Karen Uhlenbeck – The First Woman to Win the Abel Prize, the “Nobel Prize” for Mathematics

Science and Technology

One of the most prestigious awards in the field of mathematics, the Abel prize, has been awarded to the emeritus Professor Karen Uhlenbeck of the University of Texas, making her the first and only woman to have won the award, out of the twenty laureates since the Abel prize’s conception in 2002.

The Abel prize was first proposed in 1899 by Sophus Lie – after learning there would be no Nobel prize in mathematics – to be a celebration of 100 years since the birth of the pioneering Norwegian mathematician, Niels Henrik Abel.

After more than a century, it was finally awarded for the first time in 2002, and has now been awarded every year since. It accompanies a prize of 6 million Norwegian Kroner (~£530,000), although Prof. Uhlenbeck said she had not decided yet what to do with the prize money.

Born in 1942 in Cleveland Ohio, Karen received a BA in 1964 from the University of Michigan, she went on to earn an MA and PhD from the Brandeis University, but her career has not been so easy. Speaking of her time at Brandeis university in “A Personal Profile of Karen K. Uhlenbeck”, she said, “It was self-evident that you wouldn’t get ahead in mathematics if you hung around with women. We were told that we couldn’t do math because we were women….. There was a lot of blatant, overt discouragement, but there was also subtle encouragement. There were a lot of people who appreciated good students, male or female, and I was a very good student.”

Following her PhD, and some temporary work in MIT and the University of California, Berkeley, she and her husband Olke C. Uhlenbeck (whose father was the prominent theoretical physicist George Uhlenbeck) looked for more permanent positions. However the pair found it difficult to get work in the same department due to “anti-nepotism” rules.

“We were told that we couldn’t do math because we were women….. There was a lot of blatant, overt discouragement”

Eventually she took up a position at the University of Illinois, but speaking of it in an interview said that “during my time at Illinois, there was really a division between women and men in the department … I didn’t feel at home mathematically, for sure.”

She later moved to the University of Chicago, in 1983, and then finally, in 1988, to the University of Texas, of which she is an emeritus professor. Presently she is visiting Princeton as a senior research scholar.

According to the Abel prize committee, Prof. Uhlenbeck won the prize “for 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.” Her work focuses on the topics of ‘the calculus of variations’, a topic which dates back centuries to famous problems such as the ‘Brachistochrone problem’, among others.

Her work relates to finding, or showing the existence, of minimal surfaces, that is, a surface which minimises surface area for a given boundary. An example of this is the shapes that soap bubbles make on wire boundaries.

Uhlenbeck’s studies build upon the theory of her PhD supervisor Palais and his ‘Palais-Smale compactness condition’, which guarantees the existence of minima in one dimension. However Uhlenbeck realised that this condition fails in higher dimensions, and her papers explore, among other things, what happens when this condition is violated. She also co-authored foundational papers on the subject of minimising harmonic maps.

As well as being the first woman to win the Abel prize, she was also gave a highlighted plenary talk at the International Congress of Mathematics in 1990, being only the second ever woman to do so since its conception 122 years ago.

Her work also extends from the academic to outreach; she co-founded the “Women and Mathematics” program at the Institute for Advanced Study, which aims to counter “the higher attrition rate of female mathematicians compared to their male counterparts at every critical transition stage in mathematical careers”.

In the words of British theoretical physicist, Jim Al-Khalili “Young mathematicians not only know of her work, but they also know how hard she has worked to try and promote maths and encourage young women to get into the field”.

Image Credit:https://www.ias.edu/news/press-releases/2019/abel