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# Institute Professor Emeritus Isadore Singer, renowned mathematician who united math and physics, dies at 96

Singer arrived at MIT in 1950 as a CLE Moore Instructor working with Warren Ambrose and influenced by George Whitehead. Often, when they were working late on geometry as revolutionized by Chern, he and Ambrose would head over to Jack and Marion’s, then a popular deli on Harvard Street in Brookline, Massachusetts, to order rounds of corned beef sandwiches and coffee, and keep working until the early hours of the morning.

“What with interpreting my notes [from Chern’s University of Chicago lectures], reading Chern’s papers and Ambrose insisting on absolute clarity in every detail, we learned differential geometry together,” he said in a tribute to Ambrose. Equally important, “Ambrose taught me jazz.”

Between 1952 and 1956, Singer took appointments at UCLA, the Institute for Advanced Study, and Columbia University. He made deep contributions to analysis and geometry during this period.

In 1963 Singer’s career took a decisive turn during a sabbatical at Oxford University at the invitation of Michael Atiyah. Within the first day, Atiyah challenged Singer to look further into a well-established theorem in topology.

“What Michael had in mind are what are now known as integrality theorems, explaining why certain integrals are integers,” Singer later stated. Atiyah’s query was compelling to Singer, who couldn’t stop thinking about it. In six or so weeks, he approached Atiyah with an answer.

“Surprisingly, it involved analysis and the generalization of the Dirac operator to Riemannian spin manifolds,” Singer said. “I explained to Michael what I thought was going on and how most of the known integrality theorems fit together using the Dirac operator. It was not hard to conjecture the index formula; we obtained the proof of the index theorem in September.”

The major implications of their theorem would become clear only years later. Looking back, Singer would recall: “In 1962, while a Sloan Fellow … Michael Atiyah and I discovered an index theorem that combined topology, geometry, and elliptical partial differential operators in a new way. Our results extended, unified, and gave insights to some older theories. Exploring the consequences of this startling combination of different fields has kept us busy since then. Deep applications continue to be discovered. Some of the most interesting … are in high-energy theoretical physics. Mathematicians and physicists now realize the underlying gauge theories is the mathematical structure of fiber bundles. As a result, global geometry has applications to elementary particle physics, and at the same time, physicists are asking many new geometric questions. It is exciting to search for the answers.”

After the work on the index theorem, Singer’s career moved closer to the theoretical high-energy physics community, making numerous contributions there including to gauge theory, the theory of quarks, and anomaly cancellation.

His work garnered a tremendous number of distinctions. Singer was a Sloan Research Fellow from 1959 to 1962, and twice received a John D. Guggenheim fellowship in 1968 and 1975. In 1969 he received the Bôcher Memorial Prize from the American Mathematical Society. In 1985 he was awarded the National Medal of Science. The following year, Singer was selected for MIT’s highest faculty appointment as Institute Professor. In 1988 he received the Eugene Wigner Medal. In 1993, he was honored with the Distinguished Public Service Award, and in 2000 the Leroy P. Steele Prize for Lifetime Achievement, both by the American Mathematical Society. In 2004, Singer, jointly with Sir Michael Atiyah, received the Abel Prize from the Norwegian Academy of Science and Letters, and he was selected for the 2005 MIT James Rhyne Killian Faculty Achievement Award.

Singer was a fellow of the American Academy of Arts and Sciences (1959) and the American Mathematical Society (2012); a member of the American Philosophical Society (1985) and the National Academy of Sciences (1968); honorary member of the London Mathematical Society (2004); and foreign member of the Norwegian Academy of Science and Letters (2009).

Singer’s service to the mathematical and broader scientific community was also prodigious. He chaired the Committee of Science and Public Policy of the National Academy of Sciences from 1973 to 1979. He co-founded The Mathematical Sciences Research Institute (MSRI) in 1982 with Shiing-Shen Chern and Calvin Moore. From 1982 to 1988, Singer served on the White House Science Council. He was a member of the President’s Committee for selection of the National Medal of Science, ending in 1989. Between 1995 and 1999, he was on the governing board of the National Research Council.

Singer was equally committed to teaching. Singer advised many graduate student advisees — 31 from MIT and 2 from the University of California at Berkeley — and had nearly 200 mathematical descendants. Among these students were Dan Burns, Dan Freed, Dan Friedan, John Lott, Hugo Rossi, Linda Rothschild, and Nancy Stanton. He was a mentor to computer scientist Lenore Blum, helping her get into graduate school in 1963. Singer also influenced the budding young MIT student James Simons, who after a distinguished but short career in mathematics went on to found a hugely successful hedge fund.

Even late into his career, Singer insisted on teaching undergraduates, volunteering to work for several semesters as a teaching assistant for the introductory calculus course for first-year students at MIT. He liked to say that empathy made him a good teacher.

Singer is survived by his wife, Rosemarie Singer; four children, Eliot, Natasha, Emily, and Annabelle; two stepchildren, Giles and Melissa; and four grandchildren.