Isadore Singer

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Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.<ref name="MIT-directory">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=":0">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=":1">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Singer is noted for his work with Michael Atiyah, proving the Atiyah–Singer index theorem in 1962, which paved the way for new interactions between pure mathematics and theoretical physics.<ref name=":2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In early 1980s, while a professor at Berkeley, Singer co-founded the Mathematical Sciences Research Institute (MSRI) with Shiing-Shen Chern and Calvin Moore.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite news</ref>

BiographyEdit

Early life and educationEdit

Singer was born on May 3, 1924, in Detroit, Michigan, to Polish Jewish immigrants. His father Simon was employed as a printer and only spoke Yiddish, and his mother, Freda (Rosemaity), worked as a seamstress. Singer learned English swiftly and subsequently taught it to the rest of his family.<ref name="NYT obit">Template:Cite news</ref><ref name="Holden-2010">Template:Cite book</ref>

Singer studied physics at the University of Michigan, graduating in 1944 after just two-and-a-half years so that he could join the military.<ref name="NYT obit"/><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> He was stationed in the US Army in the Philippines, where he was a radar officer. During the daytime, he operated a communications school for the Philippine Army. He undertook correspondence courses in mathematics at night in order to satisfy the prerequisites for relativity and quantum mechanics.<ref name="NYT obit"/> Upon his return from military service, Singer studied mathematics for one year at the University of Chicago.<ref name="NYT obit"/> Although he initially intended to go back to physics, his interest in math was piqued, and he continued with the subject,<ref name="NYT obit"/> earning an M.S. in Mathematics in 1948 and a Ph.D. in Mathematics in 1950 under the supervision of Irving Segal.<ref name=":0" /><ref name=":1" /><ref name="MIT-directory"/>

CareerEdit

Singer held a postdoctoral fellowship as a CLE Moore instructor at the Massachusetts Institute of Technology in 1950.<ref name="MIT-directory"/> After appointments at the University of California, Los Angeles, Columbia University, and Princeton University, he returned to MIT as a professor in 1956 and was appointed as the Norbert Wiener Professor from 1970 to 1979.<ref name="MIT-directory"/> In 1979, he moved to the University of California, Berkeley as Miller Professor.<ref name="MIT-directory"/> He returned to MIT in 1983 as the first John D. MacArthur Professor, before being appointed as an Institute Professor in 1987.<ref name="MIT-directory"/>

Singer was chair of the Committee of Science & Public Policy of the United States National Academy of Sciences, a member of the White House Science Council (1982–88), and on the Governing Board of the United States National Research Council (1995–99).<ref name="MIT-directory"/> He was one of the founders of the independent non-profit Mathematical Sciences Research Institute, based in Berkeley, California.<ref name="NYT obit" />

Singer died on February 11, 2021, at his home in Boxborough, Massachusetts. He was 96.<ref name="NYT obit"/>

ResearchEdit

Partnering with British-Lebanese mathematician Michael Atiyah, Singer created a linkage between the fields of analysis, especially differential equations, and topology. In particular, they resolved a conjecture of Israel Gelfand's on how topological constructs could count the number of solutions of differential equations. The Atiyah–Singer index theorem, as it is now known, opened a new field of mathematics called index theory.<ref name="NYT obit" /> The development of their work made use of the Dirac operator, the general geometric construction of which was a notable new discovery. It is sometimes called the Atiyah–Singer operator in their honor.<ref>Lawson and Michelsohn. Spin geometry.</ref> In discussions between mathematician Jim Simons and physicist Yang Chen-Ning in the 1970s, it was found that the Atiyah–Singer theorem has a number of applications to physics.<ref name=":2" /><ref name="NYT obit" />

With Richard V. Kadison, he proposed the Kadison–Singer problem in 1959,<ref name=":3">Template:Cite news</ref> Inspired by quantum mechanics, it turned out to have reformulations in engineering and computer science. It was finally proved in 2013.<ref name="NYT obit" />

Singer also developed analytic torsion with D.B. Ray and with Henry McKean introduced heat equation formulae to the Atiyah–Singer index theorem.<ref name="NYT obit" /> Singer's other notable contributions in mathematics include the Ambrose–Singer holonomy theorem and the McKean–Singer theorem.<ref name="NYT obit2">Template:Cite news</ref>

Awards and honorsEdit

Singer was a member of the National Academy of Sciences,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> the American Philosophical Society,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> and the American Academy of Arts and Sciences.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> He was a member of the Norwegian Academy of Science and Letters.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In 2012 he became a fellow of the American Mathematical Society.<ref>List of Fellows of the American Mathematical Society, retrieved July 20, 2013.</ref>

Among the awards he has received are the Bôcher Memorial Prize (1969) from the American Mathematical Society, the National Medal of Science (1983), the Eugene Wigner Medal (1988), the Steele Prize for Lifetime Achievement (2000) from the American Mathematical Society, the Abel Prize (2004) shared with Michael Atiyah,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> the 2004 Gauss Lecture and the James Rhyne Killian Faculty Achievement Award from MIT (2005).<ref name="Brown 2005 MIT Killian Award">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Personal lifeEdit

Singer's first marriage was to Sheila Ruff, a play therapist for disabled children; they later divorced. His second marriage was to Rosemarie Singer, and they remained married until his death. He had five children: Stephen (born visually impaired), Eliot, and Natasha (with Sheila); Emily, and Annabelle (with Rosemarie).<ref name="NYT obit"/> Singer's brother Sidney was a particle physicist with Los Alamos National Laboratory in New Mexico and predeceased him in 2016.<ref name="NYT obit" />

WorksEdit

ReferencesEdit

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