[8] She won the 2019 Abel Prize for "her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.

[13] In 1988, by which time she had married mathematician Robert F. Williams,[13] she moved to the University of Texas at Austin as the Sid W. Richardson Foundation Regents Chairholder.

[3][19] Together with Jonathan Sacks in the early 1980s, Uhlenbeck established regularity estimates that have found applications to studies of the singularities of harmonic maps and the existence of smooth local solutions to the Yang–Mills–Higgs equations in gauge theory.

In particular, her work is described by Simon Donaldson in a survey of Yang–Mills geometry as foundational in the analytic aspects of the calculus of variations associated with the Yang–Mills functional.

[22] 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; Donaldson describes the work of Uhlenbeck, along with Shing-Tung Yau, Richard Schoen and several others, as developing a... ...whole circle of ideas and techniques involving the dimension of singular sets, monotonicity, 'small energy' results, tangent cones, etc.

"[24][7] British theoretical physicist and author Jim Al-Khalili describes Uhlenbeck as a "role model" for her work in promoting a career in mathematics to young people, particularly women.

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

[26] In March 2019, Uhlenbeck became the first woman to receive the Abel Prize,[27] with the award committee citing the decision for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.

"[9] 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".