Cédric Villani
Can a Mathematician Run France?

It was just a few days after the 39-year-old fresh-faced Emmanuel Macron had won the highest seat in the French office that the renowned mathematician Cédric Villani graced TV screens around the world.

Called upon by CNN for his informed opinion on what these incredibly unpredictable political times mean for France, he spoke with a calm eloquence. Seeing a man of science dressed in a manner that some have described as ‘Lord Byron on a mini break’, could have unsettled people, but Macron and Villani are the symbols of a more vibrant and open leftist energy that is refuelling European politics. Jeremy Corbyn take note.

Cédric has been an ally of Emmanuel since first meeting in 2013, in his days as the nominated Minister of Economics. At this time, Villani was enjoying an increased celebrity and numerous opportunities that arose due to winning the highest honour in his industry, the Fields Medal – the mathematical equivalent of the Nobel Prize, awarded for his complex theory on plasma physics. Unlike some politicians of late, his IQ is not to be questioned.
Villani’s worlds have now combined, juggling his time campaigning for a seat in parliament as a member of En Marche!, the nascent political party founded by Macron, and continuing his role as director of the Institut Henri Poincaré. A media darling in his homeland, this venture in politics could mean something else blowing in the wind for Villani.

You are probably most known for winning the Fields prize in 2010, for your work on plasma physics. Firstly, how do you feel about becoming a prominent figure since winning the prize?

In the last seven years of my life, the radical changes for me include becoming director of the Institut Poincaré and receiving the Fields medal. These two things happened only a year apart and they both changed my career at around the same time – there was some kind of synergy between them, which was very useful. The fame acquired by winning the Fields medal was integral in pushing the project of the Institut Poincaré, in particular, everything regarding mathematical culture, my relationship with the outside world has become most of my professional life.

The only time a Fields prize has been declined was by an intriguing character called Grigori Perelman. I thought it was interesting that he said his reason for this was the politics in the mathematics community. Do you think politics do exist in your sphere?

With the Fields medal, of course, there are experts who are consulted and there are people pushing for one candidate or another, but the candidates are not informed of anything until they receive the phone call telling them that they have won. There is a secret in the composition of the community up to the end of the process, so there is no occasion to influence the decision.

I’m not saying that there is no politics in mathematics but there is less than in the governance of nations, for instance. Let me add that Grigori Perelman is an extremely idealistic person and he has a very special psychology also. Some of his reactions were impossible to understand for us, so I would not consider this significant, but Grigori is one of the most respected figures in mathematics. His proof of the Poincaré conjecture is probably the highest mathematical achievement of the 21st century so far.

"There is a wide consensus in France that this is the last chance, this period of 5 years that is starting – the last chance before we see the emergence of the radicals and populists who want to see a revolution."

Cédric Villani on the future of France

Speaking of politics, I understand that you are now running in the election to represent a suburban constituency in Paris, so I’m interested to know what you hope to achieve, especially riding on the wave of prominence as a close ally of Macron?

Within his movement, I have been one of the most visible and the most liked by the media. Also it is because my profile is an incarnation of the direction that Macron wanted to promote, which is to take various talents and specialities and help them move into politics so we can renew the political community, one that is more diverse with more women and younger politicians with all kinds of specialities other than economists, lawyers and other jobs related to politics but also scientists, teachers and doctors.

This was the plan, and as a person who achieved a certain level of fame and popularity with a very specialised sector such as scientific research, going into politics is very emblematic of this new term.

Let me also say that I am running to become a Member of Parliament, and even though the Member of Parliament is elected in a territory, he does not represent that territory; he represents the whole nation. He also has a moral duty to act within the territory as a local influencer without any executive mandates, but the primary job is to create laws, control the action of the government and in this job I represent the whole nation, not just my electors.

"I believe that it is important to refuel the connection between citizens and Europe and organise a public debate in all European countries to do with why we love Europe."

Cédric Villani on uniting Europe

Have you had conversations with Macron about having a more pro-scientific mindset in government?

Not in government but we have talked about scientific culture for sure. When Macron stopped his job at the Elysée palace, where he was working with François Hollande, his goal was to found a startup related to the education sector. I’m not sure what exactly he had in mind, but I remember he sent me a text at the time saying that it was important we meet so that we could discuss and help improve his project. A few days later he was elected as Minister for the Economy.

I think we are witnessing an age of the unconventional emergence of power. You and Emmanuel Macron are two unorthodox characters that have come to prominence.

Oh completely.

You are now running as an MP and Macron is the French president, who was a total left-field candidate. Could you see yourself running for president in the future perhaps?

Oh, I am not thinking about this. Right now I am focused on the new job as a Member of Parliament, which will be a lot of work but fascinating to learn. There is a wide consensus in France that this is the last chance, this period of 5 years that is starting – the last chance before we see the emergence of the radicals and populists who want to see a revolution. So in this 5 year period, we have to fix the country and restore the confidence of the French people in the government and our future.

Talk to me about Europe, because you have gone on the record to say that “it’s clear that the UK has no idea what to do and the negotiations for Brexit have not advanced other members save for showing a united front and that this is a very complicated turning point in European politics.” Aside from that, I live in London where we have just seen one of the vaguest and most complex elections in recent times.

First, let me say that British politics is one of the oldest in the world and has become almost impossible to understand from the outside. It seems now to be in a very confused state. I remember two months ago when France was also in the most confusing situation that one could envision, it was really such a mess and there were days when I literally had a ball of stress in my stomach seeing the state of my nation’s politics.

Now, with Macron and the great popularity of the movement, it seems that we have overcome this period of confusion and the amazing thing is how quickly this has changed – the climate in France now is nothing like what it was two months ago. And I sincerely hope that Britain is able to reinstall some confidence climate in one way or another. In our case, maybe it was just having the right leader with the right party and a lot of luck that was one of the instrumental ingredients. Without him, I don’t know where we would be now.

It seems that in France you do still have many socioeconomic problems, and I know you said you have 5 years to prove it, but do you think Macron and his movement is just a band-aid?

No, I think it seems, with the mandate, that Macron will really have the opportunity to change things here. Because the government is seen as gathering left, right, centre, pro-Europe and pro-environment, and the parliament is soon to be a huge majority on the side of the government. So we have the powers for efficient action. And what people are expecting from Macron is really rethinking the whole system from top to bottom. Of course, you cannot improve things economically etc. just overnight, but you can restructure the whole thing so that you are starting on the right path. And people expect some really big reforms on the way, not just the mandate.

About the European situation, it is worrying for various reasons. We can say that there is still a real lack of commitment and involvement of many European citizens in the European ideal and project. There is the rise of populism here and there, there is the fact that some countries are going in a disturbing political way like Poland or Hungary.

So with En Marche!, I believe that it is important to refuel the connection between citizens and Europe and organise a public debate in all European countries to do with why we love Europe, what is the Europe that we dream of and what the subjects are that Europe should be tackling.

"I can see mathematics playing a role in stabilizing the economy and helping promote the harmonious cooperation of various agents around the world."

Cédric Villani on mathematics as a force for good

How would you sum up the feeling looking back on Marine Le Pen and her party?

There is a consensus on two things; first, for now, the danger has been avoided and this can also be seen in the fact that the votes for Marine Le Pen’s party were twice fewer in the parliamentary election than they were in the presidential election. Many voters for the Front National did not vote in the legislative elections or they voted for other candidates. So right now we don’t hear much from the Front National in the debates and in the media. It seems that for now, they are out of the game. Also, with a bit of distance now, everybody has set an image of a very bad performance by Marine Le Pen in the presidential debate between her and Macron. In short, it was just not up to level, and ridiculous in certain respects.

Let’s discuss the role of mathematics in society. You have talked about the implication that mathematics can have on cultural issues, like communication theory, information theory and game theory, machine learning and so on. So you are absolutely right that the scientific field is going to play a much more important role. What are the real world applications of your work in particular, like plasma physics, and also the new technological future that we face and the role of mathematics and algorithms in that?

First, about the applications of my work: I frankly have no idea if these works will be applicable or not, and most of the time you never know. Only a small fraction of theoretical research has application. It would work dealing with plasmas and plasma stability, which is an important issue in experiments involving plasma. My work with my collaborators is to identify some influential factors in the stability, which could lead to a more precise construction of the stability so we can identify some mathematical and physical phenomena lying behind what has already been discovered. Will this be practically used? I don’t know, but there is a general feeling among scientists that it is good to know more, and it may turn out to be useful. 

But we don’t care that much – there is an important paradox that technology and maths and science are instrumental in producing useful things for society but scientists aren’t really driven by this usefulness, they are first and foremost driven by curiosity and the appetite of knowledge. I think it is good this way.

On the second question, an algorithm is just a mathematical recipe that has been around for thousands of years. We learn about them at school and then high school, they are everywhere. But more and more sectors of the economy are depending on them and new classes of algorithms have appeared lately that are more flexible and more powerful, made possible by the progress of computer science. They have revolutionised a number of fields in technology but also in science and algorithms have taken a huge toll on the evolution of the economy.

Wherever there are algorithms, there is mathematics behind them and mathematical technique. Take Google technology; at the heart of the rise of Google was the PageRank algorithm. Now, PageRank is not a difficult algorithm, but it came with the idea that the mathematical object of the random walk in the graphs could be very useful. Now they never could have come up with this idea without a solid basis of mathematical culture, so here is a perfect example of how mathematics can be a game changer in a technological issue. Nowadays it is used in fields as various as an election campaign or playing chess. It has led to new possibilities, new economies and new services, but of course, it can also lead to new dangers. There is a book that I am constantly publicising by Cathy O’Neil called Weapons of Math Destruction, which describes a number of cases where they use intelligent algorithms and it goes horribly wrong, either because it serves unethical purposes going in the direction of oppressing or exploiting those less privileged, or because it is applied with good intentions but in a very clumsy way. The consequences of these actions can be economically bad or bad for democracy.

I believe that in the future, the ethics of algorithms will be a commonly taught subject at university.

What do you think are the biggest problems that mathematics will solve over the next few decades? Many mathematicians don’t know the consequences of the maths that they create and what it will be used for. You have talked about an interesting case with one of your favourite mathematicians Leo Szilard who started the Manhattan Project.

Mathematics can be useful everywhere, so let’s start with the biggest problems in the world and see what can be done. Of course, one of the biggest problems is climate change, and here mathematics has a role to play in the modelling and coordinating of solutions that will be used in the future. If we go for solutions with more wind and solar energy, there will be a need for coordination between the sources of energy and some kind of algorithm.

Another problem is cancer. Cancer is a very diverse disease for improving the treatment we would need it to be personalised, which will be partly based on automatic diagnosis of some kind and also the possibility to cross the clinical information with the genetic information and so on. So far, the crossing with genetic information has not been very game changing to say the least, but it may be at some point.

There are cases, there was one recently according to a lecture I heard, in which one person struck with cancer was saved by an algorithm in the sense that while the doctors thought it was just a benign tumour, the algorithm rightly concluded that it was in fact malign. These things will for sure multiply in the future so mathematics will have a say in medicine.

Now, I can see mathematics playing a role in stabilizing the economy and helping promote the harmonious cooperation of various agents around the world.

Mathematics is more and more open to other sciences and the rest of the world, so it is taking a more and more interesting role in connection with them, so I think my going into the political world with this skill is very representative both of the trends in politics and of the trends in mathematics – even though I have to admit that my case is quite singular in some respects.