Inspiration

In 2019 American mathematician Karen Uhlenbeck became the first woman to win the Abel Prize, one of the top honours in mathematics. She was recognised for methods that link geometry with the equations of physics, especially for handling the points where those equations break down.

Many problems in geometry and physics look for the smoothest or lowest-energy shape, like a soap film stretched across a wire loop. Sometimes the energy piles up at a single point and the smooth shape pinches off there, a breakdown mathematicians call bubbling. In the early 1980s, partly with Jonathan Sacks, Uhlenbeck showed how to control it: away from a few points the shape stays well behaved, and the energy lost at those points gathers into small, sphere-like pieces that can be studied in their own right. Her results became basic tools in gauge theory, the mathematics behind the forces of particle physics. Born in Cleveland in 1942, she became a MacArthur Fellow in 1983 and received the US National Medal of Science in 2000. She also co-founded a programme at the Institute for Advanced Study in Princeton to bring more women into mathematics.