PRINCETON, N.J. — On the evening of March 19, the mathematician Karen Uhlenbeck gathered with revelers at the Institute for Advanced Study for a champagne reception. Some hours earlier she’d been awarded the Abel Prize — the first time a woman had won it — for her discovery of a phenomenon called “bubbling,” among other effervescent results.

Dr. Uhlenbeck is a professor emerita at the University of Texas at Austin, where she spent the better part of her career (having declined a professorship at Harvard). She retired in 2014 and moved to Princeton. At the institute, she keeps a desk piled with boxes of books. She describes herself as a messy reader, and a messy thinker, and she is stylishly disheveled, with a preference for comfy, colorful clothing with pockets and Birkenstocks with socks.

As a procession of speeches and toasts lauded her life’s work, Dr. Uhlenbeck stood to the side of the lectern and listened, eyes mostly closed. When it finally came time to make her own remarks (unprepared), she began by simply agreeing: “From the perspective of my late seventies, I find myself as a young mathematician sort of impressive, too.”

She went on to note that, for lack of mathematical candidates, her role model had been the chef Julia Child. “She knew how to pick the turkey up off the floor and serve it,” Dr. Uhlenbeck said.