John Jay Gergen (St. Paul, Minnesota April 17, 1903 – Duke University Hospital 1967) was an American mathematician who introduced the Lebesgue–Gergen criterion for convergence of a Fourier series.
He received a B.A. from the University of Minnesota in 1925 and a Ph.D. from Rice University in 1928. From 1928 to 1930, as a National Research fellow, he visited Princeton, Oxford, the University of Paris and the University of Clermont. From 1930 to 1933 he was a Benjamin Pierce Instructor at Harvard University, and from 1933 to 1936 he was an assistant professor at the University of Rochester. He was the chairman of the Department of Mathematics at Duke University from 1937 to July 1966. His doctoral students include Walter Rudin. He had four sons, including presidential adviser and Harvard Kennedy School professor David Gergen and Swarthmore College psychology professor Kenneth J. Gergen.