Irving Ezra Segal (1918–1998) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for work on theoretical

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, q ...

. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for his developments in

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...

and in

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional s ...

and

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an e ...

, in particular his innovation of the algebraic axioms known as

C*-algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continu ...

Biography

Irving Ezra Segal was born in the

Bronx The Bronx () is a borough of New York City, coextensive with Bronx County, in the state of New York. It is south of Westchester County; north and east of the New York City borough of Manhattan, across the Harlem River; and north of the New ...

on September 13, 1918, to

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

parents. He attended school in Trenton. In 1934 he was admitted to

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

, at the age of 16. He was elected to

Phi Beta Kappa The Phi Beta Kappa Society () is the oldest academic honor society in the United States, and the most prestigious, due in part to its long history and academic selectivity. Phi Beta Kappa aims to promote and advocate excellence in the liberal a ...

, completed his undergraduate studies in just three years time, graduated with highest honors with a bachelor's degree in 1937, and was awarded the George B. Covington Prize in Mathematics. He was then admitted to

Yale Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

, and in another three years time had completed his doctorate, receiving his

Doctor of Philosophy A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

degree in 1940. Segal taught at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

, then he joined the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

on a

Guggenheim Memorial Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

, working from 1941 to 1943 with

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

and

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

. During

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

Segal served 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, c ...

conducting research in ballistics at the

Aberdeen Proving Ground Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work ...

Maryland Maryland ( ) is a U.S. state, state in the Mid-Atlantic (United States), Mid-Atlantic region of the United States. It shares borders with Virginia, West Virginia, and the District of Columbia to its south and west; Pennsylvania to its north; ...

. He joined the mathematics department at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

in 1948 where he served until 1960. In 1960 he joined the mathematics department at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

where he remained as a professor until his death in 1998. He won three

Guggenheim Fellowships Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

, in 1947, 1951 and 1967, and received the Humboldt Award in 1981. He was an Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1966 in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

and in 1970 in

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

. He was elected to 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 Nat ...

in 1973. In 1983

Victor Guillemin Victor William Guillemin (born 1937 in Boston) is an American mathematician working in the field of symplectic geometry, who has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics. He is a t ...

edited a

festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the ...

dedicated to Irving Segal. ''

Physics Today ''Physics Today'' is the membership magazine of the American Institute of Physics. First published in May 1948, it is issued on a monthly schedule, and is provided to the members of ten physics societies, including the American Physical Society ...

'' published a review of ''Introduction to Algebraic and Constructive Quantum Field Theory'' (1992), which Segal coauthored. Segal died in

Lexington, Massachusetts Lexington is a suburban town in Middlesex County, Massachusetts, United States. It is 10 miles (16 km) from Downtown Boston. The population was 34,454 as of the 2020 census. The area was originally inhabited by Native Americans, and was firs ...

, on August 30, 1998.

Edward Nelson Edward Nelson (May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematic ...

's obituary article about Segal concludes: "... It is rare for a mathematician to produce a life work that at the time can be fully and confidently evaluated by no one, but the full impact of the work of Irving Ezra Segal will become known only to future generations."

Chronometric cosmology

Segal provided an alternative to the

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from t ...

theory of

expansion of the universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...

. The cosmological

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in f ...

that motivates the expanding universe theory is due to curvature of the cosmos, according to Segal. He portrayed the spatial part of the cosmos as a large

3-sphere In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It may be embedded in 4-dimensional Euclidean space as the set of points equidistant from a fixed central point. Analogous to how the boundary of a ball in three dimens ...

. Spacetime cannot turn back on itself. At each point in the cosmos there is a convex future direction, meaning, "the future can never merge into the past", no spacetime curvature can close or loop. Building on common symmetry expressed by the

Lorentz group In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch phy ...

, Poincare group, and

conformal group of spacetime In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Se ...

, Segal saw the closing up of the universe as consistent with

compactification Compactification may refer to: * Compactification (mathematics), making a topological space compact * Compactification (physics), the "curling up" of extra dimensions in string theory See also * Compaction (disambiguation) {{disambiguation ...

of spacetime used to define the conformal group. Segal reviewed redshift data to verify his cosmology. He claimed confirmation, but generally his chronometric cosmology has not found favor. For instance, Abraham H. Taub reviewed ''Mathematical Cosmology and Extragalactic Astronomy'', saying As for the

cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...

, in the chronometric view, "The observed blackbody... is simply the most likely disposition of remnants of light on a purely random basis... and is not at all uniquely indicative of a Big Bang." In 2005 A. Daigneault spoke on "Irving Segal's Axiomitization of Spacetime and it Cosmological Consequences" in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

.A. Diagneault (2005
Irving Segal's Axiomatization of Spacetime and its Cosmological Consequences
invited lecture at Budapest. See also He concedes at the outset that Segal's cosmology is "generally ignored by astrophysicists", and that the model was first proposed by Einstein in 1917 and is "supposedly discredited".

Selected publications

For a list of 227 articles and 10 books to which Segal contributed, see the

MIT 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 ...

external link below. * 1951: * 1962: ''Lectures at the Boulder Summer Seminar'',

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 ...

* 1963: * 1968: (with

Ray Kunze Ray Alden Kunze (March 7, 1928 – May 21, 2014) was an American mathematician who chaired the mathematics departments at the University of California, Irvine and the University of Georgia. His mathematical research concerned the representation ...

) * 1976: * 1992: (with John C. Baez and Zhengfang Zhou) * 1993: (with Nicoll, J.F., Wu, P., Zhou, Z.)
Statistically Efficient Testing of the Hubble and Lundmark Laws on IRAS Galaxy Samples
',

The Astrophysical Journal ''The Astrophysical Journal'', often abbreviated ''ApJ'' (pronounced "ap jay") in references and speech, is a peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and Ja ...

465–484 * 1995: (with Zhou, Z.)
Maxwell's Equations in the Einstein Universe and Chronometric Cosmology
', ApJS. Ser. 100, 307–324 * 1997: "Cosmic time dilation", ''The Astrophysical Journal'' 482:L115–17

References

External links

* * * * John C. Baez (1999
Memories of Irving Segal

Leonard Gross and William Segal, "Irving E. Segal", Biographical Memoirs of the National Academy of Sciences (2022)
{{DEFAULTSORT:Segal, Irving 1918 births 1998 deaths Princeton University alumni Yale University alumni Harvard University faculty 20th-century American mathematicians Massachusetts Institute of Technology School of Science faculty Members of the United States National Academy of Sciences 20th-century American Jews