I was very pleased to hear yesterday that this year’s Abel Prize has been awarded to Michel Talagrand. For more about Talagrand and his mathematics, see the Abel site, Quanta, NYT, Nature and elsewhere. Also, see lots of reactions on Twitter like this one.

Almost exactly ten years ago I got an email from someone whose name I didn’t recognize, expressing interest in the notes I had made available online which would turn into the book on quantum mechanics. He was reading the notes and had some comments which he included, saying he thought they were trivial but maybe I would want to take a look. Some of them were of the type “I don’t quite understand the argument on page X”. Figuring that I’d help out an earnest reader with a weak background by explaining the argument a bit better, I took a look at the argument on page X. After a while I realized that what I had written was nonsense, a very different argument was needed. “I don’t quite understand” was his way of politely telling me “you have this completely wrong.”

I soon ran into Yannis Karatzas and asked him if he knew anything about this “Michel Talagrand”. He told me “of course! He’s amazing, almost got a Fields Medal”. Over the next year or two I benefited tremendously from Michel continuing to read carefully through my notes and send me detailed comments. He was very much responsible for improving a lot the quality and accuracy of what I was writing. He had begun his own project of trying to understand quantum field theory by writing a book about it. The result is available as What Is a Quantum Field Theory?, which is a wonderful resource for anyone interested in a precise and accurate account of much of the basics of the subject. If you’ve seen Gerald Folland’s excellent Quantum Field Theory: A Tourist Guide for Mathematicians, you can think of Talagrand’s book as a much expanded version, giving the full story that Folland only sketched.

During many of my trips to Paris since that time I’ve gotten together with Michel and his wife Wansoo, and have also seen them here in New York. It has been a great pleasure to get to know Michel in person, he is a wonderful human being as well as a truly great mathematician.

I’ve known Michel Talagrand for many years, since I solved a problem (for my graduate thesis) that he solved independently. He is a truly remarkable mathematician, and is a great choice for the prize.

There is also an interesting interview of Talagrand discussing his research on spin glasses here: https://caphes.ens.fr/history-of-replica-symmetry-breaking-in-physics/ The entire collection is actually quite interesting.

“What Is a Quantum Field Theory?” is an excellent book. I wish he had addressed path integrals though. Very curious as to any insights he may have had.

Cute detail from Le Monde article:

Il y a aussi le hasard romantique qui lui a fait rencontrer son épouse dans une petite ville de l’Ohio, aux Etats-Unis. Un concours de circonstances : à la suite d’un séjour professionnel au Canada, il rend visite à un collègue dans le pays voisin, dont la porte de bureau s’ouvre sur une étudiante coréenne, qui deviendra sa femme. Et dont le nom, Wansoo Rhee, sera associé à un futur prix de mathématiques (en probabilité, analyse fonctionnelle, informatique théorique ou combinatoire), décerné par une fondation qu’il a créée et qui est dotée des montants des prix qu’il a reçus. Il sera attribué tous les deux ans, à partir de 2032 – « soit lorsque j’aurais 80 ans, ou un an après mon décès si je meurs plus tôt », précise-t-il.

https://www.lemonde.fr/sciences/article/2024/03/22/michel-talagrand-un-improbable-mathematicien-j-ai-voulu-prendre-des-risques_6223545_1650684.html

A translation of Daniel’s comment via Google Translate:

“There is also the romantic chance that made him meet his wife in a small town in Ohio, in the United States. A combination of circumstances: following a professional stay in Canada, he visits a colleague in the neighboring country, whose office door opens to reveal a Korean student, who will become his wife. And whose name, Wansoo Rhee, will be associated with a future mathematics prize (in probability, functional analysis, theoretical or combinatorial computer science), awarded by a foundation that he created and which is endowed with the amounts of the prizes that he received. It will be awarded every two years, starting in 2032 – “either when I am 80 years old, or one year after my death if I die earlier,” he specifies.”

@Giovanni Ronchi: Google Translate messed up slightly — it should read

theoretical computer science or combinatorics,nottheoretical or combinatorial computer science.Both interpretations of the French are possible, but I don’t believe that combinatorial computer science is a recognized field of mathematics, either in English or in French.@Peter Shor: DeepL is doing much better, it also correctly translates “deviendra sa femme” into “was to become his wife” instead of “will become his wife”. Here’s the translation of DeepL: “There’s also the romantic chance that led him to meet his wife in a small town in Ohio, USA. A combination of circumstances: following a professional stay in Canada, he visited a colleague in the neighboring country, whose office door opened on a Korean student, who was to become his wife. And whose name, Wansoo Rhee, will be associated with a future mathematics prize (in probability, functional analysis, theoretical computer science or combinatorics), awarded by a foundation he has set up and which is endowed with the amounts of the prizes he has received. It will be awarded every two years, starting in 2032 – “when I’m 80, or a year after I die if I die earlier”, he explains.”

I recently received my copy of ““What Is a Quantum Field Theory?” and after a quick scanning of its pages, I realized that my training as a physicist blinded me to the sloppy physicist’s mathematics of Quantum Field Theory, and how much of a problem that it poses to mathematicians.

Can/will QFT ever be put on a sound mathematical basis? Is it a worthwhile effort in that it will advance mathematics and physics?

Anonyrat,

The thing is that there are at least two different categories of sloppy use of mathematics by physicists in QFT, with very different significance.

1. Writing things that are fundamentally correct, but in a way that makes it a struggle for someone to figure out exactly what you are saying and why it is true. The writer may or may not themselves understand exactly what the correct statement is and why it is true. Talagrand does a great job in his book of taking the usual problems of this kind in a QFT book and fixing them.

2. Writing about a topic as if it is understood when it isn’t. There are various places in QFT where understanding what is going on is an open problem. Mathematicians rarely if ever will make the mistake of writing about something like this without being aware of and addressing the problem. Physicists on the other hand, will happily write about something ignoring significant problems, assuming they are “just a technicality”. Maybe the problem is just a technicality, maybe not, there are examples where we really don’t know (e.g. non-perturbative definition of chiral gauge theory).