Isadore Singer
Singer in 1977
Born	May 3, 1924 Detroit, Michigan, US
Died	February 11, 2021(2021-02-11) (aged 96) Boxborough, Massachusetts, US
Alma mater	University of Michigan (BA) University of Chicago (MS, PhD)
Known for	Ambrose–Singer theorem Atiyah–Singer index theorem Atiyah–Hitchin–Singer theorem Ray–Singer torsion Kadison–Singer problem
Spouse	Rosemary Singer ​ (m. 1956)​
Awards	Bôcher Memorial Prize (1969) National Medal of Science (1983) Wigner Medal (1988) Steele Prize (2000) Abel Prize (2004)
Scientific career
Fields	Mathematics
Institutions	Massachusetts Institute of Technology University of California, Berkeley Princeton University Columbia University University of California, Los Angeles
Doctoral advisor	Irving Segal
Doctoral students	Richard L. Bishop Andrew Browder David G. Ebin Dan Freed John Lott Hugo Rossi Linda Rothschild Gerald Schwarz Nancy K. Stanton Frank W. Warner

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.^[1][2][3]

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.^[4] In early 1980s, while a professor at Berkeley, Singer co-founded the Mathematical Sciences Research Institute (MSRI) with Shiing-Shen Chern and Calvin Moore.^[5][6]

Biography

Research

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.^[7] 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.^[10] 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.^[4][7]

With Richard V. Kadison, he proposed the Kadison–Singer problem in 1959,^[11] Inspired by quantum mechanics, it turned out to have reformulations in engineering and computer science. It was finally proved in 2013.^[7]

Singer also developed analytic torsion with D.B. Ray and with Henry McKean introduced heat equation formulae to the Atiyah–Singer index theorem.^[7] Singer's other notable contributions in mathematics include the Ambrose–Singer holonomy theorem and the McKean–Singer theorem.^[12]

Awards and honors

Singer was a member of the National Academy of Sciences,^[13] the American Philosophical Society,^[14] and the American Academy of Arts and Sciences.^[15] He was a member of the Norwegian Academy of Science and Letters.^[16] In 2012 he became a fellow of the American Mathematical Society.^[17]

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,^[18] the 2004 Gauss Lecture and the James Rhyne Killian Faculty Achievement Award from MIT (2005).^[19]

Personal life

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).^[7] Singer's brother Sidney was a particle physicist with Los Alamos National Laboratory in New Mexico and predeceased him in 2016.^[7]

Works

• Kadison, Richard V.; Singer, I. M. (1952). "Some Remarks on Representations of Connected Groups". Proceedings of the National Academy of Sciences of the United States of America. 38 (5): 419–423. Bibcode:1952PNAS...38..419K. doi:10.1073/pnas.38.5.419. ISSN 0027-8424. PMC 1063576. PMID 16589115.
• Singer, I. M. (1952). "Uniformly Continuous Representations of Lie Groups". Annals of Mathematics. 56 (2): 242–247. doi:10.2307/1969797. ISSN 0003-486X. JSTOR 1969797.
• Ambrose, W.; Singer, I. M. (1953). "A Theorem on Holonomy". Transactions of the American Mathematical Society. 75 (3): 428–443. doi:10.2307/1990721. ISSN 0002-9947. JSTOR 1990721.
• Arens, Richard; Singer, I. M. (1954). "Function Values as Boundary Integrals". Proceedings of the American Mathematical Society. 5 (5): 735–745. doi:10.2307/2031858. ISSN 0002-9939. JSTOR 2031858.
• Atiyah, M. F.; Singer, I. M. (1968). "The Index of Elliptic Operators: I". Annals of Mathematics. 87 (3): 484–530. doi:10.2307/1970715. ISSN 0003-486X. JSTOR 1970715.
• Atiyah, M. F.; Singer, I. M. (1968). "The Index of Elliptic Operators: III". Annals of Mathematics. 87 (3): 546–604. doi:10.2307/1970717. ISSN 0003-486X. JSTOR 1970717.
• Atiyah, M. F.; Singer, I. M. (1971). "The Index of Elliptic Operators: IV". Annals of Mathematics. 93 (1): 119–138. doi:10.2307/1970756. ISSN 0003-486X. JSTOR 1970756.
• Ray, D. B.; Singer, I. M. (1973). "Analytic Torsion for Complex Manifolds". Annals of Mathematics. 98 (1): 154–177. doi:10.2307/1970909. ISSN 0003-486X. JSTOR 1970909.

References