Karen Keskulla Uhlenbeck was born on August 24, 1942, in Cleveland, Ohio, the eldest of four children of engineer Arnold Keskulla and artist and schoolteacher Carolyn Windeler Keskulla. The family later moved to New Jersey, where she grew up with a strong appetite for books and the outdoors. She read the science titles her father brought home from the library, including works by Fred Hoyle and George Gamow, and finished every science book she could find. She later recalled the excitement of grasping that there were different kinds of infinity. The things little girls were expected to care about did not interest her much. She imagined becoming a forest ranger or a scientist.
She entered the University of Michigan intending to study physics. An honors calculus course changed that. The structure, elegance, and beauty of mathematics struck her at once. She also disliked laboratory work. She graduated in 1964 with a bachelor’s degree in mathematics. After a year at New York University’s Courant Institute she married biophysicist Olke C. Uhlenbeck in 1965 and followed him when he went to Harvard. She completed a master’s degree in 1966 and a doctorate in 1968 at Brandeis University under Richard Palais, working on the calculus of variations. She has said she avoided applying to the most competitive programs because she already understood how hostile the culture could be toward women.
Her early academic path was itinerant and often difficult. She held a one-year position at MIT, then lectured at Berkeley. When she and her husband both received offers at the University of Illinois at Urbana-Champaign, she took a tenure-track job there but felt treated as a faculty wife rather than a research mathematician. Other women were largely confined to teaching calculus. She later described those years as unhappy. After the marriage ended in 1976 she moved to the University of Illinois at Chicago, where she found a group of determined women colleagues and stopped worrying in the same way about being a woman in mathematics. She later taught at the University of Chicago and, in 1988, took the Sid W. Richardson Foundation Regents Chair at the University of Texas at Austin, remaining until retirement as professor emerita. She has long been affiliated with the Institute for Advanced Study in Princeton as a member, visitor, and distinguished visiting professor.
Uhlenbeck is one of the founders of modern geometric analysis, the meeting ground of partial differential equations with geometry and topology. In the late 1970s and early 1980s, working with Jonathan Sacks, she studied energy-minimizing maps from surfaces into Riemannian manifolds. Sequences of approximate minimizers need not converge everywhere. Energy can concentrate at isolated points and “bubble off.” Their analysis of this bubbling phenomenon became a standard tool. It clarified the behavior of harmonic maps and minimal surfaces, including soap-film surfaces and higher-dimensional minimization problems.
She then turned to gauge theory and the Yang-Mills equations that appear in particle physics. She proved that, in a suitable Coulomb gauge, the equations become elliptic. She established compactness theorems for connections with curvature bounded in L2 and a removable-singularities theorem: a finite-energy Yang-Mills field on a punctured four-dimensional ball can be extended smoothly across the puncture after a gauge transformation. These results supplied the analytic foundation for later work in four-manifold topology, including Simon Donaldson’s. She also contributed to integrable systems. The Abel Committee later cited her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and the fundamental impact of her work on analysis, geometry, and mathematical physics.
Recognition came in stages. She received a MacArthur Fellowship in 1983. In 1986 she became the first woman mathematician elected to the National Academy of Sciences. She gave the Noether Lecture in 1988 and, in 1990 in Kyoto, became only the second woman to deliver a plenary lecture at the International Congress of Mathematicians. President Bill Clinton awarded her the National Medal of Science in 2000. The American Mathematical Society gave her the Leroy P. Steele Prize for seminal contribution to research in 2007 and another Steele Prize in 2020. In March 2019 she became the first woman, and so far the only woman, to win the Abel Prize, often described as mathematics’ Nobel. She donated half the prize money to organizations that promote women and other underrepresented groups in research mathematics. With Chuu-Lian Terng she co-founded the Women and Mathematics program at the Institute for Advanced Study, which has reached well over a thousand participants.
Uhlenbeck has been frank about the barriers she met. She was told women could not do mathematics and that they were supposed to go home and have babies. She treated the hostility as a form of legitimate rebellion. She has also been honest about the difficulty of serving as a role model. What students need to see, she has written, is that imperfect people can succeed. She once said that for lack of female mathematical models she had looked to Julia Child, who knew how to pick the turkey up off the floor and serve it. She has described herself as a messy reader and messy thinker. She did not have children, a source of sadness at a time when medical options were limited.
Her first love remains the outdoors: mountain climbing, backpacking, hiking, canoeing, swimming, and bicycling. She learned to surf at forty. She has lived in the Texas Hill Country with her husband, mathematician Robert F. Williams, and has spoken of being most herself in nature or in the garden. Mathematics, for her, combined solitude, abstraction, and ideas. She has said she wanders until something catches her eye and then works on it, insisting that the problems must fit one’s own imagination.
Uhlenbeck’s career changed the landscape of geometric analysis and showed that a woman could reach the highest level of the profession while remaining unmistakably herself. Her theorems sit inside the machinery of modern geometry and mathematical physics. Her example, and the programs she helped build, continue to widen the path for those who come after.