04b. The search for answers and the romance of maths.Cédric Villani Part 2/2.

So I love this picture, there is so much in it. The concept of entropy and uncertainty is everywhere and was re-discovered 80 years after Boltzmann by the great Shannon. Shannon, a mathematician and engineer, is the one who put the Theory of Communication, of transmission between computers, of coding.

Whenever we use computers or cellphones or whatever, there is Shannon inside, there is entropy without us knowing it.

In all our inventions of daily life there are some great minds who have contributed. Now, Boltzmann had this great idea that entropy always goes up can only increase, disorder should only increase under some circumstances. And that is a great idea, an idea that in physics is fundamental, but from the mathematical point of view still lacks a rigorous understanding, there are some mysteries in this Boltzmann's idea. It would be like an architect who has given the global plan but maybe in his building there are some columns missing, there are some windows not sealed there, and the mathematician wants to understand it all, and make the whole building stand, armed with only his logic. And then it is such a rich problem that it decomposes in a number of sub-problems that have esoteric names like "Regularization by grazing collisions," like "Entropy production inequality," whatever. You learn, when you work on it, to work on these problems and it is very emotional it is like a love affair in some sense. You get on one problem and then, as I said, it's very emotional; when you arrive in a new problem first thing is you are in total obscurity you don't understand anything, what's going on? I can't understand. Like darkness everywhere, like Bilbo, the Hobbit, in the Gollum cave, for those who know. (Laughter)

Everywhere so dark. And then at some point you feel some tiny breeze of wind something that shows you that there is an opening, you will see the light that's the moment I prefer, excitement. And third stage is you understand it all, light comes and it comes all of a sudden and it is so bright, and you understand how the various mathematical concepts can be put together to solve your problem.

It is a great moment like if you put together pieces of a symphony; believe it or not, André Weil, the legendary mathematician from France compared it to sexual pleasure, orgasm, only lasting longer, he said (Laughter). And to some extent that is correct. (Laughter)

So you go and go and, so excited, you tell the whole world about your discoveries and then after some time you start to become bored not excited any longer, it's time for a new mathematical romance. I've been through it a number of times finding new problems, new affairs, and trying to solve them, some of them I solved, some not. And that is my duty, to solve these problems and then to explain it.

Mathematics is not just about solving things for yourself it is about sharing: it's science, it's art, it's also social activity. Let me show for you, as an impressionistic picture, something that was part of my life; a book which took years for me to write.

This is a book on Optimal Transport, it is a problem involving mathematics, engineering, probability and geometry everything that was said. I will not try to describe it for you even though it corresponds to things in your daily experience and started as an engineering problem.

On this I spent years, literally, trying to solve the mysteries that are behind this optimal transport problem. The book is about a thousand pages, (Laughter) it was concluded exactly on the day of the fifth anniversary of my daughter, and it is also a baby of mine in some sense.

So when you have this discovery then you go and share and tell the people and that is what I have done, going around the world, meeting fellow scientists regardless of boundaries and cultures, I have been through Europe and Africa and America.

I have been in Israel, in Palestine, I've been in India, in China, in Japan, in Australia. Everywhere. Everywhere you feel solidarity between scientists all together fighting against the unknown, fighting to increase the knowledge and the understanding of the world by mankind. Always with their rigor, with tenacity, with hard work but also with the imagination and passion.

That's it. Thank you.

(Applause)