In a way it's the dream of mathematicians, but

we would never say it openly.

It would be considered as…

…very outrageous.

And…

the best thing you have to do to get the Fields Medal

is to do some good work, and not thinking about it.

BRADY HARAN: And for anyone watching,

this is Professor Villani's Fields Medal — you won this.

CÉDRIC VILLANI: Yes.

But my name is there very discreet, you know?

Here is the date: 2010.

And here is my name.

It's very small, because… You know…

We mathematicians are small in front of the mathematical accomplishment.

This is pure gold.

And this is Archimedes.

Maybe the greatest mathematician of antiquity.

The inscriptions here are in Greek and Latin language.

[reading inscription]

Means something like, you know,

"To get above oneself and conquer the world."

Something like that.

Which is about mathematical accomplishment.

Great mathematical accomplishment.

To really do things that you would not believe yourself are possible.

You have to find it within you.

With the help of many people, this Fields Medal…

…owes so, so, so much to my collaborators.

It was award for my works in statistical physics.

Study of the qualitative properties of the gases and the plasmas.

Please look at the… What is on the other side.

Because this also is important.

[reading inscription]

It means something about the mathematicians who have come from all around the Earth,

to give this to the people who most deserve it.

Something like that.

And this is one thing with the Fields Medal:

It's really an award from the community.

And is attributing the public ceremony.

In front of thousands of mathematicians.

It is given by the head of state of the country in which this conference is taking [place].

BRADY HARAN: Who did you get yours from?

CÉDRIC VILLANI: President of India. In 2010. Yes.

Such memories.

Here, you may see that…

something like a sphere,

and here's something like a cylinder.

And it's an allusion to one of the most famous theorems of Archimedes.

The identity of the volume of the sphere

and of the cylinder in which you can inscribe the sphere.

The outer cylinder.

BRADY HARAN: How did you find out you'd won it?

When is the first time you're told that you're gonna get the medal?

CÉDRIC VILLANI: I was exactly here.

This place.

And I was having an interview.

And then the phone rings.

"Hello?"

And the voice was saying,

"Hello. This is László Lovász from Budapest."

And then my heart skipped a bit.

Because, you know…

…I knew László was the President of the International Mathematical Union.

So, the only person whom I knew to be on the jury of the... Fields Medal.

Related to the committee.

And so, "Yes, Professor Lovász.

"Nice to hear you."

And then, "I have news. Good news for you."

Then you can think of me becoming all white and so on.

And, "Yes?"

And then,

"You've won the Fields Medal!"

[mimes excited exclamations]

BRADY HARAN: What, did you shout? Or did you make noise?

CÉDRIC VILLANI: "This is extraordinary! [incomprehensible]", et cetera.

"I can't believe it! Such beautiful day! Extraordinary!", blah blah blah.

And so on and so forth.

And then he explain me, "Yes, and please keep it strictly confidential.

"It's very important you keep it secret."

And then I, [exhales]

I shut down [the phone], then I was like, [exhales]

And then I realize, journalist was there.

Couple of metres away.

"Ah!"

Did I make a big blunder?

Turns out, he did not realize.

Maybe he did not speak English after all.

BRADY HARAN: The Fields Medal is often described as sort of a Nobel Prize of mathematics.

Like, it's a big prize.

Do you ever feel like you don't deserve it?

Or did you — by that point, did you think,

"Yeah, I should get the Fields Medal for this!"

CÉDRIC VILLANI: Um…

We all have this feeling, at some moment, that we don't deserve it.

Or, most of us.

And… often, I would say,

for a given round of Fields Medals,

there are those who do such amazing work,

that you know, "Okay, this guy WILL get it

"and everybody knows it."

Like Perelman — it was clear.

It was so extraordinary, that it was clear he should get it.

And there are people who did some… good stuff.

But then it's not clear. You know?

And it's… partly a matter of appreciation. And of luck.

And on this I think that I was lucid.

BRADY HARAN: Another thing that's famous about the Fields Medal,

and different from the Nobel Prize,

is the age limit.

What do you think about that rule?

It seems arbitrary.

CÉDRIC VILLANI: There is some dose of arbitrariness,

in particular in the fact that…

…changes of perspective depending on your birth date.

But there are many arbitrary rules in life.

You know, once I was discussing this with one of my colleagues.

Back in 2006, maybe.

In the International Congress of Mathematicians in Madrid.

And I was saying,

"Well, it's unfair, because this and it depends on your birth date, etc., your chance to get it."

And he looked at me with a smile, and said,

"Are you saying that life is unfair?"

You know… There are so many rules, and so much in life.

So you should not strive for perfect, um, you know… fairness.

It makes no sense.

And it's good to have rule of age limitation.

Because it favours the young.

And, um…

Historically, it's clear that the Fields Medal was conceived as an encouragement,

rather than a crowning achievement.

Then it kind of took the place in the media, that Nobel Prize usually takes,

because there was no Nobel Prize in math.

There is the Abel Prize.

Which in some sense is closer to Nobel.

I would say that it's good to have this age limit.

Also, it makes sure that

people who do something real great

get honoured…

…you know… on time.

Sometimes people, for the Nobel Prize, they have to wait thirty years.

Sometimes they are dead, and we say,

"Okay, this guy should really have got it."

But now… too late.

BRADY HARAN: When you win the thing that every mathematician dreams of winning,

how do you keep motivating yourself?

How do you keep doing good mathematics?

What makes you wake up in the morning and think, "I wanna make a new discovery"?

'Cause you've won a Fields Medal!

Like… You've done the best thing you could do!

CÉDRIC VILLANI: It's a recurring question, "What makes you wake up in the morning?"

You know… We all have our missions to do, that we have to complete.

And it would be very silly to think that when you have won the crowning achievement,

[it's] the end of the mission.

Most of the time, people get rewarded for work which is not the one they dreamed of.

There are exceptions.

Take Andrew Wiles.

He solved his child[hood] dream, the Fermat Theorem.

But for most of us, you know…

I did not solve the question that was most dear to my heart.

And most of us, rewarded, we can say the same.

Our big problem, the ones we are most motivated about… They are still open.

So much to do.

But if I had all this time, there would be a list that long, of things that I really would like to work on.

And at least four projects of books that I would like to write.

A real mathematician, a true mathematician at heart…

…always keeps in his heart issues that are extremely dear to him.

And that he wants or that she wants

to go on, and to dig, and to explore.

And a real, true mathematician can put these questions in the fridge for twenty years

and get back to them after.

Still with the same motivation.

BRADY HARAN: Andrew Wiles had Fermat's Last Theorem, very famously.

What's Cédric Villani's "Fermat's Last Theorem"?

What's the one that…

What's your… What's your "White Whale"?

What's your, you know, what's your great…

Great one that you can't crack?

What would be your dream?

CÉDRIC VILLANI: Please allow me to keep my heart for myself…

…until I solve it.

BRADY HARAN: Is it the Riemann Hypothesis?

CÉDRIC VILLANI: Wow, it would be lovely.

But no.

That one is not for me.

That one will be for somebody else.

I hope.

CHARLES FEFFERMAN: "…That is not the same thing as the full Kakeya problem,

"because maybe as the direction varies smoothly, maybe the pole would have to jump around."

BRADY HARAN: Will the Riemann Hypothesis be solved while Cédric Villani is still alive?

CÉDRIC VILLANI: I would not take bets.