Cédric Villani

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.… (más)