Buck was born in Cincinnati.[3] He studied at the University of Cincinnati and then earned his PhD in 1947[3] at Harvard University under David Widder and Ralph Boas with dissertation Uniqueness, Interpolation and Characterization Theorems for Functions of Exponential Type. For three years he was an assistant professor at Brown University, before he became in 1950 an associate professor at the University of Wisconsin, Madison, where he was promoted to professor in 1954. In 1973, he became the acting director of the University of Wisconsin Army Mathematics Research Center when J. Barkley Rosser retired.[4] At Madison he became in 1980 "Hilldale Professor" and from 1964 to 1966 he was chair of the mathematics department. In 1990 he retired as professor emeritus but remained mathematically active.[3]
^American Mathematical Monthly, Vol.87, 1980, pp. 335–345. Reprinted in Marlow Anderson, Victor Katz, Robin Wilson (eds.) Sherlock Holmes in Babylon and other tales of mathematical history, MAA 2004