French mathematician Michel Talagrand has been awarded the 2024 Abel Prize “for his groundbreaking contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics,” according to the President of the Norweigan Academy of Science and Letters (CNRS).
The Abel Prize is often seen as an equivalent to a Nobel Prize in the field of mathematics. When Alfred Nobel was creating annual prizes, he decided to omit a prize in mathematics, largely because he was not interested in the field and he did not see many practical applications of it. The Abel was first proposed by mathematicians at the turn of the 20th century when they discovered what Nobel had done, but the prize was only awarded for the first time in 2003 (Britannica).
The prize comes with a monetary award of 7.5 million Norwegian kroner, which is approximately 700,000 U.S. dollars (The Able Prize). Talagrand has pledged to use at least a large portion of these winnings for the foundation of a different mathematical prize in his name, which would be awarded to young researchers with focuses similar or adjacent to his own. For this purpose, Talagrand will also use his winnings from the Shaw Prize, another prestigious award that comes with 1.2 million U.S. dollars and that he won in 2019 (The Shaw Prize).
Talagrand’s work is primarily focused on stochastic models, or models of seemingly random processes, such as the changes in a stock price, the water level of a river, and the strength of the next earthquake. These models all have a large amount of independent variables and factors that could affect the output, which makes analysis of them far more difficult.
It has long been known in mathematics and probability that seemingly random processes often are not when they occur many times. As a simple example, flipping a coin once is, ideally, a completely random process. There is a probability of one-half that heads comes up, and a probability of one-half that tails comes up. There is no predictability. However, if you flip a coin 1000 times, you can calculate a narrow range for the number of heads and have your result fall in the range almost all the time. In fact, the probability that the number of heads is between 450 and 550 is approximately 99.7 percent. The chance that you get less than 400 or more than 600 is negligible even in the often hyper-specific world of mathematics.
Talagrand’s work expanded and built on this simple principle, using increasingly complex and multi-dimensional examples. (It is important to note that multi-dimensional, at least in this case, does not mean that it involves three or four variables, but rather that it involves thousands). Using Talagrand’s complex method, which is called generic chaining and involves multi-dimensional geometry, scientists in all fields can now accurately predict the bounds of a seemingly random value for further exploration.
There are many practical applications of Talagrand’s work as well. For example, scientists would now be able to predict the maximum water level of a river, which would allow them to better assess the risk of flooding and the need for certain protective barriers.
Talagrand also focused on the center of the distribution. Going back to the coin example, the likely numbers of heads get increasingly concentrated around half of the total number of coin flips as one continues to flip a coin. He was able to expand this principle to multi-dimensional models, which can allow scientists and fellow mathematicians to more accurately predict what is considered “normal”. This could let them know when something is “unusual” and is therefore cause for concern.
Talagrand now joins a pantheon of modern mathematicians by winning the Abel Prize, which includes figures such as Jean-Pierre Serre and Andrew Wiles, the latter of which achieved worldwide recognition and fame that transcended the esoteric mathematical community after his proof of Fermat’s Last Theorem, an idea which had gone unsolved for more than 300 years despite the efforts of some of the smartest individuals in history (University of Oxford). Interestingly, out of the 27 who have received the Abel Prize, two work (or worked) at Stony Brook University. John Milnor won in 2011 “for pioneering discoveries in topology, geometry, and algebra,” and Dennis Sullivan won in 2022 “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects” (Stony Brook University).
