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