Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus
Institute Professor
An institute is an organisational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or can also be a professional body.
In some countries, institutes can ...
in the
Department of Mathematics
Department may refer to:
* Departmentalization, division of a larger organization into parts with specific responsibility
Government and military
*Department (administrative division), a geographical and administrative division within a country, ...
at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
and a Professor Emeritus of Mathematics at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
.
Singer is noted for his work with
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...
, proving the
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...
in 1962, which paved the way for new interactions between
pure mathematics
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...
and
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
.
In early 1980s, while a professor at Berkeley, Singer co-founded the
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califo ...
(MSRI) with
Shiing-Shen Chern
Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
and
Calvin Moore.
Biography
Early life and education
Singer was born on May 3, 1924, in
Detroit
Detroit ( , ; , ) is the largest city in the U.S. state of Michigan. It is also the largest U.S. city on the United States–Canada border, and the seat of government of Wayne County. The City of Detroit had a population of 639,111 at th ...
,
Michigan
Michigan () is a state in the Great Lakes region of the upper Midwestern United States. With a population of nearly 10.12 million and an area of nearly , Michigan is the 10th-largest state by population, the 11th-largest by area, and the ...
, to Polish Jewish immigrants. His father Simon was employed as a printer and only spoke
Yiddish
Yiddish (, or , ''yidish'' or ''idish'', , ; , ''Yidish-Taytsh'', ) is a West Germanic language historically spoken by Ashkenazi Jews. It originated during the 9th century in Central Europe, providing the nascent Ashkenazi community with a ver ...
, and his mother, Freda (Rosemaity), worked as a seamstress. Singer learned English swiftly and subsequently taught it to the rest of his family.
Isadore was born with a prominent
hemangioma
A hemangioma or haemangioma is a usually benign vascular tumor derived from blood vessel cell types. The most common form, seen in infants, is an infantile hemangioma, known colloquially as a "strawberry mark", most commonly presenting on the ski ...
birthmark under his right eye.
Singer studied
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
at the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
, graduating in 1944 after just two-and-a-half years so that he could join the military.
He was stationed in the
US Army
The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cla ...
in the
Philippines
The Philippines (; fil, Pilipinas, links=no), officially the Republic of the Philippines ( fil, Republika ng Pilipinas, links=no),
* bik, Republika kan Filipinas
* ceb, Republika sa Pilipinas
* cbk, República de Filipinas
* hil, Republ ...
, where he was a radar officer. During the daytime, he operated a communications school for the
Philippine Army
The Philippine Army (PA) ( Tagalog: ''Hukbong Katihan ng Pilipinas''; in literal English: ''Army of the Ground of the Philippines''; in literal Spanish: ''Ejército de la Tierra de la Filipinas'') is the main, oldest and largest branch of the ...
. He undertook
correspondence courses
Distance education, also known as distance learning, is the education of students who may not always be physically present at a school, or where the learner and the teacher are separated in both time and distance. Traditionally, this usually in ...
in mathematics at night in order to satisfy the prerequisites for relativity and quantum mechanics.
Upon his return from military service, Singer studied mathematics for one year at the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
.
Although he initially intended to go back to physics, his interest in math was piqued, and he continued with the subject,
earning an M.S. in Mathematics in 1948 and a Ph.D. in Mathematics in 1950 under the supervision of
Irving Segal.
Career
Singer held a postdoctoral fellowship as a CLE Moore instructor at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
in 1950.
After appointments at the
University of California, Los Angeles
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...
,
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
, and
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
, he returned to MIT as a professor in 1956 and was appointed as the Norbert Wiener Professor from 1970 to 1979.
In 1979, he moved to the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
as Miller Professor.
He returned to MIT in 1983 as the first John D. MacArthur Professor, before being appointed as an Institute Professor in 1987.
Singer was chair of the Committee of Science & Public Policy of the
United States National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
, a member of the White House Science Council (1982–88), and on the Governing Board of the
United States National Research Council
The National Academies of Sciences, Engineering, and Medicine (also known as NASEM or the National Academies) are the collective scientific national academy of the United States. The name is used interchangeably in two senses: (1) as an umbrell ...
(1995–99).
He was one of the founders of the independent non-profit
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califo ...
, based in
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emer ...
.
Singer died on February 11, 2021, at his home in
Boxborough, Massachusetts
Boxborough is a town in Middlesex County, Massachusetts, United States. The population was 5,506 at the 2020 census. The town name is often simplified to "Boxboro" on highway signs and official documents.
Geography
According to the United State ...
. He was 96.
Research
Partnering with British-Lebanese mathematician
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...
, Singer created a linkage between the fields of analysis, especially
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s, and topology. In particular, they resolved a conjecture of
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел ...
's on how topological constructs could count the number of solutions of differential equations. The
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...
, as it is now known, opened a new field of mathematics called
index theory
Index (or its plural form indices) may refer to:
Arts, entertainment, and media Fictional entities
* Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index''
* The Index, an item on a Halo megastru ...
.
The development of their work made use of the
Dirac operator
In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise formall ...
, the general geometric construction of which was a notable new discovery. It is sometimes called the Atiyah–Singer operator in their honor. In discussions between mathematician
Jim Simons and physicist
Yang Chen-Ning
Yang Chen-Ning or Chen-Ning Yang (; born 1 October 1922), also known as C. N. Yang or by the English name Frank Yang, is a Chinese theoretical physicist who made significant contributions to statistical mechanics, integrable systems, gauge th ...
in the 1970s, it was found that the Atiyah–Singer theorem has a number of applications to physics.
With
, he proposed the
Kadison–Singer problem
In mathematics, the Kadison–Singer problem, posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals on certain C*-algebras were unique. The uniqueness was proved in 2013.
The statement a ...
in 1959,
Inspired by quantum mechanics, it turned out to have reformulations in engineering and computer science. It was finally proved in 2013.
Singer also developed
analytic torsion
In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister for 3-manifolds and generalized to higher dimensions by and .
Analytic torsion (or Ray ...
with D.B. Ray and with
Henry McKean
Henry P. McKean, Jr. (born 1930 in Wenham, Massachusetts) is an American mathematician at the Courant Institute in New York University. He works in various areas of mathematical analysis, analysis. He obtained his Doctor of Philosophy, PhD in 1955 ...
introduced heat equation formulae to the Atiyah–Singer index theorem.
Singer's other notable contributions in mathematics include the
Ambrose–Singer holonomy theorem and the
McKean–Singer theorem.
Awards and honors
Singer was a member of the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
, the
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
, and the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
. He was a member of the
Norwegian Academy of Science and Letters
The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway.
History
The Royal Frederick Univer ...
. In 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
Among the awards he has received are the
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five year ...
(1969) from the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, the
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...
(1983), the
Eugene Wigner Medal (1988), the
Steele Prize
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have ...
for Lifetime Achievement (2000) from the American Mathematical Society, the
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...
(2004) shared with
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...
, the 2004
Gauss Lecture and the
James Rhyne Killian
James Rhyne Killian Jr. (July 24, 1904 – January 29, 1988) was the 10th president of the Massachusetts Institute of Technology, from 1948 until 1959.
Early life
Killian was born on July 24, 1904, in Blacksburg, South Carolina. His father w ...
Faculty Achievement Award from MIT (2005).
[http://www.maths.adelaide.edu.au/mathai.varghese/MIT_2006_fall%207.pdf ]
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).
Singer's brother Sidney was a particle physicist with
Los Alamos National Laboratory
Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
in New Mexico and predeceased him in 2006.
Works
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References
{{DEFAULTSORT:Singer, Isadore
1924 births
2021 deaths
Abel Prize laureates
American Jews
20th-century American mathematicians
21st-century American mathematicians
University of Michigan alumni
Members of the United States National Academy of Sciences
National Medal of Science laureates
Members of the Norwegian Academy of Science and Letters
Fellows of the American Mathematical Society
Topologists
Differential geometers
MIT Center for Theoretical Physics faculty
Writers from Detroit
Mathematicians from Michigan
University of Chicago alumni
University of California, Berkeley faculty
Columbia University faculty
Princeton University faculty
University of California, Los Angeles faculty
United States Army personnel of World War II
United States Army officers
Massachusetts Institute of Technology School of Science faculty
Members of the American Philosophical Society