Duffin obtained a
BSc in
physics at the
University of Illinois, where he was elected to
Sigma Xi in 1932. He stayed at Illinois for his
PhD, which was advised by
Harold Mott-Smith and
David Bourgin, producing a thesis entitled
Galvanomagnetic and Thermomagnetic Phenomena (1935). Duffin lectured at
Purdue University and Illinois before joining the
Carnegie Institute in
Washington, D.C. during
World War II. His wartime work was devoted to the development of
navigational equipment and
mine detectors. In 1946, he became professor of mathematics at
Carnegie Mellon University. In 1941, Duffin and
A. C. Schaeffer put forward a conjecture in metric diophantine approximation which was resolved in 2020 by
James Maynard and
Dimitris Koukoulopoulos. In 1967 Duffin joined with
Clarence Zener and Elmor Peterson to write
Geometric Programming which developed a branch of
mathematical programming by introducing a generalization of
polynomials to
posynomials for engineering applications. Impressed with its innovations, a reviewer wrote, "common sense, ingenuity and originality in applying first principles are still competitive with other creative forms of the intellect." The methods of
geometric programming are sometimes adapted for
convex optimization. Duffin would remain at Carnegie Mellon until his retirement in 1988. and to the
American Academy of Arts and Sciences in 1974. He was joint winner of the 1982
John von Neumann Theory Prize, and winner of
Sigma Xi's Monie A. Ferst Award for 1984 in recognition of his ability as a teacher and communicator. == Selected publications ==