One of Dr. Uhlenbeck’s advances in essence described the complex shapes of soap films not in a bubble bath but in abstract, high-dimensional curved spaces. In later work, she helped put a rigorous mathematical underpinning to techniques widely used by physicists in quantum field theory to describe fundamental interactions between particles and forces.
In the process, she helped pioneer a field known as geometric analysis, and she developed techniques now commonly used by many mathematicians.
“She did things nobody thought about doing,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee, “and after she did, she laid the foundations of a branch of mathematics.”
— Karen Uhlenbeck Is First Woman to Win Abel Prize for Mathematics, New York Times, 3/19/2019