Birth of a Theorem: A Mathematical Adventure (37 page)

“Hello, Professor Lovász, how are you doing?”

“Good, I’m fine. I have news—good news for you.”

“Oh, really?”

It was just like in a movie … I knew that these were the same words that Wendelin Werner had heard four years ago. But could it really be, so early in the year?

“Yes, I’m glad to tell you that you have won a Fields Medal.”

“Oh, this is unbelievable! This is one of the most beautiful days in my life. What should I say?”

“I think you should just be glad and accept it.”

Ever since Grigori Perelman refused the Fields Medal, the committee can’t help but be uneasy: What if someone else should refuse it? But I’m hardly on Perelman’s level, and I have no qualms about saying yes.

Lovász hastened to add that the laureates were being notified of the committee’s decision earlier than usual to ensure that the formal announcement will come from the IMU, and not through a leak.

“It’s very important that you keep it perfectly secret,” Lovász went on. “You can tell your family, but that is all. None of your colleagues should know.”

I shall therefore have to keep quiet for … six months. That’s a hell of a long time! In six months (and three days) the news will be broadcast on television and radio throughout the entire world. Until then I must do everything in my power to protect this highly confidential information. I’ll have to prepare myself psychologically for a marathon, not a sprint.

In the meantime, speculation about the medal winners will be rampant. But my lips shall remain sealed. As my colleague from Lyon, Michelle Schatzman, once observed, “Those who know do not speak, those who speak do not know.”

Before Lovász’s call, I put my chances of winning the medal at 40%. Now they’ve suddenly shot up to 99%! But still not to 100%—the possibility that it may have been a hoax can’t be ruled out entirely. Landau himself once played a trick with a friend on a fellow physicist whom they despised. They sent him a phony telegram from the Royal Swedish Academy: “Congratulations, you’ve won the Nobel Prize, etc.” The bastards …

So don’t get too excited yet, Cédric. How do you know that was really Lovász on the other end? Wait until a letter arrives, formally confirming the award, before you break out the champagne!

Ah, the secret, yes—but what about the photographer in my office!?

Apparently nothing registered, he must not understand English. Let’s hope not. Our session finally got under way. A picture of me posing with the mathematical physics trophy I brought home from Prague, another one of me in front of the Institute …

“That’s good, I think I’ve got what we need. One thing I wanted to ask you—in the article it says that you might win a prize or something?”

“You mean the Fields Medal? That was just speculation on the interviewer’s part. The announcement won’t be made for quite a while, the congress doesn’t take place until August.”

“I see. Think you’ll win?”

“Ohhh, I don’t know, it’s awfully hard to predict … no one can really say!”

*   *   *

In the years after 1918, harmony needed to be restored among the war-ravaged nations of Europe, where the Treaty of Versailles weighed heavily on Germany and the other Central Powers. What was true for society was also true for science: institutions had to be rebuilt.

In France, the mathematician and politician Émile Borel drew up plans for the Institut Henri Poincaré. In Canada, the mathematician John Charles Fields, an influential member of the recently founded International Mathematical Union, had the idea of creating an award that would serve both to recognize important work, as the Nobel Prize did, and to encourage talented younger mathematicians. It was to be embodied in the form of a medal and accompanied by a modest sum of money.

Fields donated the necessary funds, commissioned the medal’s reliefs from a Canadian sculptor, and composed its inscriptions in Latin, a common language chosen to reflect the universality of mathematics.

On the obverse of the medal, Archimedes is shown in right-facing profile together with the inscription TRANSIRE SUUM PECTUS MUNDOQUE POTIRI
(Rise above oneself and grasp the world).

On the reverse, laurels frame an illustration of a theorem by Archimedes on the calculation of volumes of spheres and cylinders, with the inscription CONGREGATI EX TOTO ORBE MATHEMATICI OB SCRIPTA INSIGNIA TRIBUERE
(Mathematicians gathered from all over the world have paid tribute to a remarkable work).

On the rim, the name of the laureate and the year of the award.

And the medal itself: solid gold.

Fields did not want the prize to be named after anyone, but upon his death in 1932 it was obvious to all that it should be called the Fields Medal. It was awarded for the first time four years later, in 1936, and then every four years from 1950 onward at the International Congress of Mathematicians, the grand meeting of the mathematical world. Its location changes from one occasion to the next, with as many as five thousand men and women taking part.

In keeping with Fields’s wish that the prize should serve to stimulate future achievement, it is awarded to mathematicians under the age of forty. In 2006, the age-counting rule was clarified: eligible candidates must not yet be forty years old on the first day of January of the year in which the congress takes place. The number of laureates may vary between two and four, as the jury appointed by the Executive Committee of the IMU sees fit to decide.

A strict embargo on the announcement of the jury’s decision, combined with careful media coordination, assures Fields Medal winners of unrivaled publicity within the mathematical community and even beyond. The medals are usually presented by the head of state in the country where the congress is held. From there the news spreads throughout the world at once.

FORTY-ONE

RER B, Paris

May 6, 2010

In the world of Paris rapid transit, each of the RER lines is remarkable in its own way. In the case of the RER B, the line I take to go to work, it would not be an exaggeration to say that it breaks down every day, and that most days it is packed until midnight or one in the morning. To be fair, it also has its virtues: it assures its passengers of regular physical exercise by making them change trains frequently, and it improves their mental agility by keeping them in suspense as to exactly when a train will reach its destination and where it will stop along the way.

But this morning, on my way home from a conference in Cairo, it is very, very early and the train is nearly empty.

The outbound flight, in the company of the cutest girl you could ever hope to meet, couldn’t have been more delightful. We watched a film together on my computer, sharing earphones like brother and sister (always fly economy class, by the way, the girls are statistically cuter).

The return flight was less glamorous in every respect. Not least because I landed at Charles de Gaulle Airport after 10 p.m. (never book a flight that gets into CDG after 10 p.m., you’re just asking for trouble). Too late to take the RER into Paris. And since I didn’t feel like taking a taxi, almost on principle, I had to wait for the shuttle.… The first one was full even before it reached my stop, the second one too; as for the third one, well, maybe I could have just barely squeezed in—if I had been prepared, as some of the other people waiting in line with me were, to disregard the driver’s instructions and elbow my way on. Finally got into Paris at two in the morning. By chance my old apartment in the city was empty, so I was able to get a couple hours’ sleep before catching the first RER B back to the southern suburbs.

Going through my email offline, as always. Tons of messages … but ever since Lovász’s phone call in February, and then the official letter that came by regular post a few days later, it’s as though a great weight is being lifted from my shoulders. Not all at once—it will be a while longer before the sense of
urgency
leaves me—but gradually. Three and a half months from now, I’ll have to deal with another kind of pressure. So I’ve got to try to savor this wonderful feeling of relaxation while there’s still time.

One of the messages informs me that I’m the only person being considered for position no. 1928, a research appointment at the Université de Lyon-I. Good news. In any case 1928 is my lucky number: it’s the year that the Institut Poincaré was founded! A transfer to Lyon-I would allow me to stay in touch with friends and colleagues in Lyon without preventing ENS-Lyon from hiring a full-time professor; the number of teaching positions there is fixed just now, they’d be in a real bind if I were to stay on.

A beggar, an older woman, is trying her luck with the few passengers on the train. She approaches me, speaking in a hoarse voice.

“Coming back from vacation with this big bag?”

“Vacation? Oh no! My last vacation was at Christmas … and the next one won’t be anytime soon.”

“Where are you coming from?”

“I was in Cairo, in Egypt, on business.”

“Good for you! What is it you do?”

“I do mathematics.”

“Ah, good for you. All right, so long. And good luck with the rest of your studies!”

I can’t help but smile. It makes me really happy to know that people still take me for a student. But after all, she’s right, I still
am
a student—maybe for as long as I live.…

*   *   *

Today I was in the air and “entertained” myself by taking five minutes to try to feel all the electrical, electronic, electromagnetic, aerodynamic, and mechanical phenomena that are exerted on you in and around an airplane. All these small distinct phenomena that together make up a functioning whole! It’s fascinating to be aware of our surroundings … fascinating!

Unfortunately, at the controls of an airplane one seldom has more than 5 min. for thinking about this sort of thing.

Best wishes.

[From an email sent to me on September 9, 2010, by a complete stranger]

FORTY-TWO

Église de Saint-Louis-en-l’Île, Paris

June 9, 2010

Just a little too abruptly, I push back the censer that has been swung toward me. Black suit and black ascot as a sign of mourning; green spider pinned to my lapel as a sign of hope. I go up to the casket, touch it, bow in respect. A few inches away lies the body of Paul Malliavin, one of the foremost experts on probability theory during the second half of the twentieth century. Inventor of the famous Malliavin calculus, he did more than anyone else to unite probability with geometry and analysis. My own work on optimal transport follows in the same tradition. “In Malliavin there is Villani,” as I like to remind myself from time to time.

Malliavin was a complex and fascinating person, a conservative and an iconoclast both, blessed with an exceptional mind. He took an interest in me from the beginning of my career, encouraged me, set me on my way. He also entrusted me with real responsibility as a member of the editorial board of his beloved
Journal of Functional Analysis,
which he cofounded with two American mathematicians, Ralph Phillips and Irving Segal, in 1966.

Despite the forty-eight years that separated us in age, we became friends. Our mathematical tastes were similar, and I like to think that my admiration for him was reciprocated. We never went beyond
cher ami
in addressing each other, but this was not a mere form of politeness: the sentiment was most sincerely felt.

A few years ago we both took part in a conference in Tunisia. Malliavin was already seventy-eight, but he was still so active! At the end, it was my job to summarize the conclusions of the meeting, and in a few words I tried to acknowledge his phenomenal impact on analysis and probability; I don’t know if I called him a living legend, but that was the idea. Malliavin seemed a bit taken aback by my tribute. Later he took me aside and said very quietly, in that deadpan way of his, “You know, the Legend is a little tired.”

Tired or not, Paul Malliavin went out swinging—doing mathematics right up until the last minute, as his son-in-law reported. He died the same day as Vladimir Arnold, another mathematical giant of the twentieth century, albeit a giant of a completely different style.

We will have to carry on without you.
Vous pouvez compter sur moi, cher ami
. The
Journal of Functional Analysis
is in good hands.