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Jaffe attended Princeton University as an undergraduate obtaining a degree in chemistry, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics. He then returned to Princeton, obtaining a doctorate in physics.
For several years Jaffe was president of the International Association of Mathematical Physics, and later of the American Mathematical Society. He chaired the Council of Scientific Society Presidents.
Jaffe conceived the idea of the Clay Mathematics Institute and its programs, including the employment of research fellows and the Millennium Prizes in mathematics. The latter immediately captured public imagination worldwide. He served as a founding Member, a founding member of the Board, and the founding President of that organization.
Jaffe has associations with several other notable organizations, including his present role as Chair of the Board of the Dublin Institute for Advanced Studies, School of Theoretical Physics.
With James Glimm, he founded the subject called constructive quantum field theory. One of their major achievements was to show the mathematical compatibility of quantum theory, special relativity, and interaction. They did this by proving the existence of the first examples of non-linear, relativistic quantum fields with non-trivial scattering. Jaffe's work in several related fields of mathematics and physics is well-known, including contributions to gauge theory and to non-commutative geometry.
Awards and honors
Jaffe was married from 1971 to 1992 to Nora F. Crow (aka Nora Crow Jaffe), now a Professor of English Language and Literature at Smith College and an authority on the 18th-century Anglo-Irish satirist Jonathan Swift. Nora accompanied Jaffe on most of his national and international sojourns, including his stays at the ETH in Zürich and the IHES in Büres-sur-Yvette. She gave birth to Jaffe's daughter, Margaret Collins Jaffe, on September 10, 1986 at Beth Israel Hospital in Boston. Margaret graduated from Middlesex School and then, in 2010, from Wellesley College. She majored in Japanese and minored in English. She now lives with her mother in Northampton, Massachusetts.
In September 1992, Jaffe married Sarah Warren, who worked in the Mathematics Department at Harvard. The marriage lasted for nine years before ending in divorce. Sarah now lives in New Hampshire with her second husband, Michael Walsh. 
- Website of ACAP
- List of Fellows of the American Mathematical Society, retrieved 2013-01-26.
- Nora F. Crow and Margaret C. Jaffe, 6/12/13.
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