# Arthur Jaffe

## Arthur Jaffe grew up in Pelham, NY, where he attended the local schools and enjoyed music and science. As a Princeton undergraduate he majored in chemistry, graduating summa cum laude and with highest honors.

## In 1953, while Arthur was still in high school, the Royal Society of Medicine invited his parents to visit and inducted his father as a member. Souvenirs from that trip aroused Arthur's interest to study abroad, and six years later Arthur became a Marshall Scholar and a student at Clare College, Cambridge. He studied mathematics there, and two years later returned to Princeton, to earn his doctorate working with Arthur Wightman—thereby completing degrees in three subjects: chemistry, mathematics, and physics. During his graduate training, Arthur was lucky to spend the 1963-1964 academic year with his advisor as one of the first students at the newly-founded Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, France.

## While in Bures, he began to investigate the question: “Is quantum theory compatible with special relativity and interaction?” Another version of this question is: Does “quantum field theory” make mathematical sense? Over the next years he solved this problem in space-time of less than four dimensions, in a long series of papers, many together with J. Glimm and other collaborators. This work gave the basis to the subject known as *constructive quantum field theory*, work for which they received the Heinemann Prize and other recognition. Some related scientific questions were also resolved by this work: In particular, they established a mathematical foundation for the *theory of renormalization*, independent from perturbation theory. Another advance was to prove multiple solutions (phases) exist in quantum field theory.

## Arthur Jaffe is also interested in super-symmetry, field theory on curved space, and the possible role in physics of non-commutative geometry, a new subject to which he has also contributed mathematically. He is also interested in the philosophical foundations of mathematical proof and fundamental issues in science.

## Recently Jaffe began work with Zhengwei Liu and others in another area: developing new picturial languages for mathematics, especially suitable for quantum information.

## After spending a year at Stanford and the Institute for Advanced Study, he came to Harvard University as assistant professor in 1967, becoming Professor of Physics in 1970. He joined the Department of Mathematics in 1973, and in 1985 he succeeded George Mackey as the “Landon Clay Professor of Mathematics and Theoretical Science.” He served as visiting professor at several institutions, including Princeton University, Rockefeller University, Boston University, the Swiss Federal Institute of Technology, and the University of Rome La Sapienza.

## In 1976 Jaffe co-founded a series of Cargèse, Corsica summer schools in mathematical physics. In 2001 he established a mathematics program for talented high school students. He played an important role in enabling the 2001 International Mathematics Olympiad to take place in the United States.
Beginning in 1999 he assisted Martin Seligman and the American Psychological Foundation in initiating the Pinnacle Project for gifted children.

## He has been adept in recognizing and encouraging exceptional research talent at an early stage. In the summer of 1968, Jaffe came as Guest Professor to the E.T.H. Zurich. Shortly afterward Robert Schrader, Konrad Osterwalder, and Jürg Fröhlich came to work at Harvard, beginning a long-lasting collaboration in mathematical physics between these two institutions. Over the years, Arthur has worked with over fifty graduate students and postdoctoral fellows.

## Jaffe served for twenty one years as Chief Editor of *Communications in Mathematical Physics, *broadening its scope and cementing its role as the leading journal in mathematical physics. He appointed and collaborated with over thirty editors during that period. He served for three years as Chair of the Harvard Mathematics Department, and for six years as President of the International Association of Mathematical Physics (approximately 1,000 members). As president of the American Mathematical Society (approximately 30,000 members), the Executive Director remarked that he “redefined” the role of president. He later served as Chair of the Council of Scientific Society Presidents (comprising some 60 Societies).

## Jaffe conceived the Clay Mathematics Institute, serving as a Founding Member and Director, as well as its Founding President. In this role he designed and implemented most of their initial programs, including the *Millennium Prize Problems* in mathematics.

## In 2005 Arthur Jaffe succeeded Sir Michael Atiyah as Chair of the Board of the Dublin Institute for Advanced Study, School of Theoretical Physics.

## He is a member of the American Academy of Arts and Sciences and of the U.S. National Academy of Sciences. He is also an Honorary Member of the Royal Irish Academy.