Breaking the mould

Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin has won this year’s Abel Prize — one of the top prizes in mathematics modelled on the Nobel Prizes. The award cites “the fundamental impact of her work on analysis, geometry and mathematical physics.”

The Norwegian Academy of Science and Letters announced that seventy-six-years-old Uhlenbeck had won this year’s award on Tuesday. The Internet was flooded with stories mentioning that she’s the first woman to win this coveted prize but that is not where the import of the story lies.

British mathematician GH Hardy, who considered the discovery of untutored Indian mathematician Srinivasa Ramanujan as his greatest achievement, wrote in his famous book A Mathematician’s Apology that mathematics is a young man’s game. This is where the genius of Uhlenbeck lies and though a lot of her ideas came to her in her younger years she still had enough gumption to keep developing them as the years passed.

“No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations.

“We may consider, for example, the career of a man who was certainly one of the world's three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twenty four — 'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect,” Hardy noted.

Uhlenbeck’s achievement in being the first woman to win the Abel Prize is misplaced because her bigger achievement is breaking the empirical evidence that mathematicians are unable to do great work beyond the age of 40 — which in her case was a time when she was just about gaining momentum. Uhlenbeck 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,” The New York Times reported.

Uhlenbeck, a visiting associate at the Institute for Advanced Study in Princeton, said she had not decided what to do with the $700,000 that accompanies the honour.

“Looking back now I realise that I was very lucky,” she said. “I was in the forefront of a generation of women who actually could get real jobs in academia.” But she also noted: “I certainly very much felt I was a woman throughout my career. That is, I never felt like one of the guys.”

To find an influential woman, she looked to television. “Like many people in my generation,” Uhlenbeck said, “my role model was Julia Child.” 

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