“I find that I am bored with anything I understand,” Karen Uhlenbeck once said – and that sense of curiosity is part of why she won the prestigious Abel Prize, from the Norwegian Academy of Science and Letters.
Uhlenbeck, an influential mathematician who was for decades a professor at the University of Texas at Austin and who has sought to encourage women to study mathematics, has become the first woman to win the Abel Prize — often called the Nobel Prize of math.
Uhlenbeck’s complex and wide-ranging work includes analyzing the “minimal surfaces” of soap bubbles and finding ways to unite geometry and physics through new mathematical approaches. She’s widely respected for her work on esoteric topics, such as partial differential equations and the calculus of variations.
“Uhlenbeck’s research has led to revolutionary advances at the intersection of mathematics and physics,” said Paul Goldbart, a professor of physics who is also the dean of UT’s college of natural sciences. In a statement about Uhlenbeck winning the Abel Prize, he added, “Her pioneering insights have applications across a range of fascinating subjects, from string theory, which may help explain the nature of reality, to the geometry of space-time.”
The Norwegian academy said it recognized Uhlenbeck “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.”
The Abel Prize includes an award of 6 million Norwegian kroner (around $700,000). Uhlenbeck will formally receive the prize from Norway’s King Harald V, in a ceremony in Oslo on May 21.
“Karen Uhlenbeck is a founder of modern geometric analysis,” said Hans Munthe-Kaas, chair of the academy’s Abel Committee. “Her perspective has pervaded the field and led to some of the most dramatic advances in mathematics over the last 40 years.”
As that statement implies, Uhlenbeck has been a star in theoretical mathematics for decades. She won a MacArthur Fellowship in 1983, after publishing a sequence of influential papers on harmonic mapping and gauge theory — some of which she wrote alone and some in which she collaborated with mathematicians such as Richard Schoen and Jonathan Sacks.
In 1986, Uhlenbeck became the first female mathematician to be elected to the National Academy of Sciences. She was awarded a National Medal of Science in 2000. And the American Mathematical Society awarded her the Steele Prize in 2007, for decades of contributions to research.
As it recognized Uhlenbeck’s work in advancing the understanding of theoretical mathematics, the Norwegian committee also noted her professional impact and her standing as a role model.
“As a child, she loved reading and dreamed of becoming a scientist,” the committee said. “Today, Uhlenbeck is Visiting Senior Research Scholar at Princeton University as well as Visiting Associate at the Institute for Advanced Study (IAS). She is one of the founders of the Park City Mathematics Institute (PCMI) at IAS, which aims to train young researchers and promote mutual understanding of the interests and challenges in mathematics.”
Within IAS, Uhlenbeck co-founded the Women and Mathematics program in 1993, seeking to encourage women’s interest in the field.
“I am aware of the fact that I am a role model for young women in mathematics,” Uhlenbeck said, according to a release from Princeton University, where she has also worked. “It’s hard to be a role model, however, because what you really need to do is show students how imperfect people can be and still succeed. … I may be a wonderful mathematician and famous because of it, but I’m also very human.”
When she accepted the Steele Prize in 2007, Uhlenbeck said it was her work in education, not her mathematical theorems, that gave her the most pride. She also said that changing a culture that doesn’t encourage girls and women to pursue careers in mathematics “is a momentous task in comparison” to her other accomplishments.
“I remain quite disappointed at the numbers of women doing mathematics and in leadership positions,” she said. “This is, to my mind, primarily due to the culture of the mathematical community as well as harsh societal pressures from outside.”
Uhlenbeck worked at the University of Texas at Austin for more than 25 years. She attended the University of Michigan and received her Ph.D. at Brandeis University in 1968.
Uhlenbeck has said the variety of fields she studied — and her knack for applying ideas from one area to explore concepts in another — stemmed from “an addiction to intellectual excitement.”
Here’s how she described her work in 1997:
“Mathematicians look at imaginary spaces constructed by scientists examining other problems. I started out my mathematics career by working on Palais’ modern formulation of a very useful classical theory, the calculus of variations. I decided Einstein’s general relativity was too hard, but managed to learn a lot about geometry of space-time. I did some very technical work in partial differential equations, made an unsuccessful pass at shock waves, worked in scale invariant variational problems, made a poor stab at three manifold topology, learned gauge field theory and then some about applications to four manifolds, and have recently been working on equations with algebraic infinite symmetries. I find that I am bored with anything I understand.”
That’s from Uhlenbeck’s contribution to the book Journeys of Women in Science and Engineering: No Universal Constant, as quoted in the release from Princeton, where Uhlenbeck is currently a visiting scholar.