Saff received in 1964 his bachelor's degree from the Georgia Institute of Technology and in 1968 his PhD from the University of Maryland, College Park under Joseph L. Walsh with thesis Interpolation and Functions of Class H (k, a, 2).
At Vanderbilt University he is, since 2001, a professor and director of the Center for Constructive Approximation and was from 2004 to 2007 the Executive Dean of the College of Arts and Sciences.
and potential theory (minima of energy under boundary value constraints or external fields).
He was the coeditor, with Theodore J. Rivlin, of a volume of Joseph L. Walsh's Selected Works published in 2000.
He was elected in 2013 a Foreign Member of the Bulgarian Academy of Sciences and made in 1987 an Honorary Professor of the Zhejiang Normal University in China.