Edward Witten (born August 26, 1951) is an American

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

theoretical physicist 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 experime ...

. He is a Professor Emeritus in the School of

Natural Sciences Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeat ...

at 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 schola ...

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 nin ...

. Witten is a researcher in

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...

, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

by the

International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...

, for his mathematical insights in physics, such as his 1981 proof of the

positive energy theorem The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an ...

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witt ...

.Duff 1998, p. 65

Early life and education

Witten was born on August 26, 1951, in

Baltimore Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was ...

Maryland Maryland ( ) is a state in the 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; and Delaware and the Atlantic Ocean t ...

, to a

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 ...

family. He is the son of Lorraine (née Wollach) Witten and Louis Witten, a

specializing in

gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...

and

. Witten attended the

Park School of Baltimore The Park School of Baltimore, known as Park, is a private, coeducational, non-sectarian, progressive day school for children in Pre-Kindergarten (age 4) through grade twelve. Park is located in Brooklandville, Maryland, near the city of Baltimor ...

(class of '68), and received his

Bachelor of Arts Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

degree with a major in history and minor in linguistics from

Brandeis University , mottoeng = "Truth even unto its innermost parts" , established = , type = Private research university , accreditation = NECHE , president = Ronald D. Liebowitz , p ...

in 1971. He had aspirations in journalism and politics and published articles in both ''

The New Republic ''The New Republic'' is an American magazine of commentary on politics, contemporary culture, and the arts. Founded in 1914 by several leaders of the progressive movement, it attempted to find a balance between "a liberalism centered in hu ...

'' and ''

The Nation ''The Nation'' is an American liberal biweekly magazine that covers political and cultural news, opinion, and analysis. It was founded on July 6, 1865, as a successor to William Lloyd Garrison's '' The Liberator'', an abolitionist newspaper t ...

'' in the late 1960s. In 1972 he worked for six months on George McGovern's presidential campaign. Witten attended 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 ...

for one semester as an economics graduate student before dropping out. He returned to academia, enrolling in

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...

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 ...

in 1973, then shifting departments and receiving a

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * '' Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. al ...

in physics in 1976 and completing a dissertation, "Some problems in the short distance analysis of gauge theories", under the supervision of David Gross. He held a fellowship 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 highe ...

(1976–77), visited

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

(1977–78), was a junior fellow in the Harvard Society of Fellows (1977–1980), and held a

MacArthur Foundation The John D. and Catherine T. MacArthur Foundation is a private foundation that makes grants and impact investments to support non-profit organizations in approximately 50 countries around the world. It has an endowment of $7.0 billion and p ...

fellowship (1982).

Research

Fields medal work

Witten was awarded the

by the

in 1990. In a written address to the ICM, Michael Atiyah said of Witten: As an example of Witten's work in pure mathematics, Atiyah cites his application of techniques from

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 and ...

to the mathematical subject of low-dimensional topology. In the late 1980s, Witten coined the term ''

topological quantum field theory In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathe ...

'' for a certain type of physical theory in which the expectation values of observable quantities encode information about the

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...

. In particular, Witten realized that a physical theory now called

Chern–Simons theory The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and Jam ...

could provide a framework for understanding the mathematical theory of

knots A knot is a fastening in rope or interwoven lines. Knot may also refer to: Places * Knot, Nancowry, a village in India Archaeology * Knot of Isis (tyet), symbol of welfare/life. * Minoan snake goddess figurines#Sacral knot Arts, entertainme ...

and

3-manifold In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...

s. Although Witten's work was based on the mathematically ill-defined notion of a

Feynman path integral The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional ...

and therefore not mathematically rigorous, mathematicians were able to systematically develop Witten's ideas, leading to the theory of Reshetikhin–Turaev invariants. Another result for which Witten was awarded the Fields Medal was his proof in 1981 of the

. This theorem asserts that (under appropriate assumptions) the total

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...

of a gravitating system is always positive and can be zero only if the geometry of

is that of flat

Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the iner ...

. It establishes Minkowski space as a stable ground state of the

gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational pheno ...

. While the original proof of this result due to

Richard Schoen Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984. Career Born in Celina, Ohio, and a 1 ...

and Shing-Tung Yau used variational methods, Witten's proof used ideas from

supergravity theory In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such ...

to simplify the argument. A third area mentioned in Atiyah's address is Witten's work relating

supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...

and Morse theory, a branch of mathematics that studies the

of manifolds using the concept of a

differentiable function In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in ...

. Witten's work gave a physical proof of a classical result, the Morse inequalities, by interpreting the theory in terms of supersymmetric quantum mechanics.

M-theory

By the mid 1990s, physicists working on

had developed five different consistent versions of the theory. These versions are known as type I, type IIA,

type IIB In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theorie ...

, and the two flavors of

heterotic string In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbrevi ...

theory ( SO(32) and E₈×E₈). The thinking was that of these five candidate theories, only one was the actual correct

theory of everything A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...

, and that theory was the one whose low-energy limit matched the physics observed in our world today. Speaking at the string theory conference at

University of Southern California , mottoeng = "Let whoever earns the palm bear it" , religious_affiliation = Nonsectarian—historically Methodist , established = , accreditation = WSCUC , type = Private research university , academic_affiliations = , endowment = $8.1 ...

in 1995, Witten made the surprising suggestion that these five string theories were in fact not distinct theories, but different limits of a single theory, which he called

. Witten's proposal was based on the observation that the five string theories can be mapped to one another by certain rules called dualities and are identified by these dualities. It led to a flurry of work now known as the

second superstring revolution The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum ...

Other work

Another of Witten's contributions to physics was to the result of gauge/gravity duality. In 1997, Juan Maldacena formulated a result known as the

AdS/CFT correspondence In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter ...

, which establishes a relationship between certain

quantum field theories 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 ...

and theories of

. Maldacena's discovery has dominated high-energy theoretical physics for the past 15 years because of its applications to theoretical problems in quantum gravity and quantum field theory. Witten's foundational work following Maldacena's result has shed light on this relationship. In collaboration with Nathan Seiberg, Witten established several powerful results in quantum field theories. In their paper on string theory and

noncommutative geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some g ...

, Seiberg and Witten studied certain noncommutative quantum field theories that arise as limits of string theory. In another well-known paper, they studied aspects of supersymmetric gauge theory. The latter paper, combined with Witten's earlier work on topological quantum field theory, led to developments in the topology of smooth 4-manifolds, in particular the notion of Seiberg–Witten invariants. With

Anton Kapustin Anton Nikolayevich Kapustin (born November 10, 1971, Moscow) is a Russian-American theoretical physicist and the Earle C. Anthony Professor of Theoretical Physics at the California Institute of Technology. His interests lie in quantum field theo ...

, Witten has made deep mathematical connections between S-duality of gauge theories and the geometric Langlands correspondence. Partly in collaboration with Seiberg, one of his recent interests include aspects of field theoretical description of topological phases in condensed matter and non-supersymmetric dualities in field theories that, among other things, are of high relevance in condensed matter theory. In 2016, he has also brought tensor models to the relevance of holographic and quantum gravity theories, by using them as a generalization of the Sachdev-Ye-Kitaev model. Witten has published influential and insightful work in many aspects of quantum field theories and mathematical physics, including the physics and mathematics of anomalies, integrability, dualities, localization, and homologies. Many of his results have deeply influenced areas in theoretical physics (often well beyond the original context of his results), including string theory, quantum gravity and topological condensed matter.

Awards and honors

Witten has been honored with numerous awards including a MacArthur Grant (1982), the

(1990), the Golden Plate Award of the

American Academy of Achievement The American Academy of Achievement, colloquially known as the Academy of Achievement, is a non-profit educational organization that recognizes some of the highest achieving individuals in diverse fields and gives them the opportunity to meet ...

(1997), the Nemmers Prize in Mathematics (2000), 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 ...

(2002), Pythagoras Award (2005), the

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. The prize is sponsored by the Daniel Iagolnitzer Founda ...

(2006), the

Crafoord Prize The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...

(2008), the

Lorentz Medal Lorentz Medal is a distinction awarded every four years by the Royal Netherlands Academy of Arts and Sciences. It was established in 1925 on the occasion of the 50th anniversary of the doctorate of Hendrik Lorentz. The medal is given for impor ...

(2010) the Isaac Newton Medal (2010) and the Fundamental Physics Prize (2012). Since 1999, he has been a Foreign Member of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

(London), and in March 2016 was elected an Honorary Fellow of the

Royal Society of Edinburgh The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

Pope Benedict XVI Pope Benedict XVI ( la, Benedictus XVI; it, Benedetto XVI; german: link=no, Benedikt XVI.; born Joseph Aloisius Ratzinger, , on 16 April 1927) is a retired prelate of the Catholic church who served as the head of the Church and the sovereig ...

appointed Witten as a member of the

Pontifical Academy of Sciences The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the mat ...

(2006). He also appeared in the list of ''

Time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

'' magazine's

100 most influential people ''Time'' 100 (often stylized as ''TIME'' 100) is an annual listicle of the 100 most influential people in the world, assembled by the American news magazine '' Time''. First published in 1999 as the result of a debate among American academics, ...

of 2004. 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, meeting ...

. Witten was elected as a member of 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, a ...

in 1984, 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 Nat ...

in 1988, and a member of 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 ...

in 1993. In May 2022 he was awarded an honorary Doctor of Sciences from the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a Private university, private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest- ...

. In an informal poll at a 1990 cosmology conference, Witten received the largest number of mentions as "the smartest living physicist".

Personal life

Witten has been married to Chiara Nappi, a professor of physics at

, since 1979. They have two daughters and a son. Their daughter Ilana B. Witten is a neuroscientist at Princeton University, and daughter Daniela Witten is a biostatistician at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seatt ...

. Witten sits on the board of directors of Americans for Peace Now and on the advisory council of J Street. He supports the

two-state solution The two-state solution to the Israeli–Palestinian conflict envisions an independent State of Palestine alongside the State of Israel, west of the Jordan River. The boundary between the two states is still subject to dispute and negotiation ...

and advocates a boycott of Israeli institutions and economic activity beyond its 1967 borders, though not of Israel itself."For an Economic Boycott and Political Nonrecognition of the Israeli Settlements in the Occupied Territories"
''NYRB'', October 2016.

Selected publications

* ''Some Problems in the Short Distance Analysis of Gauge Theories''.

, 1976. ( Dissertation.) * Roman Jackiw, David Gross, Sam B. Treiman, Edward Witten, Bruno Zumino. ''Current Algebra and Anomalies: A Set of Lecture Notes and Papers''. World Scientific, 1985. * Green, M., John H. Schwarz, and E. Witten. ''Superstring Theory. Vol. 1, Introduction''. Cambridge Monographs on Mathematical Physics. Cambridge, UK: Cambridge University Press, 1988. . * Green, M., John H. Schwarz, and E. Witten. ''Superstring Theory. Vol. 2, Loop Amplitudes, Anomalies and Phenomenology''. Cambridge, UK: Cambridge University Press, 1988. . * ''Quantum fields and strings: a course for mathematicians''. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by

Pierre Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord P ...

, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey,

David Kazhdan David Kazhdan ( he, דוד קשדן), born Dmitry Aleksandrovich Kazhdan (russian: Дми́трий Александро́вич Кажда́н), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 Ma ...

John W. Morgan John W. Morgan, (born May 7, 1964), is a Canadian lawyer, politician, and businessman. He was the mayor of the Cape Breton Regional Municipality (CRBM) in Nova Scotia from 2000 to 2012. Morgan is a graduate of the University College of Cape Bret ...

, David R. Morrison and Edward Witten. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1999. Vol. 1: xxii+723 pp.; Vol. 2: pp. i–xxiv and 727–1501. , 81–06 (81T30 81Txx).

References

External links

Faculty webpage

Publications on ArXiv
* *
A Physicist's Physicist Ponders the Nature of Reality, Interview with Nathalie Wolchover in ''Quanta Magazine'', November 28, 2017
{{DEFAULTSORT:Witten, Edward 1951 births 20th-century American physicists 21st-century American physicists Albert Einstein Medal recipients Albert Einstein World Award of Science Laureates Brandeis University alumni Clay Research Award recipients Fellows of the American Academy of Arts and Sciences Fellows of the American Mathematical Society Fellows of the American Physical Society Fields Medalists Foreign Members of the Royal Society Harvard Fellows Institute for Advanced Study faculty Jewish American scientists Jewish physicists Kyoto laureates in Basic Sciences Living people MacArthur Fellows Mathematical physicists Members of the French Academy of Sciences Members of the Pontifical Academy of Sciences Members of the United States National Academy of Sciences National Medal of Science laureates Lorentz Medal winners Park School of Baltimore alumni Princeton University alumni Princeton University faculty Scientists from Baltimore American string theorists Fellows of the Royal Society of Edinburgh Members of the American Philosophical Society