Math stories Recent Work

Prizes, Thievery and Higher-Dimensional Doughnuts

And how mathematical collaborations yield breakthroughs.

The biggest math heist in years happened the morning of Aug. 1 in a Rio de Janeiro auditorium packed with witnesses — none of whom saw it happen.

The math world’s largest conference, the International Congress of Mathematicians, occurs every four years, and during the meeting, two to four researchers under age 40 receive the Fields Medal. It’s a big deal, like math’s Nobel Prize, only with less money.

One of this year’s four winners, Cambridge University’s Caucher Birkar, was recognized for his pioneering work in an abstract subfield called algebraic geometry. But less than half an hour after receiving the solid gold medal, he discovered it was missing, along with his briefcase, wallet and cell phone. Birkar soon received a replacement medal, making him the first mathematician to receive two Fields Medals in the same year.

Christopher Hacon was in the room where it happened. A few years ago, the University of Utah mathematician and Birkar co-authored one of the most important papers in the field of algebraic geometry, cited in Birkar’s award. It spoke to how they could classify complicated polynomial equations — the kind with multiple terms with a range of variables and exponents, such as x2y2 + z2 = 1.

As one of two recipients of 2018’s Breakthrough Prize in Mathematics, Hacon also had an award-winning year. Discover talked with him about the year in math, what it’s like to win big and the future of “the queen of the sciences.”

Q: What does a breakthrough in mathematics look like?

A: In my experience, breakthroughs typically happen in two phases. First, there’s an important and interesting problem that’s been out there for a while that you’re aware of. You know the background to that problem, read papers, know about other people’s research, know what difficulties everybody has come up against and where people have become stuck. Then, if you’re really, really lucky, you develop a new tool, a new trick, a new approach to attack the problem in question. Often the trick itself is relatively simple.

Read more at Discover m