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

Isadore Institute Professor Emeritus M. Singer, a hugely influential figure in 20th-century science whose work united mathematics and physics, died Feb. 11. He was 96 years old.

In a career that spanned more than 50 years, Singer not only profoundly influenced the development of mathematics, but discovered connections between mathematics and physics that led to the creation of a new field, theory. clues. Singer has received numerous awards and honors for his pioneering work, including the National Medal of Science and the Abel Prize, often considered the Nobel Prize in mathematics.

Among his greatest achievements, Singer and Richard Kadison formulated the Kadison-Singer conjecture in 1959 as part of their work on formalizing the foundations of quantum mechanics by English physicist Paul Dirac. It was later found to be equivalent to key problems in applied mathematics, engineering, and theoretical computer science and was not proven until 2013, more than half a century after it was first posed.

In 1963, Singer and Michael Atiyah made an even deeper connection to the Atiyah-Singer index theorem. This theorem has deeply and irremediably linked the mathematical fields of analysis, geometry, topology. A key part of their work was Singer’s rediscovery and generalization of the Dirac operator, fundamental to understanding the quantum theory of the electron. The newly generalized Dirac operator revealed deep mathematical mysteries, setting mathematics and physics on a collision course that continues to play out to this day.

Since arriving at MIT in 1950, Singer has always credited the Institute with giving him the freedom to pursue this interdisciplinary research. For years, his famous weekly physics-mathematics seminar served as a breeding ground for new ideas, inspiring new collaborations between mathematicians and physicists.

Its success is all the more remarkable in that its beginnings are modest. Born on May 3, 1924, to Polish immigrants, Singer grew up in Detroit during the Great Depression in a home where money was tight. Her father was a printer and her mother a seamstress; his younger brother, Sidney Singer, would later become a particle physicist at Los Alamos National Laboratory.

Singer attended the University of Michigan on a scholarship, where he worked in Professor Harrison Randall’s spectroscopy lab. He often recalled how he sold the weekly football tickets that Michigan students received to pay for his food. After graduating, he served as a lieutenant in the Signal Corps in the Philippines, before attending graduate school.

Singer’s drive to understand physics through mathematics was already formed by this time. “My penchant for intellectual pursuits was encouraged by my teachers of English and chemistry at Central High School in Detroit. I majored in physics at the University of Michigan (1941-1944) but I regret not taking advantage of their wonderful math department,” Singer said in a 1979 Smithsonian lecture. Having failed, I concluded that I needed a year of math before returning to physics, and became a graduate student at the University of Chicago in 1947. [one] year spanning a [lifetime].”

Singer graduated from the University of Chicago with an M.A. (1948) and Ph.D. (1950) in mathematics, under Irving Segal. Later, he attributed his strong background in analysis to Segal’s instructions. During Singer’s final year of graduate school, mathematician Shiing-Shen Chern arrived from Europe to introduce American researchers to the latest advances in geometry. Singer took notes from Chern’s class that were to prove essential in developing his differential geometry research program at MIT.

Singer arrived at MIT in 1950 as a CLE Moore instructor working with Warren Ambrose and influenced by George Whitehead. Often, when working late on the geometry Chern revolutionized, he and Ambrose would go to Jack and Marion, then a popular grocery store on Harvard Street in Brookline, Massachusetts, to order corned beef sandwiches and coffee, and carry on. to work. until the wee hours of the morning.

“What about the interpretation of my notes [from Chern’s University of Chicago lectures], reading Chern and Ambrose’s papers 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 was appointed to UCLA, the Institute for Advanced Study, and Columbia University. He made profound 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. From day one, Atiyah challenged Singer to explore a well-established theorem in topology.

“What Michael had in mind were what are now called integrality theorems, explaining why some integrals are integers,” Singer later said. Atiyah’s question was compelling to Singer, who couldn’t stop thinking about it. In about six weeks, he approached Atiyah with an answer.

“Amazingly, this involved analyzing and generalizing 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 completeness theorems fit together using the Dirac operator. It wasn’t hard to guess the formula for the index; we obtained the proof of the index theorem in September.

The main implications of their theorem would only become clear years later. In retrospect, Singer would recall, “In 1962, when a Sloan Fellow…Michael Atiyah and I discovered an index theorem that combined elliptical topology, geometry, and partial differential operators in a new way. Our results have extended, unified and provided insight into some older theories. Exploring the consequences of this surprising combination of different fields has occupied us ever since. Deep applications continue to be discovered. Some of the most interesting … are in theoretical high energy physics. Mathematicians and physicists now realize that underlying gauge theories are the mathematical structure of fiber bundles. As a result, global geometry has applications to elementary particle physics, and at the same time physicists pose many new geometric questions. It’s exciting to search for the answers.

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

His work has earned him an impressive number of accolades. 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 nomination as a professor of the Institute. In 1988, he received the Eugène Wigner Medal. In 1993 he received the Distinguished Public Service Award and in 2000 the Leroy P. Steele Prize for Lifetime Achievement, both awarded by the American Mathematical Society. In 2004, Singer, together with Sir Michael Atiyah, received the Abel Prize from the Norwegian Academy of Sciences and Letters, and he was shortlisted for the MIT James Rhyne Killian Faculty Achievement Award 2005.

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

Singer’s service to the wider mathematical and scientific community has also been prodigious. He chaired the Science and Public Policy Committee 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 Presidential Committee for the selection of the National Medal of Science, which ended in 1989. Between 1995 and 1999, he served on the board of directors of the National Research Council.

Singer was also engaged in teaching. Singer advised numerous graduate students – 31 from MIT and 2 from the University of California, 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 mentored computer scientist Lenore Blum, helping her enter graduate school in 1963. Singer also influenced budding young MIT student James Simons, who after a brilliant but short career in mathematics , went on to an extremely successful career in finance and philanthropy. .

Even late in his career, Singer insisted on teaching undergraduates, volunteering to work for several semesters as a teaching assistant for the introductory freshman calculus course 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.

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