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Prize: Leroy P. Steele Prize (1970 - 1992)

Leroy P. Steele Prize (1970 - 1992) 1992 Jacques Dixmier; James Glimm; Peter D. Lax

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). 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. 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.]

Leroy P. Steele Prize (1970 - 1992) 1991 Jean-François Treves; Eugenio Calabi; Armand Borel

To Jean-François Treves for *Pseudodifferential and Fourier Integral Operators*, Volumes 1 and 2 (Plenum Press, 1980). To Eugenio Calabi for his fundamental work on global differential geometry, especially complex differential geometry.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.

Leroy P. Steele Prize (1970 - 1992) 1990 R. D. Richtmyer; Bertram Kostant; Raoul Bott

To R. D. Richtmyer for his book *Difference Methods for Initial-Value Problems* (Interscience, 1st Edition 1957 and 2nd Edition, with K. Morton, 1967). 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. 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.

Leroy P. Steele Prize (1970 - 1992) 1989 Daniel Gorenstein; Alberto P. Calderón; Irving Kaplansky

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. 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. 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.

Leroy P. Steele Prize (1970 - 1992) 1988 Sigurdur Helgason; Gian-Carlo Rota; Deane Montgomery

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). 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. 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.

Leroy P. Steele Prize (1970 - 1992) 1987 Martin Gardner; Herbert Federer; Wendell Fleming; Samuel Eilenberg

To Martin Gardner for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American. To Herbert Federer and Wendell Fleming for their pioneering paper, *Normal and integral currents*, Annals of Mathematics, volume 72 (1960), pp. 458-520. 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.

Leroy P. Steele Prize (1970 - 1992) 1986 Donald E. Knuth; Rudolf E. Kalman; Saunders Mac Lane

To Donald E. Knuth for his expository work, *The Art of Computer Programming*, 3 Volumes (1st Edition 1968, 2nd Edition 1973). 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. 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.

Leroy P. Steele Prize (1970 - 1992) 1985 Michael Spivak; Robert Steinberg; Hassler Whitney

To Michael Spivak for his five-volume set, *A Comprehensive Introduction to Differential Geometry* (second edition, Publish or Perish, 1979). 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). 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.

Leroy P. Steele Prize (1970 - 1992) 1984 Elias M. Stein; Lennart Carleson; Joseph L. Doob

To Elias M. Stein for his book, *Singular integrals and the differentiability properties of functions*, Princeton University Press (1970). 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. 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.

Leroy P. Steele Prize (1970 - 1992) 1983 Paul R. Halmos; Steven C. Kleene; Shiing-Shen Chern

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

Leroy P. Steele Prize (1970 - 1992) 1982 Lars V. Ahlfors; Tsit-Yuen Lam; John W. Milnor; Fritz John

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). 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). 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.

Leroy P. Steele Prize (1970 - 1992) 1981 Oscar Zariski; Eberhard Hopf; Nelson Dunford; Jacob T. Schwartz

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

Leroy P. Steele Prize (1970 - 1992) 1980 André Weil; Harold M. Edwards; Gerhard P. Hochschild

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. 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. To Gerhard P. Hochschild for his significant work in homological algebra and its applications.

Leroy P. Steele Prize (1970 - 1992) 1979 Antoni Zygmund; Robin Hartshorne; Joseph J. Kohn; Salomon Bochner; Hans Lewy

To Antoni Zygmund for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis. 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. 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. To Salomon Bochner for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry. 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.

Leroy P. Steele Prize (1970 - 1992) 1975 George W. Mackey; Blaine Lawson; Lipman Bers; Martin D. Davis; Joseph L. Taylor

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. To H. Blaine Lawson for his paper, *Foliations*, Bulletin of the American Mathematical Society, volume 80 (1974), pp. 369-418. To Lipman Bers for his paper, *Uniformization, moduli, and Kleinian groups*, Bulletin of the London Mathematical Society, volume 4 (1972), pp. 257-300. To Martin D. Davis for his paper, *Hilbert's tenth problem is unsolvable*, American Mathematical Monthly, volume 80 (1973), pp. 233-269.To Joseph L. Taylor for his paper, *Measure algebras*, CBMS Regional Conference Series in Mathematics, Number 16, American Mathematical Society, 1972.

Leroy P. Steele Prize (1970 - 1992) 1972 Edward B. Curtis; William J. Ellison; Lawrence E. Payne; Dana S. Scott

To Edward B. Curtis for his paper, *Simplicial homotopy theory*, Advances in Mathematics, volume 6 (1971), pp. 107-209. To William J. Ellison for his paper, *Waring's problem*, American Mathematical Monthly, volume 78 (1971), pp. 10-36. To Lawrence E. Payne for his paper, *Isoperimetric inequalities and their applications*, SIAM Review, volume 9 (1967), pp. 453-488. 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.

Leroy P. Steele Prize (1970 - 1992) 1971 James B. Carrell; Jean A. Dieudonné; Phillip A. Griffiths

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. To Jean A. Dieudonné for his paper, *Algebraic geometry*, Advances in Mathematics, volume 3 (1969), pp. 233-321, and for his paper, written jointly with James B. Carrell, *Invariant theory, old and new*, Advances in Mathematics, volume 4 (1970), pp. 1-80. 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.

Leroy P. Steele Prize (1970 - 1992) 1970 Solomon Lefschetz

To Solomon Lefschetz for his paper, *A page of mathematical autobiography*, Bulletin of the American Mathematical Society,volume 74 (1968), pp. 854-879.