The First Impression
Andreas pointed out to me that the article in the Zeit is publicly available (in German only):
I’ve started reading the book now and can confirm what they write: Villani does not care if anybody understands the science he is writing about - actually, it is impossible to understand it just by reading this book (at least as far as I got). But obviously, that is not the purpose of the book: its subject is rather HOW mathematicians work.
Probably, every mathematician knows the question: “What are you actually doing the whole day?” Maybe, at the end of some days you can’t answer this question to yourself. Villani’s book introduces the reader to the discussions he had with his coworkers, and how they find problems and tackle them - his actual everyday’s work.
Nevertheless, I have one concern right now: most of you will know the (in)famous movie “Matrix” of the 90’s. By using specialised terminology, it created a pseudo-scientific and pseudo-intellectual atmosphere which was only “cool” as long as you didn’t know the precise meaning of the terms used. But I am quite confident that this will not happen with Villani’s book.