Short and sweet. I would have liked there to be more technical stuff (or at least, some explanation of what the technical stuff was), but hey, what can you expect for a popular autobiography? I'd recommend it. ( )

The book gives a great feeling for the process of mathematics, and for the lifestyle of a mathematician. It is hard to give a sense of the actual mathematical research, but everything around that is conveyed well. For example, Villani gives a fantastic sense for developing the main theorem, sketched out in emails with his collaborator, as they write a LaTeX paper (by emailed drafts, without version control) and develop the proofs simultaneously. He conveys the ups and downs, the false breakthroughs, the mistakes as well as the actual breakthroughs. He also gets across the social life and itinerancy of a mathematician, traveling the world between institutes with few solid relationships outside his immediate family.

It mixes in some history of mathematics (with brief portraits of famous mathematicians). It does not really attempt to convey any of the mathematics itself, except in a very sketchy, impressionistic way; this was fine for me.

The writing is extremely overindulgent. I could do without reading his random dreams, or the stories he reads to his children, or the list of all his favorite songs on Spotify (with an explanation for why he likes each song, and the lyrics for some of them!). There is lots of filler! His language is often overly flowery; for example, he describes a math conference with, "Revelers swanning about from one event to the next in luxury limos and romantic rickshaws, everywhere celebrating the unity and diversity of mathematics, its ever-shifting shapes and forms; everywhere overcome with joy at what has so far been accomplished and wonder before all that yet remains to be discovered; everywhere, day and night, dreaming of the unknown." Perhaps this was his honest experience—who am I to say? He had just won the Fields Medal. But it rings false.

Additionally, Villani has an incredible ego. He tries to disguise it to some extent, but it still comes through very strongly. He is obsessed, for example, with the Fields Medal, and is convinced that every other mathematician is equally obsessed. (In fact, I think he is in small minority.) I am not sure of his professional ethics—several times he announces a result without having a proof—but he is obviously brilliant. ( )

A strangely compelling account of a few years in the life of a celebrated french mathematician. There are many equations and descriptions of mathematical techniques that will baffle almost everyone who reads this book. Although I had no clue what he was writing about most of the time, Villani's passion for his chosen profession made me want to read through to the end. ( )

Un livre qui (re-)donne envie de faire des maths, et ce même si l’on ne comprend pas le dixième des formules égrainées au fil des pages par Villani, totalement absconses mais d’une forme si esthétique. Le style est direct et vivant, notamment grâce à la retranscription des courriels qu’il échange avec son collègue. On suit avec grand intérêt la démarche scientifique de l’auteur, au gré de ses rencontres fertiles avec ses pairs, de ses doutes et de ses égarements, jusqu’à la preuve ultime du théorème, acte qui revêt alors une nature quasi-sacrée.

J’apprécie notamment ce trait de caractère mélangeant intrépidité et excès de confiance en soi — ce qui le rapproche ainsi de beaucoup autres hommes et femmes qui ont fait l’histoire — lorsqu'il n’hésite pas à présenter à toute la communauté scientifique une preuve encore partielle de son théorème, au risque d’être mis en défaut par ses confrères, mais ce qui lui permet en définitive d’améliorer sa démonstration, prouvant au lecteur la vertu du « trial and error » et de la critique constructive.

On peut juste peut-être regretter que le mathématicien esquisse à peine les contours de sa vie privée, l’homme s’effaçant derrière le chercheur sans doute ici un peu plus que dans la réalité. ( )

Cédric Villani was the recipient of the Fields Medal in 2010. He recall the months leading to 2010.

This is an hard act to follow for people who are not mathematics graduate students. ( )