04a. The search for answers and the romance of maths.Cédric Villani Part 1/2.
Hello everybody. So, let me introduce me.
(Laughter)
I am a French mathematician, as was said. French, probably you have ideas about what this means: good food, great literature, cute girls, of course, all that is true. I believe that I need my crispy baguette, good cheese, raw milk to be happy in my daily life.
But it is less known that France is also a great country for science and in particular mathematics, and has been so for hundreds of years. As I was a high school student, shy, kind of nerdy, I went through this very elitist French system of preparatory classes and grandes écoles inherited from Napoleon.
I attended courses in École Normale Supérieure in Paris. It is the institution that claims the most Fields Medalists among its former students, more than any other institution in the world.
Last year my name was added to the list, and that was it. When you receive such an award of course you are full with joy and pride but also with a bit of terror like all of a sudden you become a spokesperson for your field and you will meet many people who will like to hear you talk about what you do.
So you meet everybody, you meet CEOs, you meet politicians, you meet kids in high schools, you meet musicians, you go in public newspapers, everybody sees you in the street. I even made my way to fashion magazines.
(Laughter)
You know, these French people, they like fashion. Ok. So I met everybody, from garbage men to presidents of republics, and all of them, they wanted me to talk about science and mathematicians. It is maybe a surprise for some people in the audience that there is a job called mathematician, what the hell is this?
Do they exist? What do they do? Compute? No, mathematics is not about figures. It is a job, a damned good job, (Laughter) and in fact when the very serious Wall Street Journal had the weird idea to rank all jobs in the world, guess what came first? Was it princess? Or lawyer? Or trader? No, my friends, it was mathematician.
(Laughter)
Well, I hate rankings but, well, knowing they are in the good direction, it's OK. Now, mathematician, these people define as somebody who applies mathematical theories and formulas to teach or solve problems in the business, educational or industrial climate.
To some extent this is fine but these guys forgot what for me is the most important: to create mathematics, to invent mathematics, to discover new mathematics. And that's my job. The world is full of mathematical problems that are still not solved.
Problems with numbers are the simplest to explain, there are problem about numbers that you can explain to eight year-old kids in a couple of minutes and though the smartest mathematician in the world would not be able to solve them.
My inspiration is not in numbers, it comes rather from physics. The world around us. It's so full of great problems, whenever you boil water, this is a problem, a mathematical problem that nobody has solved yet. Think about... in this room, there are all the particles of gas going around, the speech that I am making, waves of sound, the heat going on. Close your eyes for a second, maybe, and try to imagine the complexity of the surrounding gas, with its billions and billions of molecules going and bumping into each other and exchanges of energy all around your body and around you billions and billions of molecules.
This is crazy. The world is so difficult to understand. And still it is a marvel that Einstein was very surprised of, for instance, that the world in some sense can be explained and studied, thanks to mathematical formulas and physics. And it is our job, understanding the world with the help of mathematical formulas armed with only our logic.
Here are some of the objects we work with, take them as artistic objects if you want. Each of them for a mathematician's eyes stands for some natural feature. Here in blue you have the equation of fluids, incompressible fluids, all are equations.
Here the equation for gas, here the equation for plasmas and so on. And the first one on top, here, this is the Boltzmann equation, I made my PhD on this equation. When my adviser first wrote down the equation for me and told me: "You know, OK, we'll do this and this" and after a couple of years when you start to master the equation you even can do this: "Wait a minute! Am I going to spend two or three years of my life on this one-line damned equation? Aren't there better things to do?" And I did it and I loved it. (Laughter) Not only did I do it, but I spent ten years on the damned equation. (Laughter) And little by little I appreciated how rich it is, what beauty there is in it, what complexity of natural phenomena are hidden.
Many papers, many things that I still don't understand about this equation but some things I understood and this is part of what awarded me the Fields Medal. Boltzmann was a great scientist, this equation is from 140 years ago. He understood a concept that is universal deep and associated with the equation, the concept of Entropy.
Entropy is associated with uncertainty, disorder. When we look at some system and we can make some experiments like feeling the pressure with our hand, or something it always involves a great number of particles so we only have access to it in statistical sense, not the exact position of all the molecules. So there is a great deal of uncertainty, and Entropy captures this uncertainty, this disorder. Here is the formula of Entropy:
S=k.log W
This is me near the grave of Boltzmann in Vienna. I love this picture. It shows me like a heir of Boltzmann, thinking about his ideas you know there is communion throughout the centuries I worked at the same problem as he. And this formula is magical, I swear; when I met a stranger in this huge cemetery and I asked him if he knew about Boltzmann's grave the guy looked at me and said something like "S = k log W ..." like a secret, a secret password, you know for those who know.
