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.”

, 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 , 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 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.

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“The prize is certainly deserved,” says  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.

Why 2024 Abel prize winner Michel Talagrand became a mathematician

After losing an eye at the age of 5, the 2024 Abel prize winner Michel Talagrand found comfort in mathematics

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.”

Neither the Republicans nor the Democrats would gain an advantage if every voter in US elections was given the opportunity to vote by mail, according to a new statistical analysis.

The debate surrounding postal voting in the US has come to a boil this year, as the country determines how best to hold a presidential election in the midst of a pandemic. Voting by mail has been put forward as a solution to staging an election while minimising the risk of spreading the coronavirus, but President Donald Trump has claimed it would result in voter fraud and give his Democrat opponents an unfair advantage.

Michael Barber at Brigham Young University in Utah and John Holbein at the University of Virginia devised a model to look at the effect of voting by mail, by combining county-level voting data from 1992 to 2018 with US census records.

In 2018, only 175 of the 3100 or so counties in the US had switched to mostly or entirely staging their elections by postal vote, including all those in Oregon and Colorado. The pair first modelled how election turnout and party vote shares morphed as these counties switched to postal voting.

They also compared turnout and vote share in postal-voting counties with counties that still held in-person elections. Using all this data, they were able to estimate what would happen to the average county if its election was conducted by mail.

Barber says the model works because the counties that switched to postal voting are representative of the country. “Some are more conservative, while others are more liberal,” he says. “You also have both rural and urban counties.”

The model showed that giving everyone a postal vote would increase voter turnout by 2 per cent. It also showed that the Democrats would have a non-statistically significant increase in their vote share by 0.7 per cent. As there was no effect at a county level on election outcome, the pair argue that mail-in voting would have no effect at a national level either. “The conventional wisdom that an increased turnout gives an advantage to Democrats is incorrect,” says Barber. He also says that the low rise in voter turnout suggests that the convenience of voting by mail will have little effect on those who wouldn’t normally vote anyway. As this data only goes up to 2018, it is unclear how much it can tell us about the 2020 presidential election.

Due to the coronavirus pandemic, at least three-quarters of voters will be eligible to receive a ballot in the mail, according to an analysis by . “These findings suggest that when policymakers are evaluating whether to adopt a vote by mail system, they need not focus on its consequences for their own re-election,” says Marc Meredith at the University of Pennsylvania.