In conversation with Cédric Villani

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Early on a February morning, we’re standing outside one of the many trendy cafes in Fitzrovia. Down the street we spot a man striding our way, wearing a full suit, a hat, a giant spider brooch and hastily tying a cravat. It could only be superstar mathematician Cédric Villani.

Cédric is passing through London on his way back from the US, but this is no holiday. In his two days here, he is attending a scientific conference, giving a public lecture, and taking part in a political meeting. His packed schedule leaves the increasingly-busy Fields medallist just enough time to join us for breakfast.

Fields medal

One afternoon in early 2010, Cédric was in his office at the Henri Poincaré Institute in Paris, getting ready to pose for publicity photographs. The photographer, from a popular science magazine, was setting up his tripod when the office phone rang. Cedric leant over and picked it up. It was Lázló Lovász, president of the International Mathematical Union.

Fields medal ceremonies are held every four years, and six months before each ceremony, the winners are alerted by telephone about their success. During these six months, they are sworn to secrecy, but with the photographer in the room, Cédric suddenly realised that he might be in possession of the shortest-kept secret ever. By some miracle, the tripod had proved sufficiently interesting for the photographer, or perhaps he didn’t follow the English conversation, and the secret remained safe.

Cédric had first realised that winning the Fields medal was a possibility at some point in 2004, when he was 31. Fields medals are only awarded to mathematicians under the age of 40, and until the phone call arrived, Cédric only placed his chances of winning at around 40%. “The prospect of winning the medal does put some pressure on you during your 30s. But everybody knows—it’s part of the common mythology—that if you try too hard to win it, you will fail.”

In August 2010, Cédric was officially awarded the medal at the International Congress of Mathematicians in front of 4000 mathematicians and journalists. Finally, he was allowed to celebrate: he did so by taking a dozen colleagues to a fancy restaurant in Germany, thereby relieving himself of half the CAN$15,000 prize money.

The Boltzmann equation and Landau damping

While enjoying a hearty breakfast, Cédric explains his research to us. “In this room, we are surrounded by air. You can use the Navier–Stokes equations to describe this air. But at higher altitutes, where the atmosphere is more dilute, these equations do not work so well. Here, it is better to use the Boltzmann equation.” The Boltzmann equation describes the statistical behaviour of a gas, and Cédric has worked on two areas related to this equation: the influence of grazing collisions, where two particles pass very close to each other; and on the increase in entropy as time passes.

Cédric’s other work, completed with Clément Mouhot, looked at the mechanics of plasmas: high-energy soups of electrons and positively-charged ions which are formed by superheating gases. Roughly speaking, if a plasma is exposed to a brief electric field, then the electric field will become very small as time goes by. This decay effect is called Landau damping. In the 1940s, Lev Landau proved that this damping occurs for a linearised approximation of a plasma. Cédric and Clément proved this result for the full non-linear system of equations.

It was the work in these two areas that led to Cédric being awarded the Fields medal, although he has worked in other areas as well. Imagine you have a large pile of sand and a hole to fill (with the same volume as the sand). How should you go about moving the sand to fill the hole, while minimising the total work you have to do? This is an example of an optimal transport problem.

He used the ideas of entropy from his study of the Boltzmann equation and applied them to this problem, and used this to establish a link between the non-Euclidean curvature of a manifold and properties of the entropy. This led to a “whole bunch of research related to non-Euclidean geometry”.

Career choices

If the young Cédric had had his way, his research life would be very different. “When I was a kid, I wanted to go into palaeontology. I recently had a great discussion with Jack Horner, the world’s most famous expert on the subject—‘Mr Dinosaur’, and it was like reconnecting with my youth.”

So is he happy in mathematics academia? “Academia is where my heart belongs. I like industry, and I sit on the advisory boards of several companies, but I’m an academic guy. My research has not had an application so far that I am aware of. But, with applications, when they come it will be much later.”

Traces of Cédric’s early passion can still be spotted though. He owns a cuddly toy dinosaur called Philibert, and leaves maths books open to keep him entertained. Years later, he found that Alan Turing, one of his greatest heroes, used to do the same with his teddy bear at university.

In fact, Turing is the hero in his recently-penned graphic novel,  Les Rêveurs Lunaires. Excited readers will be disappointed, however, as “even though England is everywhere in the book, English publishers have not yet been interested in making an translation.” This is a double-shame, as you will remember from Chalkdust issue 04 that comic books about maths are `hot’.

He is, however, less sure whether he would like to travel back in time to work with Turing or other mathematicians. “People like Gauss—so fascinating, so superhuman. But he was known for being rather grumpy; maybe it would not be so pleasant! Then take Riemann—a genius! But a bit depressive; maybe he was not so fun to work with. I’m not sure if he would want to see me.”

A day in the life of a Fields medallist

Life is rarely routine for Cédric. In a usual year he travels to 20–25 countries, and has roughly 30 different appointments each week. When he can, he enjoys a quiet family breakfast at home. The contents of this breakfast have not changed since he was a child, and include bread, jam and hot unpasteurised milk. For today, however, he makes do with a full English with scrambled eggs.

Dairy products seem to feature heavily in Cédric’s day-to-day life. Impressively, he is able to visualise every shelf in his favourite cheese shop and name, in turn, every item on sale. This is very important to him, as otherwise he could return home from grocery shopping to find himself without one of his many favourite cheeses.

He is in London to give a lecture to the public, something that he spends a large amount of time doing these days, “much more so than to mathematicians. But both are good: different feelings, different preparations.” Overall, since winning the Fields medal and gaining fame, Cédric claims that his time for research has been “divided by hundreds”.

Indeed, the public lecture is not his only commitment in London. He is currently attending a meeting at the Royal Society about the numerical abilities of animals. This meeting included great revelations about the mathematical abilities of frogs—evidenced through their calls involving sounds of varying number and length—as well as fish, bees and chimpanzees. “One of the crazy things that emerged from this conference is that the tendency to put small numbers on the left and large numbers on the right is not merely a side effect of how we write numbers. You can also find this—in some sense—in newborn chicks and fish.”

When in France, Cédric is recognised everywhere he goes, and is (still) posing for photographs. He is regularly featured on the covers of science magazines, and is often confronted by giant billboards of his face. If you are planning on winning a Fields medal, do not panic: he assures us that you will quickly get used to this.

Politics

When we meet Cédric, the French election is in full flow. As part of his stay in London, he is attending a meeting for the candidate he describes as the “young, centrist guy”. He is one of seven scientists on a board that provides scientific policy advice to the European Commission. However, he doesn’t recommend becoming too involved in politics, as he thinks there is no way to find time to pursue both a serious research career and a serious political career.

“The current political climate is far from science in general. Science, as a field, is much more respected by society than politics. So there is reputation to be lost by going into politics. But the most popular politician in French history is Napoleon, and he was keen on mathematics, and a big protector of mathematicians and scientists. He was elected to the academy of sciences, attending when he could, and enjoyed discussions with many of the best mathematicians of his time. But he was always late…”

Keen not to be late himself, Cédric finishes his eggs and heads off to his next commitment. It would seem, however, that Cédric does not always listen to his own advice: in June he became an elected member of the French parliament, as a member of the young, centrist guy’s party.