly with James B Carrell "Invariant theory, old and new".

... for his paper "Periods of integrals on algebraic manifolds".

... for his paper "Simplicial homotopy theory".

... for his paper "Waring's problem".

... for his paper "Isoperimetric inequalities and their applications".

... for his paper "A proof of the independence of the continuum hypothesis".

... for his paper "Uniformization, moduli, and Kleinian groups".

... for his paper "Hilbert's tenth problem is unsolvable".

... for his paper "Measure algebras".

... for his paper "Ergodic theory and its significance for statistical mechanics and probability theory".

... for his paper "Foliations".

... for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry.

... 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".

... for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis.

... for his expository research article "Equivalence relations on algebraic cycles and subvarieties of small codimension", and his book "Algebraic geometry".

... for his fundamental paper "Harmonic integrals on strongly convex domains. I, II".

... 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.

... for mathematical exposition in his books "Riemann's zeta function", and Fermat's last theorem".

... for his significant work in homological algebra and its applications.

... for his work in algebraic geometry, especially his fundamental contributions to the algebraic foundations of this subject.

... 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 equationu_{t}+uu_{x}=u_{xx}".

... for their expository book "Linear operators", Part I, "General theory", Part II, "Spectral theory",1963, and Part III, "Spectral operators".

... for his expository work in "Complex analysis", and in "Lectures on quasiconformal mappings", and "Conformal invariants".

... for his expository work in his book "Algebraic theory of quadratic forms", and four of his papers "K_{0}andK_{1}-an introduction to algebraic K-theory", "Ten lectures on quadratic forms over fields", "Serre's conjecture", and "The theory of ordered fields".

... for a paper of fundamental and lasting importance "On manifolds homeomorphic to the7-sphere".

... 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.

... for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.

... 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".

... 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.

... ... for his book "Singular integrals and the differentiability properties of functions".

... 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".

... for his fundamental work in establishing probability as a branch of mathematics and for his continuing profound influence on its development.

... for his five-volume set "A Comprehensive Introduction to Differential Geometry".

... 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".

... 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.

... for his expository3-volume work "The Art of Computer Programming".

... 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".

... for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.

... for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American.

... for their pioneering paper "Normal and integral currents".

... 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.

... for his books "Differential Geometry and Symmetric Spaces", "Differential Geometry, Lie Groups, and Symmetric Spaces", and "Groups and Geometric Analysis".

... for his paper "On the foundations of combinatorial theory, I. Theory of Möbius functions".

... 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.

... 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".

... for his paper "Uniqueness in the Cauchy Problem for Partial Differential Equation".

... 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.

... for his book "Difference Methods for Initial-Value Problems".

... for his paper "On the existence and irreducibility of certain series of representations".

... 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.

... for "Pseudodifferential and Fourier Integral Operators", Volumes1and2.

... for his fundamental work on global differential geometry, especially complex differential geometry.

... 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.

... for his books "von Neumann Algebras(Algébres de von Neumann)", "C*-Algebras(Les C*-Algèbres et leurs Representations)", and "Enveloping Algebras(Algèbres Enveloppantes)".

... for his paper "Solution in the large for nonlinear hyperboic systems of conservation laws".

... 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.

... for his books "Principles of Mathematical Analysis", and "Real and Complex Analysis".

... for his paper "Strong rigidity of locally symmetric spaces".

... 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.

... for her book "Ten Lectures on Wavelets".

... for his proof of the Bieberbach Conjecture.

... for his numerous basic contributions to linear and nonlinear partial differential equations and their application to complex analysis and differential geometry.

... for his1970book "Cours d'Arithmétique", with its English translation "A Course in Arithmetic".

... 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 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 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.

... for the four volumes "Ramanujan's Notebooks, Parts I, II, III, and IV".

... for his book "Intersection Theory".

... 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".

... 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.

... 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.

... 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.

... 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).

... 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.

... for their joint paper "Rational functions certify combinatorial identities".

... for his books "The Arithmetic of Elliptic Curves", and "Advanced Topics in the Arithmetic of Elliptic Curves".

... 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.

... 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).

... for his remarkable paper "The embedding problem for Riemannian manifolds".

... for his many mathematics books. Among Lang's most famous texts are "Algebra" and "Algebraic Number Theory".

... Singer's series of five papers with Michael F Atiyah on the Index Theorem for elliptic operators(which appeared in1968-71)and his three papers with Atiyah and V K Patodi on the Index Theorem for manifolds with boundary(which appeared in1975-76)are among the great classics of global analysis.

... for his paper "Modular curves and the Eisenstein ideal".

... in recognition of his many expository contributions in automata, the theory of games, lattices, coding theory, group theory, and quadratic forms.

... for his many and deep contributions to probability theory and its applications.

... for the paper "A fast algorithm for particle simulations".

... in recognition of the completion of his two-volume work "Enumerative Combinatorics".

... for helping to weave the fabric of modern algebraic geometry, and to Elias Stein for making fundamental contributions to different branches of analysis.

... for the papers "Intersection homology theory", and "Intersection homology. II".

... for his book on harmonic analysis.

... 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.

... for his paper "The fine structure of the constructible hierarchy".

... for his paper "Categoricity in power".

... for his book "Bounded Analytic Functions".

... for greatly influencing mathematics in the broad sense throughout her long and distinguished career.

... 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".

... 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.

... for profoundly influencing many fields of research through his own work and through his interactions with other mathematicians and students.

... for his paper "Problems in the theory of automorphic forms". This is the paper that introduced what are now known as the Langlands conjectures.

... for his book "Convex Polytopes".

... 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.

... for their paper "Korteweg de Vries equation and generalizations. VI. Methods for exact solution".

... for his book "The Analysis of Linear Partial Differential Operators".

... for his rich and magnificent mathematical career and for his work in analysis, which has a strong orientation towards probability theory.

... 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".

... for his beautiful expository accounts of a host of aspects of algebraic geometry, including "The Red Book of Varieties and Schemes"(Springer,1988).

... for entirely reshaping representation theory, and, in the process, changing much of mathematics.

... for his paper "On sets of integers containing no k elements in arithmetic progression".

... for his book "Elliptic Partial Differential Equations of Second Order", written with the late David Gilbarg.

... one of the world's greatest mathematicians studying nonlinear partial differential equations.

... for his paper "Three-manifolds with positive Ricci curvature".

... for his book "Symmetric Functions and Hall Polynomials" .

... 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.

... for his book, "Commutative Algebra: With a View Toward Algebraic Geometry".

... for his construction of the "Monster" sporadic finite simple group.

... 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.

... for his long record of excellent exposition, both in books and in classroom notes.

... for her paper, "Orthonormal bases of compactly supported wavelets".

... for his many pioneering advances in the numerical solution of partial differential equations over the last half century.

... for their work, "The classification of finite simple groups: groups of characteristic2type"

... for his contributions to low dimensional topology, and in particular for a series of highly original papers, starting with "Hyperbolic structures on3-manifolds. I. Deformation of acylindrical manifolds(Ann. of Math.(2)124(1986), no.2,203246), that revolutionized3-manifold theory.

... for his pivotal role in shaping the theory of dynamical systems and for his groundbreaking contributions to ergodic theory, probability theory, statistical mechanics, and mathematical physics

... in recognition of their book, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields"

... 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 our fundamental knowledge in mathematics, particularly algebraic geometry, differential geometry, and differential equations.

... for their book A Course in Metric Geometry, in recognition of excellence in exposition and promotion of fruitful ideas in geometry.

... for their paper, "Partial regularity of suitable weak solutions of the Navier-Stokes equations." Communications Pure and Applied Math, vol35no6,771-831(1982).

... for his groundbreaking contributions to Lie Theory and its applications to Mathematics and Mathematical Physics.

... for his books "Positivity in Algebraic Geometry I and II", published in2004. These books were instant classics that have profoundly influenced and shaped research in algebraic geometry over the past decade.

... for his influential paper "Degrees of growth of finitely generated groups and the theory of invariant means," which appeared in Russian in1984in 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 his impact on the education and research of a generation of mathematical scientists through his significant research achievements, his highly influential books, and his mentoring of graduate students and postdocs.

... 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 two papers published in the Memoirs of the AMS in1983: "The existence of multidimensional shock fronts", Vol43, Number281, and "The stability of multidimensional shock fronts", Vol41, Number275.

... for his fundamental contributions to number theory and harmonic analysis, and in particular for his proof of the Arthur-Selberg trace formula.

... for their book J-holomorphic Curves and Symplectic Topology. It not only develops the topic from the basics, explaining essential notions and results in detail, but also describes many of the most spectacular results in this area.

... for his fundamental contributions to Geometric Analysis and in particular for his1983paper 'Asymptotics for a Class of Non-Linear Evolution Equations, with Applications to Geometric Problems', published in the Annals of Mathematics.

... for the breadth of his contributions made in the advancement of mathematics.

... for "Proofs from THE BOOK".

... for their paper "Cluster algebras I: Foundations," published in2002in the Journal of the American Mathematical Society.

History of the AMS

Presidents of the AMS

AMS Colloquium Lecturers

AMS Gibbs Lecturers

**AMS Prizes:**

AMS/SIAM Birkhoff Prize

AMS Bôcher Prize

AMS Cole Prize in Algebra

AMS Cole Prize in Number Theory

AMS Conant Prize

AMS Fulkerson Prize

AMS Satter Prize

AMS Steele Prize

AMS Veblen Prize

AMS Wiener Prize

**Other Web site:**

Index of Societies | Index of Honours, etc. |

Main index | Biographies Index |

JOC/EFR February 2019

The URL of this page is:

https://www-history.mcs.st-andrews.ac.uk/history/Societies/AMSSteelePrize.html