What is it that French people do better than all the others? If you would take polls, the top three answers might be: love, wine and whining.
Maybe. But let me suggest a fourth one: mathematics. Did you know that Paris has more mathematicians than any other city in the world? And more streets with mathematicians’ names, too. And if you look at the statistics of the Fields Medal, often called the Nobel Prize for mathematics, and always awarded to mathematicians below the age of 40, you will find that France has more Fields medalists per inhabitant than any other country.
What is it that we find so sexy in math? After all, it seems to be dull and abstract, just numbers and computations and rules to apply. Mathematics may be abstract, but it’s not dull and it’s not about computing. It is about reasoning and proving our core activity. It is about imagination, the talent which we most praise. It is about finding the truth. There’s nothing like the feeling which invades you when after months of hard thinking, you finally understand the right reasoning to solve your problem. The great mathematician André Weil likened this — no kidding — to sexual pleasure. But noted that this feeling can last for hours, or even days.
The reward may be big. Hidden mathematical truths permeate our whole physical world. They are inaccessible to our senses but can be seen through mathematical lenses. Close your eyes for moment and think of what is occurring right now around you. Invisible particles from the air around are bumping on you by the billions and billions at each second, all in complete chaos. And still, their statistics can be accurately predicted by mathematical physics. And open your eyes now to the statistics of the velocities of these particles.
The famous bell-shaped Gauss Curve, or the Law of Errors — of deviations with respect to the mean behavior. This curve tells about the statistics of velocities of particles in the same way as a demographic curve would tell about the statistics of ages of individuals. It’s one of the most important curves ever. It keeps on occurring again and again, from many theories and many experiments, as a great example of the universality which is so dear to us mathematicians.