2024 Abel prize: Michel Talagrand wins maths award for making sense of randomness

Michel Talagrand has won the 2024 Abel prize, sometimes called the Nobel prize of mathematics, for his work on probability theory and describing randomness. The news came as a surprise to Talagrand, who found out on what he thought was a departmental Zoom call. “My brain completely stopped for five seconds. It was an amazing experience. I never, ever could have expected such a thing.”

Talagrand, based at the French National Centre for Scientific Research (CNRS), has spent a large part of his four-decade career characterising the extremes of random, or stochastic, systems. These problems are common in the real world – for example, bridge builders might need to know the maximum wind strength to expect from the local weather.

Such random systems can often be extremely complex and contain many random variables, but Talagrand’s methods, which convert these systems to geometric problems, can extract useful values. “He is a master in obtaining precise estimates and knowing exactly what to add or subtract in order to get sharp estimates,” says Helge Holden, chair of the Abel prize committee.

Talagrand also developed mathematical tools and equations for systems that, while random, display some predictability in their randomness, a statistical principle called concentration of measures. His equations, known as Talagrand inequalities, can be used for many systems that show a concentration of measures, says Assaf Naor at Princeton University, such as famous algorithmic puzzles like the travelling salesman problem. “In addition to just being a great discoverer himself, he is influential. He provided the world with an amazing collection of insights and tools,” says Naor.

Perhaps inspired by his own work, Talagrand says he sees his career as a random process. “It’s absolutely frightening if I look at my life and the important things which happened, they are determined by minor random influences, and there is no planning whatsoever,” he says.

Though many of his achievements were general, he also had a particular interest in the mathematical underpinnings of spin glasses, an unusual magnetic arrangement where a material’s atoms can act like tiny magnets that point in random directions and show no obvious order, similar to the lack of a repeating crystal structure in regular glass.

“The prize is certainly deserved,” says Giorgio Parisi at Sapienza University of Rome, Italy, who won the 2021 Nobel prize for physics for his own work on spin glasses. Although Parisi and his colleagues first suggested a formula to describe these materials, named after Parisi, it wasn’t mathematically proven until work by Talagrand and Italian physicist Francesco Guerra. “It’s one thing to believe that the conjecture is correct, but it’s another to prove it, and my belief was that it was a problem so difficult it could not be proved,” says Parisi.

It also helped draw the attention of other mathematicians to the field, says Parisi. “It was a wonderful proof and completely changed the situation, because this was a starting point for a much deeper understanding of the theory.”

For Talagrand, one of the keys to his success has been persistence. “I’m not able to learn mathematics easily, I have to work. It takes a very long time and I have a terrible memory. I forget things. So I try to work, despite these handicaps, and the way I worked was trying to understand really well the simple things.”

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