Karen Keskulla Uhlenbeck (born August 24, 1942) is an American mathematician and one of the founders of modern

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of ...

. She is a professor emeritus of mathematics at the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

, where she held the Sid W. Richardson Foundation Regents Chair. She is currently a distinguished visiting professor 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 ...

and a visiting senior research scholar at

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 ...

. Uhlenbeck was elected to 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 2007. She won the 2019

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 Pri ...

for "her pioneering achievements in geometric

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie grou ...

, and

integrable system In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...

s, and for the fundamental impact of her work on

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

." She is the first, and so far only, woman to win the prize since its inception in 2003. She donated half of the prize money to organizations which promote more engagement of women in research mathematics.

Life and career

Uhlenbeck was born in

Cleveland Cleveland ( ), officially the City of Cleveland, is a city in the United States, U.S. U.S. state, state of Ohio and the county seat of Cuyahoga County, Ohio, Cuyahoga County. Located in the northeastern part of the state, it is situated along ...

, Ohio, to engineer Arnold Keskulla and schoolteacher and artist Carolyn Windeler Keskulla. While she was a child, the family moved to

New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, southeast, and south by the Atlantic Ocean; on the west by the Delawa ...

. Uhlenbeck's maiden name, Keskulla, comes from ''Keskküla'' and from her grandfather who was Estonian. Uhlenbeck received her B.A. (1964) from 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 ...

. She began her graduate studies at the Courant Institute of Mathematical Sciences at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, th ...

, and married biophysicist Olke C. Uhlenbeck (the son of physicist George Uhlenbeck) in 1965. When her husband went to Harvard, she moved with him and restarted her studies at

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

, where she earned an MA (1966) and PhD (1968) under the supervision of

Richard Palais Richard Sheldon Palais (born May 22, 1931) is a mathematician working in geometry who introduced the principle of symmetric criticality, the Mostow–Palais theorem, the Lie–Palais theorem, the Morse–Palais lemma, and the Palais–Smale c ...

. Her doctoral dissertation was titled ''The Calculus of Variations and Global Analysis''. After temporary jobs 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 th ...

and

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 un ...

, and having difficulty finding a permanent position with her husband because of the "anti-nepotism" rules then in place that prevented hiring both a husband and wife even in distinct departments of a university, she took a faculty position at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Un ...

in 1971. However, she disliked Urbana and moved to the

University of Illinois at Chicago The University of Illinois Chicago (UIC) is a public research university in Chicago, Illinois. Its campus is in the Near West Side community area, adjacent to the Chicago Loop. The second campus established under the University of Illinois ...

in 1976 as well as separating from her first husband Olke Uhlenbeck in the same year. She moved again to 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 ...

in 1983. In 1988, by which time she had married mathematician Robert F. Williams, she moved to the

as the Sid W. Richardson Foundation Regents Chairholder. Uhlenbeck is currently a professor emeritus at the University of Texas at Austin, a visiting associate at the

and a visiting senior research scholar at

Research

Uhlenbeck is one of the founders of the field of

, a discipline that uses

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and mult ...

to study the solutions to

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, ...

s and vice versa. She has also contributed to

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 ...

and

s.. Together with Jonathan Sacks in the early 1980s, Uhlenbeck established regularity estimates that have found applications to studies of the singularities of

harmonic map In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for ...

s and the existence of smooth local solutions to the

Yang–Mills–Higgs equations In mathematics, the Yang–Mills–Higgs equations are a set of non-linear partial differential equations for a Yang–Mills field, given by a connection, and a Higgs field, given by a section of a vector bundle (specifically, the adjoint bundle) ...

. In particular,

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. H ...

describes their joint 1981 paper ''The existence of minimal immersions of 2-spheres'' as a "landmark paper... which showed that, with a deeper analysis, variational arguments can still be used to give general existence results" for harmonic map equations. Building on these ideas, Uhlenbeck initiated a systematic study of the moduli theory of

minimal surfaces In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces tha ...

in hyperbolic

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 (also called minimal submanifold theory) in her 1983 paper, ''Closed minimal surfaces in hyperbolic 3-manifolds''. In particular, her work is described by

in a survey of Yang–Mills geometry as foundational in the analytic aspects of the calculus of variations associated with the Yang–Mills functional. A wider survey of her contributions to the field of calculus of variations was published by Simon Donaldson in the March 2019 issue of ''

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine sinc ...

''; Donaldson describes the work of Uhlenbeck, along with

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathem ...

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 several others, as developing a...

Outreach

In 1991, Uhlenbeck co-founded, with Herbert Clemens and Dan Freed, the Park City Mathematics Institute (PCMI) with the mission to "provide an immersive educational and professional development opportunity for several parallel communities from across the larger umbrella of the mathematics profession." Uhlenbeck also co-founded the Women and Mathematics Program at the Institute for Advanced Study "with the mission to recruit and retain more women in mathematics." British theoretical physicist and author

Jim Al-Khalili Jameel Sadik "Jim" Al-Khalili ( ar, جميل صادق الخليلي; born 20 September 1962) is an Iraqi-British theoretical physicist, author and broadcaster. He is professor of theoretical physics and chair in the public engagement in scie ...

describes Uhlenbeck as a "role model" for her work in promoting a career in mathematics to young people, particularly women.

Personal life

Uhlenbeck is a self-described "messy reader" and "messy thinker", with boxes of books stacked on her desk at Princeton's Institute for Advanced Study. In spontaneous remarks made to Institute colleagues after winning the Abel Prize in March 2019, Uhlenbeck noted that for lack of prominent female role models during her apprenticeship in the field of mathematics, she had instead emulated chef

Julia Child Julia Carolyn Child (née McWilliams; August 15, 1912 – August 13, 2004) was an American cooking teacher, author, and television personality. She is recognized for bringing French cuisine to the American public with her debut cookbook, '' ...

: "She knew how to pick the turkey up off the floor and serve it".

Awards and honors

In March 2019, Uhlenbeck became the first woman to receive the

, with the award committee citing the decision for "her pioneering achievements in geometric

and

s, and for the fundamental impact of her work on

and

." Hans Munthe-Kaas, who chaired the award committee, stated that "Her theories have revolutionised our understanding of minimal surfaces, such as more general minimisation problems in higher dimensions". She donated half of the cash prize to two organizations, the EDGE Foundation (which subsequently set up the Karen EDGE Fellowship Program), and the Institute for Advanced Study's Women and Mathematics (WAM) Program. Uhlenbeck also won 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 ...

in 2000, and the Leroy P. Steele Prize for Seminal Contribution to Research 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 ...

in 2007, "for her foundational contributions in analytic aspects of mathematical gauge theory", based on her 1982 papers "Removable singularities in Yang–Mills fields" and "Connections with bounds on curvature". She became a MacArthur Fellow in 1983 and a Fellow 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 1985. She was elected as 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 1986. She became a

Guggenheim Fellow 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 2001, an honorary member of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...

in 2008, and a Fellow of the

in 2012. The

Association for Women in Mathematics The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment o ...

included her in the 2020 class of AWM Fellows for "her groundbreaking and profound contributions to modern geometric analysis; for establishing a career as one of the greatest mathematicians of our time, despite the considerable challenges facing women when she entered the field; for using her experiences navigating these challenges to create and sustain programs to address them for future generations of women. For a lifetime of breaking barriers; and for being the first woman to win the Abel Prize". She was the

Noether Lecture The Noether Lecture is a distinguished lecture series that honors women "who have made fundamental and sustained contributions to the mathematical sciences". The Association for Women in Mathematics (AWM) established the annual lectures in 1980 as t ...

r of the

in 1988. In 1990, she was a plenary speaker at 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 rena ...

, as only the second woman (after

Emmy Noether Amalie Emmy NoetherEmmy is the '' Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noeth ...

) to give such a lecture. Her other awards include the University of Michigan alumna of the year (1984), the

Sigma Xi Sigma Xi, The Scientific Research Honor Society () is a highly prestigious, non-profit honor society for scientists and engineers. Sigma Xi was founded at Cornell University by a junior faculty member and a small group of graduate students in 1886 ...

Common Wealth Award for Science and Technology (1995), and honorary doctorates from the

(2000),

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best pub ...

(2001),

(2004),

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 ...

(2007), and

(2012).

Selected publications

Books

Research articles

References

External links

* * * * https://mathshistory.st-andrews.ac.uk/Biographies/Uhlenbeck_Karen/ * https://scientificwomen.net/women/karen-uhlenbeck-130 {{DEFAULTSORT:Uhlenbeck, Karen 1942 births 20th-century American mathematicians 20th-century women mathematicians 21st-century American mathematicians 21st-century women mathematicians Abel Prize laureates American people of Estonian descent American women mathematicians Brandeis University alumni Courant Institute of Mathematical Sciences alumni Fellows of the American Mathematical Society Fellows of the American Academy of Arts and Sciences Fellows of the Association for Women in Mathematics Living people MacArthur Fellows Members of the United States National Academy of Sciences National Medal of Science laureates People from Cleveland University of Chicago faculty University of Illinois Chicago faculty University of Illinois Urbana-Champaign faculty University of Michigan alumni University of Texas at Austin faculty 21st-century American women