Duren received in 1956 his bachelor's degree from Harvard University and in 1960 his PhD from MIT under Gian-Carlo Rota with thesis Spectral theory of a class of non-selfadjoint infinite matrix operators. As a postdoc he was an instructor at Stanford University. At the University of Michigan, he became in 1962 an assistant professor, in 1966 an associate professor, in 1969 a professor, and in 2010 a professor emeritus.
Duren was in 1968/69 at the Institute for Advanced Study, in 1975 a visiting professor at the Technion in Haifa, in 1964/65 a visiting scientist at Imperial College and the University of Paris-Sud in Orsay, in 1982 a visiting professor at the University of Maryland and in 1982/83 at the Mittag-Leffler Institute, the University of Paris-Sud and at the ETH Zürich. In 1989 he was a visiting scientist at Stanford University, in 1993 at the University of Hawaii and in 1996 at the Norwegian Institute of Technology in Trondheim. He has also been a visiting scientist in Halle, at the Max-Planck Institute in Leipzig, at the University of Witwatersrand, in Santiago de Chile, at the Autonomous University of Madrid, at Bar-Ilan University and the Academia Sinica in Beijing.
Duren's research and expository writing deals with function theory and functional analysis, including Hardy spaces, schlicht functions, harmonic analysis, geometric function theory, potential theory, and special functions.
- Invitation to classical analysis, American Mathematical Society 2012
- Harmonic maps in the plane, Cambridge University Press 2004
- with Alexander Schuster: Bergman Spaces, American Mathematical Society 2004
- as editor with the assistance of Richard A. Askey and Uta C. Merzbach: A century of mathematics in America, 3 vols., American Mathematical Society 1988 (Centenary of the AMS)
- Univalent Functions, Grundlehren der mathematischen Wissenschaften, Springer Verlag 1983
- Theory of -Spaces, Academic Press 1970, Dover 2000
- biographical information from American Men and Women of Science, Thomson Gale 2004
- Peter Duren at the Mathematics Genealogy Project
- Rochberg, Richard (2005). "Review: Bergman spaces, by Peter Duren and Alex Schuster". Bull. Amer. Math. Soc. (N.S.) 42 (2): 251–256.
- Dauben, Joseph W. (Dec 1991). "Review: A century of mathematics in America, by Peter Duren; Richard A. Askey; Uta C. Hagen". Isis 82 (4): 765–768.
- Baernstein II, Albert (1985). "Review: Univalent functions, by Peter L. Duren". Bull. Amer. Math. Soc. (N.S.) 12 (1): 158–165.