Michel Pierre Talagrand

Quick Info

Born

15 February 1952
Béziers, Hérault, France

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Summary

Michel Talagrand is a French mathematician who has made extraordinary contributions to several areas of probability theory. These contributions are both in his research results and in the exceptional books he has written. He has won many major prizes including the Shaw Prize (2019) and the Abel Prize (2024).

Biography

Michel Talagrand is the son of Pierre Clément Joseph Talagrand (1925-2019) and Raymonde Paulette Molly-Mitton (1924-1976). Pierre was born on 10 November 1925 in Lozère, France to Clément Jean Baptiste Félix Talagrand (1902-1981) and Noémie Marie Victorine Gibelin (1894-1981). Clément had little education and, after many varied jobs, became a railway worker. Noémie never learnt to write. Pierre's teacher, however, persuaded his parents to keep him in school rather than work to help support the family. He became a professor of mathematics at a Lycée. Raymonde also came from a poor family but studied French and became a school teacher. Pierre and Raymonde were married in 1950 and Michel, born in 1952 in Béziers, southern France, was their first child.

In 1955 the family moved to Lyon when Pierre Talagrand became a mathematics professor at the Lycée du Parc. They built a house in Caluire-et-Cuire, the fifth-largest suburb of the city of Lyon. In 1957 Michel lost the sight of his right eye when he suffered from a retinal detachment. From 1958 to 1961, Michel attended the École de Vassieux in Caluire-et-Cuire. He developed some interest in science through reading a scientific magazine to which his father subscribed. His performance at the school was, however, very poor [56]:-

My spelling and grammatical skills were terrible. This was unfortunate, because at the time students were evaluated largely on their spelling skills. ... I could not spell, and therefore I was a bad student, and therefore I should not have been admitted to junior high school.

Talagrand was fortunate since his father was a mathematics professor at the Lycée du Parc, the best high school in Lyon, and was able to persuade the head of the school to admit his son to the Lycée du Parc in 1961. Although he was admitted, he was put into one of the lowest sections alongside pupils who had no interest in learning. As a consequence, the class was taught by poorly qualified teachers. Talagrand was at best an average pupil, more interested in playing with his fellow pupils than with learning. His father tried to encourage him by teaching him some mathematics, showing him some basic group theory, but it did little to encourage him. Everything changed, however, after he suffered a terrible misfortune at the age of fifteen.

For the ten years from five to fifteen he had lived rather differently from other children since, with only sight in one eye, he had not done any sport for fear that he would lose the sight in that eye. Just before his fifteenth birthday, the retina in his left eye began to detach. He suffered continuing problems, including a six month stay in hospital trying to save the sight of his left eye. Although his eyes were bandaged and he could not see, his father came to the hospital every evening and taught him mathematics. The abstract nature of mathematics meant that he could learn without being able to see. Returning to his studies at the Lycée du Parc, he was able to drop language studies and concentrate on science subjects. This was made possible by his father pleading on his behalf with the head of the Lycée.

Talagrand now lived with the continual fear of losing his sight; it had the effect that he put all his efforts into learning mathematics, the subject at which he was best. Back at the Lycée, he was now an excellent student in mathematics and physics. He benefitted from the fact that in the classes for older pupils he was taught by well-qualified teachers. His attitude to learning now completely changed and he was enthusiastic and diligent, attempting to solve every problem in the textbook. He complained to his mathematics teacher that the examinations were too easy and she then put harder bonus questions into the papers especially for him.

In his final year at the Lycée du Parc he sat the Concours Général and was ranked the third best student in France in both mathematics and physics. The natural route for high achievers would now have meant two years of study to prepare for entry to one of the Paris Grandes Écoles. Talagrand parents, however, thought that this highly demanding route would be too stressful given his severe health problems. Consequently, in 1969 he entered his local university, the Université Claude Bernard: Lyon 1; he thrived at this university [21]:-

... at the University of Lyon I was saved again by the high level of the lectures. I would even say too high, because it was too difficult for most of the students, but it saved me, because I could learn things in the proper way. In particular, I took a course in measure theory. I fell in love with measure theory, that was my first mathematical love, and it greatly influenced me during the rest of my life.

Being in continual fear that he would go blind, Talagrand felt that he had to obtain a government position and the best for him would be, like his father, a teacher at a Lycée. The route to this was the Agrégation de Mathématiques, the national competition by which secondary school mathematics teachers are selected in France. He therefore put all his efforts into preparing to sit the Agrégation; he scored 318 out of 320, a remarkable achievement. By a stroke of good fortune, although he had not undertaken any research at this time, he had already been accepted for a position at the CNRS, the French National Centre for Scientific Research, in 1974. Let us explain the good fortune.

France was still experiencing the so-called "thirty glorious years", 1945-1975. The French economy was growing at 5% a year and there was money for 17 new positions at the CNRS in the year 1974; many more than there were a couple of years later. To fill these positions they would have to hire a very small number of people without research experience. Jean Braconnier (1922-1985), an expert in topological groups and harmonic analysis, was director of the new mathematics teaching and research unit at the University of Lyon. Before Talagrand sat the Agrégation examinations, he suggested that he apply for one of the CNRS research positions. Jean-Pierre Kahane was on the CNRS hiring committee and, after receiving Talagrand's application with strong recommendations from four Lyon University professors, he wrote to Talagrand asking him to say why they should hire him. Talagrand wrote a long letter explaining his health problems and his achievements; he was offered a research intern position which he quickly accepted.

Talagrand joined Gustave Choquet's seminar at the Université Paris VI where he undertook research advised by Choquet [55]:-

I didn't know anything at all when I arrived in Choquet's seminar where people have been doing this kind of mathematics for years. I sit there and I have no idea what they are talking about. There's no easy solution because I asked for a paper that I could read, I looked at the paper and in the introduction it mentioned ten other papers which I had no idea about so it was difficult to start.

He went to Choquet and asked him to give him some research problems. He solved some quickly and Choquet was impressed and, perhaps even more importantly, it gave Talagrand the confidence he needed. In 1975 he defended his thèse de 3e cycle, Sommes vectorielles d'ensembles de mesure nulle: Convolution de mesures portées par des surfaces convexes sur une conjecture de H H Corson Ⓣ. He announced results in Comptes Rendu in 1975 and published the 36-page paper Sommes vectorielles d'ensembles de mesure nulle Ⓣ in the Annales de l'Institut Fourier Université de Grenoble in 1976. He begins the paper as follows:-

Our starting point was a question posed in 1973 at the Introductory Seminar on Analysis by M Goullet de Rugy: If an analytic set A of R is such that for every compact set X in R, with zero Lebesgue measure, A + X is also of zero measure, is A countable? We will provide a positive answer to this problem and study its generalisations to Lie groups and locally compact abelian groups.

I would like to thank M Choquet for the invaluable help he provided me, on the one hand through his unwavering moral support, and on the other hand by suggesting that the framework of Lie groups concealed the true nature of the problem, and by proposing a much more suitable one, which led me to Theorem 3.

Also in 1975 he published the three papers: Solution d'un problème de R Haydon; Sur une conjecture de H H Corson Ⓣ; and Convolution de mesures portées par une surface convexe Ⓣ. He was awarded his doctorate in 1977 after defending his thesis Mesures invariantes, compacts de fonctions mesurables et topologie faible des espaces de Banach. Tome 1: Simplexes de mesures invariantes. Tome 2: Compacts de fonctions mesurables; espaces de Banach faiblement K-analytiques Ⓣ. We note that MathSciNet lists 34 papers which Talagrand published between 1975 and 1978.

In 1978 Talagrand was awarded the Bronze Medal by the CNRS:-

The Bronze Medal recognises a researcher's first work, establishing them as a talented specialist in their field. This award represents an encouragement from the CNRS to pursue well-established and already fruitful research.

Talagrand was invited to spend the autumn of 1978 at the University of British Columbia in Vancouver. He greatly enjoyed the visit and he decided to visit a number of places in North America where people he knew were working before returning to France. One of these people was Joseph Diestel (1943-2017), an expert in functional analysis, particularly Banach space theory and the theory of vector measures, who was Professor of Mathematics at Kent State University, Ohio. While Talagrand was talking to Diestel in his office, a PhD student, Wansoo Rhee, came to give Diestel a draft of her thesis on probability theory, Studies on the Rate of Convergence in the Central Limit Theorem. Talagrand wrote [56]:-

I was fascinated, so I arranged lunch with her. After having talked to her I felt madly in love, and remain so to this day. I proposed to her almost immediately. "You are crazy" she said. It only took three years and many flights, including a long stay in Korea, to convince her that I was not.

Talagrand was back at Kent State University in 1979 when he attended the 'International conference of Banach spaces and classical analysis' organised by Joe Diestel in August 1979. He wrote [57]:-

I have fond memories of the first class Banach Spaces conference in Kent that Joe organised in the summer of 1979. I arrived in Kent several weeks before the conference, and, without my asking, Joe managed to fund my stay in a royal way: he did care about people.

Michel Talagrand and Wansoo Rhee were married in Franklin, Ohio on 28 December 1981. Wansoo Theresa Rhee had been born in South Korea on 13 April 1950. Talagrand said [21]:-

... her father, who was a very prominent scholar in South Korea, had taught his children that the only real value in life is scholarly knowledge. For a mathematician to find a wife who has been told that as a child, this is an absolute miracle. She always totally respected my work, and I wouldn't be here without her constant support.

Michel Talagrand and Wansoo Rhee have two sons, Eugene Rhee Talagrand (born 3 October 1983) and Daniel Rhee Talagrand (born August 1986). Speaking about his family, Talagrand said [65]:-

The most precious resource in life is time. I manage my time very well. You can ask my children, even though I was doing mathematics, I spend a lot of time with them. Time and mental energy is what is in short supply for mathematicians. Time together with the family is number one priority.

We note that MathSciNet list 29 papers co-authored by Michel Talagrand and Wansoo Rhee. The first is On Berry-Esseen type bounds for m-dependent random variables valued in certain Banach spaces (1981) and the 29th is The random weighted interval packing problem: the intermediate density case (2000).

Before his marriage, however, Talagrand had avoided going blind because of what turned out to be a very fortunate incident. In 1981 he made a trip to India and, when in a train station, someone had cut through his bag with a razor blade and stolen his camera lenses and sunglasses. He had been terrified of losing his sight since the age of fifteen but had reacted to it as he grew older by stopping going to an ophthalmologist for a check up. Back in France he had to visit an ophthalmologist to get a prescription for new sunglasses. She insisted he made an appointment to have his retina checked. This showed his retina were about to detach. By this time laser surgery was able to ensure that he would have no further problems. Had he not had this check, he would have become blind in a few months time.

Talagrand is famed for his extraordinary contributions to probability theory but, up to the early 1980s he had not worked on this topic. In interviews he has given after winning major prizes for his work on probability theory he has played down the contributions he made in the first ten years of his research career, but this were of a very high standard as is evidenced by his being awarded the Bronze Medal by the CNRS in 1978, the Peccot-Vimont Prize by the Collège de France in 1980, and the Servant Prize by the Académie des Sciences in 1985. His move towards probability, in particular to the boundedness of stochastic processes and concentration of measure, was, in large part, due to Gilles Pisier and Vitali Milman. His move towards probability started, however, with his work on measure theory. This was influenced by David Fremlin (born 1946) who worked at the University of Essex, Colchester, England, but held temporary positions at the Université Paris VI in the late 1970s and early 1980s. Fremlin and Talagrand wrote seven joint papers between 1978 and 1985, the first, with Jean Bourgain also a co-author, being Pointwise compact sets of Baire-measurable functions (1978) which begins:-

In this paper we study sets of real-valued functions defined on a topological space which lie within some class of "measurable" functions and satisfy some criterion of compactness or relative compactness in that class, which is always given the topology of "pointwise" or "simple" convergence.

The last of the seven papers is Subgraphs of random graphs (1985) in which, among many other results, Fremlin and Talagrand prove a long-standing conjecture of Erdős.

Talagrand's first book [47] was a measure theory work with title Pettis integral and measure theory (1984). He writes in the Introduction:-

I was introduced to this kind of measure theory by D H Fremlin back in 1976. This work contains many of his results and is considerably influenced by his powerful ideas. Part of the research presented here, as well as the actual writing of the book was done while I visited the Department of Mathematics at The Ohio State University.

J J Uhl, Jr, who co-authored the book Vector Measures (1977) with Joseph Diestel, reviewed Talagrand's book and writes [62]:-

The memoir is pleasing to read because it begins with elementary material and becomes increasingly deeper and deeper, thus allowing a reader to complete it or to bail out at the right time. ... This impressive memoir will leave its imprint on measure theory for a long time.

For more information about this book, and eight other books by Talagrand, see THIS LINK.

We mentioned above Gilles Pisier and Vitali Milman as two people who were major influences in Talagrand studying the boundedness of stochastic processes and concentration of measure. Pisier was appointed as a professor at the Université Paris VI in October 1981 and he introduced Talagrand to the problem of characterising the boundedness of Gaussian processes. Talagrand soon was highly successful and wrote the paper Regularity of Gaussian processes (1987). Michael Marcus, in a review of this paper, writes:-

In this paper the author obtains necessary and sufficient conditions for the continuity or boundedness of a Gaussian process. ... This is a deep and important paper. An understanding of it is essential for any further serious research in Gaussian processes.

From 1985 Talagrand was CNRS Director of Research in the Equipe d'analyse fonctionnelle at the Mathematics Institute of Jussieu, the largest research centre for fundamental mathematics in France. Also from 1985, he spent part of each year at Ohio State University.

Talagrand has won many major awards for his outstanding contributions including the Line and Michel Loève International Prize in Probability (1995), the Fermat Prize (1997):-

... for his fundamental contributions in various domains of probability,

the Shaw Prize (2019):-

... for his work on concentration inequalities, on suprema of stochastic processes and on rigorous results for spin glasses,

the Stefan Banach Medal (2022):-

... for groundbreaking results in functional analysis, the theory of Banach spaces, probability theory and in statistical mechanics: the theory of "spin glasses,

and the Abel Prize (2024):-

... for his groundbreaking contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics.

For more information about why Talagrand was awarded these prizes, see THIS LINK.

Of course, these prizes came with a substantial monetary award. He set up the Wansoo Rhee and Michel Talagrand Foundation and endowed it with his prize money. It is required to create a future mathematics prize in probability, functional analysis, theoretical computer science, or combinatorics. It will be awarded every two years, starting in 2032, when he will be 80 years old, or one year after his death if he dies earlier.

In addition to these awards and prizes we should mention other honours given to Talagrand. He was invited to lecture in Section 9: Operator Algebras and Functional Analysis at the International Congress of Mathematicians in Kyoto, Japan in August 1990. He gave the lecture Some Isoperimetric Inequalities and Their Applications. He introduced his lecture as follows:-

Consider a product of measure spaces, provided with the product measure. Consider a subset A of this product, of measure at least one half. An important fact (the so-called concentration of measure phenomenon) is that even a small "enlargement" of A has measure very close to one. The inequalities we present describe this phenomenon for several notions of "enlargement".

He was invited again to lecture to the International Congress of Mathematicians, this time to deliver a one-hour plenary lecture to the Congress in Berlin in August 1998. He gave the lecture Huge Random Structures and Mean Field Models for Spin Glasses. The paper based on his lecture in the Proceedings of the Congress has the following Abstract:-

To explain (at least qualitatively) the unconventional magnetic behaviour of certain materials, the physicists have been led to formulate and to study simple mathematical models. The concepts and methods they developed in this process appear to apply to a number of important random combinatorial optimisation problems, for which they have proposed remarkable formulas. Their discoveries point towards a new branch of probability theory. Finding rigorous arguments to support their conjectures is a formidable challenge and a long range programme, some steps of which are described in the present paper.

Talagrand retired in 2017 but five years before that he began a project to understand Quantum Mechanics in a mathematically rigorous way. The final result was the book What Is a Quantum Field Theory? (2022). He begins the Introduction as follows [38]:-

As a teenager in the sixties reading scientific magazines, countless articles alerted me to "the infinities plaguing the theory of Quantum Mechanics". Reaching 60 after a busy mathematician's life, I decided that it was now or never for me to really understand the subject. The project started for my own enjoyment, before turning into the hardest of my scientific life. I faced many difficulties, the most important being the lack of a suitable introductory text. These notes try to mend that issue.

The book has been very highly praised. From example, Sourav Chatterjee, Stanford University, writes:-

This book accomplishes the following impossible task. It explains to a mathematician, in a language that a mathematician can understand, what is meant by a quantum field theory from a physicist's point of view. The author is completely and brutally honest in his goal to truly explain the physics rather than filtering out only the mathematics, but is at the same time as mathematically lucid as one can be with this topic. It is a great book by a great mathematician.

For more information about this book including a longer extract from Talagrand's Introduction and extracts from various reviews, see THIS LINK.

Talagrand had terrible worries with his eyesight for many years but, from the age of 30, laser treatment had saved his sight. He then took up activities that he had not done in his youth because of his health problems. Between ages of 30 and 44, he ran 10 kilometres every day which helped him clear his brain after a day of mathematics. Soon after he turned 60, he developed a new health problem [56]:-

About 10 years ago it became clear that blood was not circulating well in my brain, so I had an MRI. It was quite an intense emotion when the radiologist told me that I had holes in my frontal lobes and had me rush to take low doses of aspirin. As I had not felt anything special, I kept living and working as usual. What else could be done? Early 2020, I fainted in my bathroom, had a bad fall, and a brain haemorrhage. The visible consequences were manageable, so again, what could I do but keep doing what was already started? The amazing thing is that I discovered the final word about random Fourier series after this haemorrhage.

He continues to take exercise and climbs 88 stairs in his building which takes him about 20 minutes.

Let us end this biography with a two quotes. The first from the mathematicians who nominated Michel Talagrand for the Banach Medal [64]:-

Astonishing is the richness and value of his achieved results. None of them is "easy". They demand a lot of perseverance and extraordinary deep insight. Many of them are solutions of famous old problems.

The second quote is from Helge Holden, chair of the Abel Prize Committee [35]:-

Talagrand is an exceptional mathematician, and a formidable problem solver. He has made profound contributions to our understanding of random, and in particular, Gaussian, processes. His work has reshaped several areas of probability theory. Furthermore, his proof of the celebrated Parisi formula for free energy of spin glasses is an amazing accomplishment.

For further information about Talagrand's life and work, see one or both of his autobiographies.

Talagrand's Shaw Prize autobiography is at THIS LINK.

Talagrand's Abel Prize autobiography is at THIS LINK.

References (show)

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53. M Talagrand, Upper and lower bounds for stochastic processes: Decomposition Theorems (Springer Verlag, Berlin, Heidelberg, 2021).
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    https://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/Memories_and_Stories_about_Joe_files/Michel_Talagrand.pdf
58. The ceremony of awarding the Stefan Banach Medal, Polish Academy of Sciences (22 August 2022).
    https://web.archive.org/web/20220922155626/https://www.impan.pl/en/events/news/2022/wreczenie-medalu-banacha
59. The Shaw Prize in Mathematical Science 2019, YouTube (27 April 2020).
    https://www.youtube.com/watch?v=22hR2CkNGXE&t=81s
60. C Thorsberg, Mathematician Who Made Sense of the Universe's Randomness Wins Math's Top Prize, Smithsonian Magazine (25 March 2024).
    https://www.smithsonianmag.com/smart-news/mathematician-who-made-sense-of-the-universes-randomness-wins-maths-top-prize-180984020/
61. E Trevino-Aguilar, Review: Upper and lower bounds for stochastic processes: Decomposition Theorems, by Michel Talagrand, Mathematical Reviews MR4381414.
62. R Zaharopol, Review: The generic chaining: upper and lower bounds of stochastic processes, by Michel Talagrand, SIAM Review 49 (2) (2007), 363-365.
63. R Zaharopol, Review: The generic chaining: upper and lower bounds of stochastic processes, by Michel Talagrand, SIAM Review 49 (2) (2007), 363-365.
64. F Prztycki, Banach Medal to Professor Michel Talagrand, Newsletter of the Institute of Mathematics of the Polish Academy of Sciences 15 (2022/2023), 13.
    https://old.impan.pl/wydarzenia/gazeta/newsletter_winter_2022_15.pdf
65. N Koul, From Challenges to Triumph: How Michel Talagrand's Mindset Can Inspire You, Medium (23 May 2024).
    https://medium.com/@nimritakoul01/from-challenges-to-triumph-how-michel-talagrands-mindset-can-inspire-you-d37320237edc

Additional Resources (show)

Other pages about Michel Talagrand:

1. Michel Talagrand's awards
2. Michel Talagrand's books
3. Michel Talagrand's Shaw Prize autobiography
4. Michel Talagrand's Abel Prize autobiography

Other websites about Michel Talagrand:

1. Mathematical Genealogy Project
2. MathSciNet Author profile
3. zbMATH entry

Honours (show)

Honours awarded to Michel Talagrand

1. The Shaw Prize in Mathematical Sciences 2019
2. The Abel Prize 2024

Cross-references (show)

1. Other: Recent Changes — up to June 2025

Written by J J O'Connor and E F Robertson
Last Update June 2025