By China Science Daily reporter Hanyang Mei
On March 20, the Abel Prize, considered the "Nobel Prize" of mathematics, was announced.
The Norwegian Academy of Science and Letters has decided to award the 2024 Abel Prize to French probabilist Michel Talagrand. The prize recognizes his "seminal contributions to probability theory and functional analysis, and their outstanding applications to mathematical physics and statistical mechanics."
"Talagrand is a brilliant mathematician and an outstanding problem solver. He has made profound contributions to our understanding of stochastic processes, and in particular Gaussian processes. His work has reshaped several areas of probability theory. Furthermore, his proof of Parisi's formula for the free energy of the celebrated spin-glass state is a major achievement," said Professor Helge Holden, chair of the Abel Committee.
Image credit: Peter Badge/Typos1/ Abel Prize 2024
"My mind was like, for at least four seconds, completely blank," Talagrand told Nature of his reaction to the news. "I would not have been more surprised if I had been told a spaceship had just landed on the White House lawn."
Established in January 2002 and first awarded on June 3, 2003, the Abel Prize was created in part to compensate for the lack of a Nobel Prize in mathematics. It is funded by the Norwegian government, carries a cash award of 7.5 million Norwegian kroner (US$788,700), and is considered, along with the Fields Medal and the Wolf Prize in Mathematics, to be one of the "holy trinity" of mathematics prizes.
A 'Serendipitous' Mathematician
Michel Talagrand, now 72, is a self-described "serendipitous" mathematician and marathon runner who has visited more than 100 countries, often with his family in tow.
Born on February 15, 1952, in Lyon, France, Talagrand is the son of a mathematics professor and a French teacher. He is married to Wansoo Rhee, a professor emerita of management and human resources at Ohio State University, and they have two sons.
Due to a genetic predisposition to retinal detachment, Talagrand lost the sight in his right eye from the condition when he was five. At the age of 15, he underwent emergency surgery for another retinal detachment, this time in his left eye, causing him to miss almost a full year of school. The near-blinding experience refocused Talagrand on his studies. After recovering, he became an intensely driven student, discovering a talent for mathematics and physics, and began excelling in national mathematics competitions.
After graduating from the University Claude Bernard Lyon 1 in 1974, Talagrand joined France's largest research organization, the Centre National de la Recherche Scientifique (CNRS), where he remained until his retirement in 2017. During that time, he earned his doctorate; developed a growing interest in probability, publishing hundreds of papers on the subject; and met his future wife in an encounter that reportedly led to a marriage proposal just three days later.
Talagrand has served as a research director at the CNRS since 1985. However, his path was far from straightforward—he began his career researching high-dimensional geometry and spent more than a decade doing what he characterized as "basic stuff." "For 10 years, I had no idea what I was good at," he has said. But he does not regret the detour. The switch to probability theory, he says, "gave me another point of view ... It made me look at things in a different way." It allowed him to study stochastic processes through the lens of high-dimensional geometry.
Happy to Start with 'Small Questions'
Unlike many mathematicians who pursue "big ideas," Michel Talagrand is an "atypical" mathematician who has always followed his fancy to work on problems that interest him most. He doesn't mind working on narrow problems, seeing them as stepping stones to bigger discoveries.
"It helps to be humble and to start by trying to understand simple situations as well as possible," he has described his approach. "When studying a conjecture, I also find it helpful to try to prove it and to try to disprove it. Progress comes in jumps, like when two pieces of a puzzle fall into place. It is almost instantaneous. Now you see it and before you didn't. After such a jump, you may have a clearer vision of the problem."
Talagrand was elected a member of the French Academy of Sciences in 2004 and was awarded the Knight of the French Legion of Honour in 2011. He has received numerous awards, including the Loève Prize in Probability (1995), the Fermat Prize (1997), and the Shaw Prize (2019).
After winning the Shaw Prize, he invited the mathematical community to "get rich with my prize" by solving puzzles offering cash prizes of $5,000 to $10,000 for solving problems such as the Bernoulli Conjecture and "An Exercise on Convolution." Of course, there are caveats: "I will offer the prizes below only if I am not too old to understand the proof I receive and if I do understand it. I will not pay if I do not understand."
The first sentence on his personal website sums up his optimistic outlook on life and science: "Mathematics gives you wings." Talagrand's mathematical mind has taken him far.
On 'Probability' and 'Randomness'
Talagrand won the prize for his work in probability theory, the branch of mathematics that seeks to solve problems about "random" phenomena. A common example is the stock market, where the ups and downs of stocks are driven by a multitude of factors, including company performance, macroeconomic conditions, and political developments.
Such "random" phenomena also occur in Talagrand's own life—including the unexpected news that he had won one of the world's top mathematics prizes this year.
Among his proudest achievements are his inequalities, which are formulas that bound the fluctuations of random processes. His formulas express how the contributions of many factors often cancel each other out—leading to much less variability in the overall outcome than might otherwise be expected.
The development of probability theory was originally driven by problems arising in gambling and assessing risk. In the modern world, which is made up of constantly fluctuating random events, a thorough understanding of random phenomena is essential. Talagrand's groundbreaking discoveries help us understand and study the random processes we see all around us.
Much of Talagrand's work involves understanding and using the Gaussian distribution, often known as the "normal distribution" or "bell curve." Our entire lives are governed by Gaussian distributions—for example, the weight of babies at birth, students' test scores in school, and the retirement ages of athletes are all random events that follow a Gaussian distribution. 口语化
好吧，让我们了解一下今年的阿贝尔奖得主塔拉格兰德。他的获奖基于他在三个特定领域的杰出工作。
首先是随机过程的上确界。想象一下海滩上的浪花。浪花的高度是随机的，而上确界就是这些随机浪花高度中最大的那个。知道明年可能冲击海滩的最大浪花高度当然很有用。
其次是测量的集中性。直觉上，当一个过程受到许多不同的随机因素影响时，它会变得更加难以预测。但令人惊讶的是，这些随机因素有时会相互抵消，反而让结果更容易预测。塔拉格兰德给出了对此现象的精确定量估计。
最后，还有自旋玻璃态。抛开抽象的概率论，自旋玻璃态是一种特殊的物质状态，其中的原子排列方式让物理学家感到惊讶。塔拉格兰德运用了他的统计学和概率论知识，证明了自旋玻璃物质行为的极限，从而完成了 2021 年诺贝尔奖得主乔治·帕里西的工作。
据阿贝尔奖官方网站称，塔拉格兰德是一位多产的数学家，他的研究彻底改变了概率论、泛函分析和统计学。他的研究致力于在最基本层面理解有趣的问题，并在此过程中建立新的数学理论。他的专著非常有影响力，传播了他的许多见解。他将技术精湛与深刻的分析和几何见解相结合，创造了新的强大工具，回答了长期存在的难题，并将继续对数学及其应用产生重大影响。
专业化
2024 年阿贝尔奖授予塔拉格兰德，以表彰他在以下三个特定领域的杰出贡献：
随机过程的上确界 - 随机过程生成一系列随机值，而“上确界”是这些值集合中预期的最大值。例如，如果海浪高度是一个随机过程，则知道明年可能冲击海滩的最大浪花高度很有用。
测量的集中性 - 与直觉相反，当一个过程依赖于一系列不同的随机来源时，不同的随机因素不仅不会增加复杂性，反而有可能相互补偿并产生更可预测的结果。塔拉格兰德对此给出了精确的定量估计。
自旋玻璃态 - 自旋玻璃态是一种特殊的物质形式，原子可以在其中排列自己，这让物理学家最初感到惊讶。塔拉格兰德用他的统计学和概率论知识证明了自旋玻璃物质行为的极限，从而完成了乔治·帕里西（2021 年诺贝尔奖得主）的工作。
阿贝尔奖官方网站称：塔拉格兰德是一位非常多产的数学家，他的工作改变了概率论、泛函分析和统计学。他的研究特点是渴望在最基本的层面上理解有趣的问题，并在此过程中建立新的数学理论。他研究专著非常有影响力——传播了他的许多见解。他将技术精湛与深刻的分析和几何见解相结合，构建了新的强大工具并回答了长期存在的难题，并将继续对数学及其应用产生巨大影响。
