Author: Siobhan Roberts / Source: New York Times
Kym Cox/Science Source
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.
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Jo Nelson, a mathematician at Rice University and a friend of Dr. Uhlenbeck, was thrilled that her visit to the institute coincided with a celebration for one of her mentors. “It’s amazing to hear a woman’s mathematical achievements celebrated and discussed in such detail,” she said.
Even Robert MacPherson, a topologist and faculty member in mathematics at the institute, made a rare social appearance. “This is wonderful in so many ways,” he said, holding a mini cosmos of brut rosé bubbles.
A decade ago, Dr. MacPherson and a collaborator formulated an equation describing how, in three and higher dimensions, individual bubbles evolve in live foams — the fleeting foam at the meniscus in his champagne flute, for instance, or the more enduring head on a pint of beer.
Researchers of all stripes have written “many thousands of papers” on bubbles, Andrea Prosperetti, a mechanical engineer at the University of Houston, has estimated. Bubbles entice for their seeming simplicity, which approaches the existential.
“Bubbles are emptiness, non-liquid, a tiny cloud shielding a mathematical singularity,” he wrote. “Born from chance, a violent and brief life ending in the union with the nearly infinite.”
And bubbles are everywhere, on every scale, once you start looking: high-tech drug-delivery mechanisms, emulsified salad dressings, soapsuds, black holes and beyond. In architecture, the Beijing National Aquatics Center is a box of bubbles. It is an application of the Weaire-Phelan foam, the most efficiently packed foam of equal-volume polyhedral bubbles, discovered in 1994 by Irish physicist Denis Weaire and his student Robert Phelan (first using a computer simulation, then created in a lab in 2012).
Dr. Uhlenbeck’s contribution is less practical. The Abel Prize cited “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 whimsical name for her work — “bubbling” — belies its prickly technicalities.
“It’s much more abstract and theoretical, and metaphorical,” Dr. Uhlenbeck said.
“Can the poetry of bubbles survive this?”
The definitive piece of literature on bubbles and soap films — a film is the wall of a bubble, and a bubble is one cell in a foam — is “Experimental and Theoretical Statistics of Liquids Subject to Molecular Forces Only,” published in 1873 by Belgian physicist Joseph Plateau.
He experimented with soap bubbles for decades, capturing their behavior in what are now called Plateau’s laws. In a review of the book in Nature, Scottish physicist James Clerk Maxwell lamented, “Can the poetry of bubbles survive this?”
A soap bubble is the physical world’s solution for a mathematical challenge: to minimize a surface area — in this case, one that surrounds a prescribed volume of air. Nature is always seeking to optimize, to maximize gain at minimal cost in energy cost. So “minimal surfaces” problems are all around, even in higher dimensions, and all kinds of researchers are working to describe the governing rules.
“It is a timeless subject,” said Dr. Uhlenbeck, at her dining room table. On the afternoon of prize day, she had been hiding out at her house, conserving her strength for the party. A founder of a field called geometric analysis, Dr. Uhlenbeck approaches minimal surfaces esoterically, under the banner of “variational methods in geometry.”
“I’ll give you a problem,” she said. “Take a fixed length of string, lie it down on the plane”— such as a table — “and…
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