I finished reading the book now, and will try to give a short resumee. In all of my former blog entries, I did not speak much about the actual story of the book, so I’ll start with an overview of what happens. Cedric Villani is a scientist at the ENS in Lyon working in mathematical physics. He and his colleague C. Mouhot start working on the problem of nonlinear Landau damping. In the book which is similar to a diary, the time when they develop their theory is described. Villani and his family move to Princeton for a reseach stay. He gets appointed to the director of the Poincare Institute in Paris. In the end, Villani gets awarded the Fields medal for his work.
I liked the book since it is a realistic description of the working routine of a mathematician. It shows the ups and downs, the moments when you think you have a breakthrough, or when you are desperate and don’t see any hope for rescue. He doesn’t try to simplify the mathematics to make it “understandable” because he knows that it is impossible. Instead, the mathematics is kind of a background which is always present, never obvious, and therefore adds a deeper secret level behind the story, unaccessible to most readers. Comparing to popular literature, it’s like the old story of Middle Earth in the Lord of the Rings books: you can feel it, but with only the books you can never understand it. But it makes the world much more lively and fascinating. And since I mentioned “Matrix” in one of my earlier blog entries, my fears didn’t come true: the “back story” in Villani’s bok is not only superficial, but full of life and deeper contents.
One may remark that it is a little bit narcissistic to write a book about his own successes as Villani did - but on the other hand, given his great achievements in science, he has reason to become narcissistic. After all, I can recommend the book to anyone who wants to get an idea of how mathematicians work, and to mathematicians who wonder how they can present their work to the public.