Paul Bateman

Paul T. Bateman was a distinguished mathematician in the Department of Mathematics at the University of Illinois at Urbana-Champaign, where he specialized in number theory. He received his Ph.D. from the University of Pennsylvania in 1946, with a thesis on the representation of numbers as sums of three squares under the supervision of Hans Rademacher. Following postdoctoral positions at Yale University and the Institute for Advanced Study, Bateman joined the UIUC mathematics faculty in 1950. He served as department head from 1965 to 1980, guiding the department through significant growth, and retired as professor emeritus in 1989, remaining active in research and departmental activities thereafter.

Bateman's research encompassed a broad spectrum of analytic number theory, including sums of squares, the distribution of prime numbers, Beurling's generalized prime numbers, modular forms, geometric extrema, coefficients of cyclotomic polynomials, and arithmetic functions. He directed twenty Ph.D. dissertations and coauthored papers with more than twenty collaborators. Key contributions include the Bateman-Horn conjecture of 1962 with Roger A. Horn, which provides a heuristic asymptotic formula concerning the distribution of prime numbers represented by irreducible polynomials, and the New Mersenne conjecture of 1987 with John L. Selfridge and Samuel S. Wagstaff Jr. He coauthored the textbook Analytic Number Theory: An Introductory Course with Harold G. Diamond, published in 2004. Bateman played prominent roles in the American Mathematical Society, serving as associate secretary for sixteen years, a member of the board of trustees for four years, and on the Mathematical Reviews Committee for five years; he was also problems editor for The American Mathematical Monthly from 1986 to 1991. His enduring impact is reflected in the Paul T. Bateman Fellowship and Prize in Number Theory at UIUC, as well as international conferences held in his honor for his 70th and 90th birthdays. He organized regular number theory conferences at Illinois, fostering a vibrant research community.