for his work in functional analysis and rings, especially for collaborating with Leonard Gillman on one of the standard texts in the field, Rings of Continuous Functions D.J. Lewis (Ph.D. 1950), mathematician specializing in number theory; chaired the Department of Mathematics at the University of Michigan (1984–1994); director of the Division of Mathematical Sciences at the National Science Foundation James Raymond Munkres, professor emeritus of mathematics at MIT, author of classic textbook Topology Ralph S. Phillips (Ph.D.), mathematician; academic; known for his contributions to functional analysis, scattering theory, and servomechanisms Leonard Jimmie Savage (BS 1938, Ph.D. 1941), author of The Foundations of Statistics (1954); rediscovered Bachelier and introduced his theories to Paul Samuelson, who corrected Bachelier and used his thesis on randomness to advance derivative pricing theory Joel Shapiro (Ph.D.), mathematician; leading expert in the field of composition operators Isadore M. Singer (BA 1944), winner of the Abel Prize, the "Nobel of mathematics", and the Bôcher Memorial Prize Stephen Smale (BS 1952, MS 1953, Ph.D. 1957), Fields Medal winner; winner of the 2007 Wolf Prize in mathematics; 1965 Veblen Prize for Geometry, awarded every five years by the American Mathematical Society; 1988 Chauvenet Prize from the Mathematical Association of America; 1989 Von Neumann Award from the Society for Industrial and Applied Mathematics George W. Snedecor (MA 1913), mathematician and statistician Edwin Henry Spanier (Ph.D. 1947), mathematician at the University of California at Berkeley, working in algebraic topology Frank Spitzer (BA, Ph.D.), mathematician who made fundamental contributions to probability theory, including the theory of random walks, fluctuation theory, percolation theory, and especially the theory of interacting particle systems; his first academic appointments were at the California Institute of Technology (1953–1958); most of his academic career was spent at Cornell University, with leaves at the Institute for Advanced Study in Princeton and the Mittag-Leffler Institute in Sweden Norman Steenrod (A.B. 1932), algebraic topologist, author of The Topology of Fiber Bundles; believed to have coined the phrase "abstract nonsense," used in category theory Clarence F. Stephens (Ph.D.), ninth African American to receive a Ph.D. in mathematics; credited with inspiring students and faculty at SUNY Potsdam to form the most successful United States undergraduate mathematics degree programs in the past century Robert Simpson Woodward (A.B. 1872); professor of mechanics, mathematical physics at Columbia (1899–1904); President of the American Mathematical Society (1899–1900); in 1904 became president of the newly formed Carnegie Institution Cornelia Strong (M.A.