Isadore Singer

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Isadore Singer
Isadore Singer 1977 (re-scanned 2; border-less) (cleaned).jpg
Singer in 1977
BornMay 3, 1924
DiedFebruary 11, 2021(2021-02-11) (aged 96)
Alma materUniversity of Michigan (BA)
University of Chicago (MS, PhD)
Known forAmbrose–Singer theorem
Atiyah–Singer index theorem
Atiyah–Hitchin–Singer theorem
Ray–Singer torsion
Kadison–Singer problem
Spouse(s)
Rosemary Singer
(m. 1956)
AwardsBôcher Memorial Prize (1969)
National Medal of Science (1983)
Wigner Medal (1988)
Steele Prize (2000)
Abel Prize (2004)
Scientific career
FieldsMathematics
InstitutionsMassachusetts Institute of Technology
University of California, Berkeley
Princeton University
Columbia University
University of California, Los Angeles
Doctoral advisorIrving Segal
Doctoral studentsRichard L. Bishop
Andrew Browder
David G. Ebin
Dan Freed
John Lott
Hugo Rossi
Linda Rothschild
Gerald Schwarz
Nancy K. Stanton
Frank W. Warner [de]

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[edit]

Early life and education[edit]

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.[7][8] Isadore was born with a prominent hemangioma birthmark under his right eye.[citation needed]

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.[7][9] 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.[7] Upon his return from military service, Singer studied mathematics for one year at the University of Chicago.[7] Although he initially intended to go back to physics, his interest in math was piqued, and he continued with the subject,[7] earning an M.S. in Mathematics in 1948 and a Ph.D. in Mathematics in 1950 under the supervision of Irving Segal.[2][3][1]

Career[edit]

Singer held a postdoctoral fellowship as a CLE Moore instructor at the Massachusetts Institute of Technology in 1950.[1] 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.[1] In 1979, he moved to the University of California, Berkeley as Miller Professor.[1] He returned to MIT in 1983 as the first John D. MacArthur Professor, before being appointed as an Institute Professor in 1987.[1]

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).[1] He was one of the founders of the independent non-profit Mathematical Sciences Research Institute, based in Berkeley, California.[7]

Singer died on February 11, 2021, at his home in Boxborough, Massachusetts. He was 96.[7]

Research[edit]

Partnering with British-Lebanese mathematician Michael Atiyah, Singer worked on creating a linkage between the fields of analysis, especially differential equations, and topology. While the consensus of the time was that the two fields could not be combined, Atiyah and Singer applied Atiyah's topological constructs to solve Singer's differential equation problems. This paved way to a field of mathematics called Index theory.[7] The development of the Atiyah-Singer index theorem relied upon the Dirac operator, where Singer rediscovered its importance to mathematics before the formulation of his famous contribution.[10]

In 1975, he worked with mathematician Jim Simons and physicist Yang Chen-Ning to extend the same construct to physics, drawing a linkage between gauge theory and fiber bundle.[7] This theory was a significant unification effort between pure mathematics and theoretical physics.[4][7]

With Richard V. Kadison, he proposed the Kadison–Singer problem in 1959,[10] 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.[11]

Awards and honors[edit]

Singer was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was a member of the Norwegian Academy of Science and Letters.[12] In 2012 he became a fellow of the American Mathematical Society.[13]

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,[14] the 2004 Gauss Lecture and the James Rhyne Killian Faculty Achievement Award from MIT (2005).[15]

Personal life[edit]

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 four children: Natasha, Eliot, Emily, and Annabelle.[7] Singer's brother Sidney was a particle physicist with Los Alamos National Laboratory in New Mexico and predeceased him in 2006.[7]

Works[edit]

References[edit]

  1. ^ a b c d e f g "Isadore Singer". math.mit.edu. Department of Mathematics, MIT. Retrieved February 15, 2021.
  2. ^ a b "Isadore M. Singer | Department of Mathematics at University of California Berkeley". math.berkeley.edu. Retrieved April 20, 2018.
  3. ^ a b "Singer biography". www-history.mcs.st-andrews.ac.uk. Retrieved April 20, 2018.
  4. ^ a b Devlin, Keith (April 2004). "Abel Prize Awarded: The Mathematicians' Nobel". Devlin's Angle. Mathematical Association of America.
  5. ^ MSRI. "Mathematical Sciences Research Institute". www.msri.org. Retrieved April 20, 2018.
  6. ^ "Shiing-Shen Chern". Institute for Advanced Study. Retrieved April 20, 2018.
  7. ^ a b c d e f g h i j k l m n Rehmeyer, Julie (February 12, 2021). "Isadore Singer, Who Bridged a Gulf From Math to Physics, Dies at 96". The New York Times. Retrieved February 12, 2021.
  8. ^ Holden, Helge; Piene, Ragni, eds. (2010). "2004: Sir Michael Atiyah and Isadore M. Singer". The Abel Prize : 2003-2007 : the first five years. Berlin: Springer Science+Business Media. p. 110. ISBN 9783642013737.
  9. ^ "Isadore Manuel Singer". MacTutor History of Mathematics Archive. University of St Andrews. Retrieved February 12, 2021 – via mathshistory.st-andrews.ac.uk.
  10. ^ a b Klarreich, Erica (November 24, 2015). "'Outsiders' Crack 50-Year-Old Math Problem". Quanta Magazine. Retrieved February 11, 2021.
  11. ^ Rehmeyer, Julie (February 12, 2021). "Isadore Singer, Who Bridged a Gulf From Math to Physics, Dies at 96". The New York Times. Retrieved February 12, 2021.
  12. ^ "Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy of Science and Letters. Archived from the original on November 10, 2013. Retrieved October 7, 2010.
  13. ^ List of Fellows of the American Mathematical Society, retrieved July 20, 2013.
  14. ^ "The Abel Prize". Abelprisen.no. Retrieved February 12, 2021.
  15. ^ http://www.maths.adelaide.edu.au/mathai.varghese/MIT_2006_fall%207.pdf