He studied at Stuyvesant High School, graduating in 1949, and was a member of the school's math team along with his brother Benjamin Widom (1944, 1948). Widom attended City College of New York until 1951, during which he was one of the winners of the William Lowell Putnam Mathematical Competition (1951). At the University of Chicago he obtained an M.S. (1952) and Ph.D., the latter on a thesis Embedding of AW*-algebras advised by Irving Kaplansky (1955).
He was appointed to the Department of Mathematics at the University of California, Santa Cruz in 1968 and became professor emeritus in 1994. He taught mathematics at Cornell University (1955–68) where he started his work on Toeplitz and Wiener-Hopf operators, partly inspired by Mark Kac. Widom was appointed in the Department of Mathematics at the University of California, Santa Cruz and became professor emeritus in 1994.
His research areas were in integral equations and operator theory, in particular the determination of the spectra of a semi-infinite Toeplitz matrix and Wiener-Hopf operators, and the asymptotic behavior of the spectra of various classes of operators. More recently, his mathematical contributions with his long term collaborator Craig Tracy have been recognized through the award of several prizes for their joint work on Tracy–Widom distribution functions for random matrices. They used integral operators to obtain explicit representations, in terms of Painlevé transcendents, of the limiting distributions of the largest and smallest eigenvalues in many models of random matrices (see Fredholm determinants).
These same distributions have since been shown to arise in numerous other physical models, in random growth models, and in asymptotic combinatorics. He is an honorary editor of Integral Equations and Operator Theory.
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Member American Mathematics Society.
Married Lois Sanow, March 20, 1955 (divorced September 1976). Children: Barbara, Jennifer, Steven. Married Linda Novick, May 26, 1985.