An enthusiastic ambassador from the realm of mathematics, Cédric Villani compares the academic research and startup worlds and talks about computer programming as an educational subject.

Cédric Villani: Computer programming is “practically the only discipline where a child can self-correct”

Cédric Villani, the Director of the Henri Poincaré Institute, is a renowned mathematician who won the Fields Medal in 2010. When he is not buried deep in his research work he takes to media stages and conference platforms to discuss the role of mathematics in our society. Reading his 2012 book Théorème vivant, published this year in English as ‘Birth of a Theorem’, we are instantly reminded of what we had perhaps forgotten – that, contrary to the image they have today, mathematicians are basically on a quest, similar to that of poets and philosophers, to understand and explain the world.

His main distinguishing feature is his probing dark eyes. He has the gaze of a curious child. He is also the sort of person who pauses for silence before projecting words into the air. Speaking on a L’Atelier numérique (L’Atelier Digital) broadcast, he returned to the topic of his session at the USI (Unexpected Sources of Inspiration) conference in Paris in early July – ‘The Birth of an Idea’ – pointing out the differences between the research domain and the startup world, but strongly arguing the value of computer programming as a basic educational discipline.

L'Atelier: At USI you spoke on the theme of ‘The Birth of an Idea’. We often hear about an idea being ‘born’, inspired by a muse or conceived by someone touched by divine grace – i.e. inspiration from an unexplained source. What’s your view on that?

Cédric Villani: Yes, we sometimes, or perhaps very often, have that impression. We can theorise about it as a form of inspiration from a muse. The great Indian mathematician Ramanujan was absolutely convinced that a goddess was whispering good ideas into his ear. But when you’re working on a project it’s certain that what will make the difference is that subtle combination of relentless systematic work on the one hand, where experience play an important role, and on the other those small flashes of illumination, little sparks ignited by your intuition and your subconscious. Everything makes its contribution to that moment of clarity: the environment you’re in, conversations you’re having, and so on. And there’s an unexplained element which – in a situation that perhaps has nothing to do with the problem you’re trying to solve – sets off the trigger mechanism.

Is there any similarity between a maths research project and the life of a startup? A startup generally follows a process of iteration. They create a prototype. They sometimes pivot off into another direction. I imagine this could also be the case for an academic researcher? Would a startup not do well to draw inspiration from the methodology followed by you and your colleagues?

Well I think that the methodology of startups is established through long experience and through a rather rough-and-ready process of natural selection. Over time they hone their reflexes and develop best practice. Our kind of research is a non-stop succession of ‘pivots’, of changes of direction. In fact it’s rather surprising but we still lack a word for this phenomenon, though we encounter it on a daily basis. However, beyond these questions of iteration, prototyping and so on, we can nevertheless see a parallel between the startup and academic research approaches to our work. In a startup it’s quite common to have a fairly small team, crazy working hours with total commitment, where the line between private and working life gets blurred, there’s very little hierarchy and people react fast. These are also well-known features of the academic research world. Industrial research, on the other hand, especially when it comes to major projects, is much more similar to the processes of a large company, with deadlines, process monitoring, a much greater degree of hierarchy and more emphasis on the certainty of the outcome. In an industry research project, there are more forceputs in terms of finishing the project on time, to a fixed deadline, and meeting fairly precise criteria. It’s about ‘safety first’. On the other hand, when you do basic research, it’s just you and your team. There’s nothing much at stake, apart from your reputation of course. You can allow yourself the luxury of taking risks and challenging any set process. So there’s more opportunity, more personal engagement.

For a number of years now you’ve been highlighting in the media the role maths can play in society. Recently we were fortunate to welcome Gérard Berry, a member of the French Academy of Sciences and winner of the 2014 CNRS (French National Centre for Scientific Research) Gold Medal, who pointed out that he was one of the few ‘Academicians’ who was a computer specialist.  Is this a subject that needs further examination?

For years the line of attack I’ve been using in the media is that mathematics is in fact an integral part of our world, our culture. Mathematics deserves its place in the literary sphere. I illustrate this approach to maths in the tales and stories which I tell on stage. I want to emphasise that maths – and more generally science and technology too – are part of our world, are all part of what makes human beings what we are today. Without scientific development we would think differently, describe things in a different way, speak differently, and our cultural references would also be quite different.

Moreover, there’s no computing without maths! At the same time computing gives something back to mathematics, provides the amplifier which allows it to move into the spheres of economics and technological progress. Gérard Berry, as you mentioned, is one of the very few computer specialists who are members of the French Academy of Sciences. This isn’t very surprising given that the Academy is an institution that’s rather slow to change. It’s going to take quite some time before we reach the stage where a sufficient number of Academicians are computer experts. This will happen as new disciplines gradually appear and distinguish themselves from others. In the past, science was an entire world in itself, also comprising philosophy. Gradually these disciplines have separated out into different branches. There was a time when mathematics and philosophy were seen as one and the same subject. They split only a few decades ago, but their independence is relative since they are still closely bound together and will remain so.

There’s increasing talk of incorporating computer programming into the school curriculum. Does this imply that computer coding is a language, in the same way as English, German or Latin are?

I’m surprised that people are using the expression ‘computer coding’. It gives a false impression. We used to call it ‘programming’, and that term says what it actually means.

You can’t compare learning programming to learning English or German, but you could compare it to learning Latin. English and German are living languages which you learn by speaking, by absorbing them, whereas Latin is a language which you basically learn through the rules of grammar. Latin is still used today as an academic exercise in translation, whether into or out of one’s native language but modern teaching methods generally no longer use translation as a way of learning a language. Nowadays the student is encouraged to understand and speak directly in the language being taught. But above all we must not make the blunder of thinking that maths and programming as ‘languages’ are in any way the same as a foreign language. This is simply not the case. They involve different neural circuits and also require completely different learning methods. On the one hand we have languages which help human beings to communicate with each other, on the other hand there are ‘languages’ that help in the human struggle to understand our world – which enable you to encode things in a precise quantitative fashion and provide a language that can be used by other scientific fields. That’s where mathematics comes in. The main usefulness of Latin lies in helping to activate a certain thought discipline, the mental gymnastics which force you to take on board the sets of rules, combinations and configurations, which are in some way similar to the processes you need to follow in mathematical and computer reasoning.

I don’t know why in France people make such a song and dance about learning computer programming at school. It ought to have been obligatory for everyone for a long time now. Especially now that you have programming software such as Scratch, which children really like. Youngsters are keen on Scratch because it allows them a lot of independence. A kid of ten can begin programming using Scratch. This has enormous advantages in the teaching process. Just think, this is practically the only discipline where a child can self-correct. They can see that their computer programme has been written incorrectly if it doesn’t work when they launch it or if it gives a clearly erroneous result. A mathematical error wouldn’t normally be spotted unless pointed out by the teacher. You can go on making the same mistakes if you don’t have any guidance to get you back on the right track.


Photo: (c) Eric Le Roux, University of Lyon

By Lila Meghraoua
Journaliste/Productrice radio