Isadore M. Singer

from Wikipedia, the free encyclopedia
Isadore Singer, 1977

Isadore Manuel Singer (born May 3, 1924 in Detroit , † February 11, 2021 in Boxborough , Massachusetts ) was an American mathematician at the Massachusetts Institute of Technology specializing in analysis .

Live and act

Isadore Singer was the child of Simon and Freda Singer, Polish immigrants. His father, who only spoke Yiddish, was a printer. His mother was a seamstress. Isadore quickly learned English and taught the language to his family. He had a brother, Sidney, who was a physicist who died in 2016.

Singer graduated from the University of Michigan and received his bachelor's degree in 1944. After three years in the US Army, he went to the University of Chicago , where he received his doctorate under Irving Segal in 1950 (Lie Algebras of unbounded operators) . After completing his doctorate, he became a Moore Instructor at the Massachusetts Institute of Technology (MIT) and an Assistant Professor at the University of California, Los Angeles (UCLA) in 1952 . In 1954/5 he was Visiting Assistant Professor at Columbia University and in 1955/56 at the Institute for Advanced Study . He was then an assistant professor and from 1958 associate professor at MIT, where he received a full professorship in 1959. From 1970 he was there “ Norbert Wiener Professor”. In 1977 he went to the University of California, Berkeley as a visiting professor and from 1979 as a full professor . In 1983 he returned to MIT.

Singer was a member of the National Academy of Sciences , since 1959 the American Academy of Arts and Sciences and since 1985 the American Philosophical Society . In 1969 he received the Bôcher Memorial Prize , in 1988 the Wigner Medal and in 2000 the Leroy P. Steele Prize of the American Mathematical Society (AMS), of which he was a fellow. In 1983 he received the National Medal of Science. In 1970/72 he was Vice President of the AMS. In 1974 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Vancouver (Eigenvalues ​​of the Laplacian and Invariants of Manifolds). In 2004 he gave the Gauss lecture of the German Mathematicians Association (DMV).

In 2004 he was awarded the Abel Prize together with Michael Francis Atiyah for the discovery and proof of the Atiyah-Singer index theorem . The work began in 1968 and was continued in the 1970s in collaboration with Vijay Kumar Patodi (index theorem for bounded manifolds ). Patodi also expanded the access to geometric information about a manifold (such as curvature ) discovered by Singer and Henry McKean via the core of the heat conduction equation ( Laplace operator ). Warren Ambrose and Singer's theorem connects the curvature form with the holonomy of the cohesive form in a main fiber bundle .

With Daniel Burrill Ray , he developed the theory of analytic torsion between 1971 and 1973 , which provides invariants of Riemannian manifolds , formed from the eigenvalues ​​of the Laplace operator.

The Kadison-Singer problem (1959) in the theory of operator algebras, solved in 2013 by Daniel Spielman and others, is named after him and Richard Kadison . With Kadison he founded the field of triangular operator algebras.

Singer also read regularly for beginners and wrote an introduction to topology and geometry. He was also interested in the connections between modern differential geometry and theoretical physics.

He was married to Sheila Ruff from 1961, with whom he had five children.

He died at home on February 11, 2021 at the age of 96.

His PhD students include Daniel Freed , Frank W. Warner , Nancy Stanton , Linda Rothschild , Hugo Rossi, and John Lott .


  • with S. Sternberg: The infinite groups of Lie and Cartan. I. The transitive groups. J. Analyze Math. 15 1965 1-114.
  • with H. McKean: Curvature and the eigenvalues ​​of the Laplacian. J. Differential Geometry 1 1967 no. 1, 43-69.
  • with M. Atiyah: The index of elliptic operators. Ann. of Math. (2) I : 87 1968 484-530. III : 87 1968 546-604. IV : 93 1971 119-138. V : 93 1971 139-149.
  • with D. Ray: R-torsion and the Laplacian on Riemannian manifolds. Advances in Math. 7, 145-210. (1971).
  • with D. Ray: Analytic torsion for complex manifolds. Ann. of Math. (2) 98: 154-177 (1973).
  • with M. Atiyah. V. Patodi: Spectral asymmetry and Riemannian geometry. Math. Proc. Cambridge Philos. Soc. I : 77: 43-69 (1975). II : 78 (1975) no. 3, 405-432. III : 79 (1976), no. 1, 71-99.
  • with S. Axelrod: Chern-Simons perturbation theory. II. J. Differential Geom. 39 (1994), no. 1, 173-213.
  • with J. Thorpe: Lecture notes on elementary topology and geometry, Springer 1967, Undergraduate Texts in Mathematics, 1976.


  • Interview in Joel Segel (Ed.), Recountings, Conversations with MIT mathematicians, AK Peters 2009.
  • S.-T. Yau (Ed.): The founders of index theory: reminiscences of Atiyah, Bott, Hirzebruch and Singer, International Press, Somerville 2003.
  • Interview with Atiyah and Singer, Mitteilungen DMV, 2004, No. 4.
  • Interview with Atiyah and Singer, Notices AMS, 2005, No. 2.

Web links

Individual evidence

  1. Isadore Singer, Who Bridged a Gulf From Math to Physics, this at 96 , New York Times, February 12, 2021; accessed on February 13, 2021
  2. Isadore M. Singer May 3, 1924 - Feb 11, 2021. In: MIT. Retrieved February 12, 2021 .
  3. ^ Mathematics Genealogy Project