Mathematician Karen Uhlenbeck has become the first woman to win the Abel prize, sometimes called the Nobel prize of mathematics. She has been awarded the 6 million Norwegian kroner ($700,000) prize for her work in the fields of gauge theory and geometric analysis, which have been credited with far-reaching impact in both mathematics and physics.

Gauge theory underpins much of modern theoretical physics, and is integral to cutting-edge research in particle physics, general relativity�����Ի� string theory. Her work laid the foundations for one of the major milestones of 20th–century physics, the unification of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force.

“The holy grail in physics has always been unification of forces,” says Jim Al-Khalili at the University of Surrey, UK, who gave a talk about Uhlenbeck’s prizewinning work today. “She has made a big contribution to the mathematics that allowed us to progress some considerable way along this path.”

Among her other meaningful contributions was her work on the calculus of variations, the study of how small changes in one quantity can help find the minimum or maximum value of another. A real-world example comes in blowing soap bubbles, which always adjust their shape so that their surface area is minimised. Predicting comparable structures in higher dimensions is enormously challenging, but Uhlenbeck’s work has greatly helped.

Uhlenbeck has always blazed a trail for women in mathematics. Her plenary lecture at the 1990’s International Congress of Mathematicians was the first delivered by a woman since Emmy Noether in 1932.

When she was awarded the American Mathematical Society’s Steele Prize for Seminal Contribution to Research in 2007, she blamed the culture of the mathematical community for the small number of women in leadership positions. In a self-deprecating summation of her award-winning work, she said “changing the culture is a momentous task in comparison to the other minor accomplishments I have mentioned”.

For many, her work as an advocate for greater diversity in the field is as noteworthy as her scientific breakthroughs. “I think her contribution transcends just her work in mathematics,” says Al-Khalili.

First awarded in 2003, the Abel Prize is presented by the King of Norway to a mathematician who has made extraordinary contributions to the field. Previous winners include Andrew Wiles for his proof of Fermat’s last theorem, and Nobel-prizewinning game theorist John Nash, who was made famous by the movie A Beautiful Mind.

Simple proof?

One of the most important unsolved problems in mathematics may have been solved, retired mathematician Michael Atiyah is set to claim on Monday. In a talk at the Heidelberg Laureate Forum in Germany, Atiyah will present what he refers to as a “simple proof” of the Riemann hypothesis, a problem which has eluded mathematicians for almost 160 years.

Born in 1929, Atiyah is one of the UK’s most eminent mathematical figures, having received the two awards often referred to as the Nobel prizes of mathematics, the Fields medal and the Abel Prize. He also, at various times, served as president of the London Mathematical Society, the Royal Society and the Royal Society of Edinburgh.

If a solution to the Riemann hypothesis is confirmed, it would be big news. Among other things, the hypothesis is intimately connected to the distribution of prime numbers, those indivisible by any whole number other than themselves and one. If the hypothesis is proven to be correct, mathematicians would be armed with a map to the location of all such prime numbers, a breakthrough with far-reaching repercussions in the field.

As one of the six unsolved , any solution would also be eligible for a $1 million prize. The prestige has tempted many mathematicians over the years, none of which has yet been awarded the prize.

Atiyah is well aware of this history of failure. “Nobody believes any proof of the Riemann hypothesis, let alone a proof by someone who’s 90,” he says, but he hopes his presentation will convince his critics.

In it, he pays tribute to the work of two great 20th century mathematicians, John von Neumann and Friedrich Hirzebruch, whose developments he claims laid the foundations for his own proposed proof. “It fell into my lap, I had to pick it up,” he says.

91av contacted a number of mathematicians to comment on the claimed proof, but all of them declined. Atiyah has produced a number of papers in recent years making remarkable claims which have so far failed to convince his peers.

“People say ‘we know mathematicians do all their best work before they’re 40’”, says Atiyah. “I’m trying to show them that they’re wrong. That I can do something when I’m 90.”