Nov 282011
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Cedric Villani, professor for mathematics in Lyon and winner of the Field's medal in 2010, click on the picture to find out more about Cedric Villani

Charly Chaplin once said to Albert Einstein: „I am applauded, because everybody understands me; you are applauded, because nobody understands you.“ Cedric Villani, professor for mathematics at Universit? Claude Bernard in Lyon, would probably strongly disagree with Chaplin’s dictum. A celebrated mathematician, his awards include the Fields Medal in 2010 and the prize of the European Mathematical Society in 2008 but he believes that his difficult work on partial differential equations is communicable to everyone. His talk “Breaking the Walls between Economics, Physics and Geometry. How Optimal Allocation of Resources and Entropy Meet in the Non-Euclidean World”, which he presented at this year’s Falling Walls Conference in Berlin, was a tour de force of scientific communication. The Journal of Unsolved Questions had the honor to talk to Cedric Villani about communication of mathematics to the public, scepticism towards numbers, population growth, and the climate change.

JUnQ: Prof. Villani, when you open the newspaper in the morning, how much do you think about the complex problems presented there in terms of mathematical concepts?

Villani: How much I think about the news in mathematical terms depends very much on the mood, on the problem, on many things. You can compare it to music: If you know music, you can either listen in a naive way or listen with the ears of a specialist, recognizing the chords, harmonies and so on. If you really want to understand what is happening in the world, though, you will need mathematics directly or indirectly.

JUnQ: A recent example for math appearing in the news is the world population reaching 7 billion. It is not trivial to calculate when exactly this mark was reached, nevertheless not many formulas were presented in the papers, only this huge number: 7 billion! Why is it so much harder to communicate an abstract formula than a single number?

Villani: Do you understand 7 billions? Can your brain comprehend such a number? I think mine can’t. This is just enormous, impossible to get. The abstract formulas are not intrinsically hard to communicate. I have recently seen a clown show where kids were given an idea of the predator-prey system. This is abstract and can be conveyed without any precise figures. Formulas are just set in a different language. If you learn the language, it will sound easy. And it will be extremely useful. Even simple formulas for population growth contain so much more information than just a single number. I can represent the development of the population, see the movement, program it on my computer and so on.

JUnQ: But recently we have seen a lot of examples where these formulas failed. Take the financial crisis as an example. The mathematical models of the rating agencies were unreliable. The risk calculations of the banks obviously failed. There is skepticism and even anger directed towards the experts in charge of the calculations. Is this skepticism justified?

Villani: About the financial crisis, yes, things are so complicated. The blame should not be put on mathematics, though, but rather on the fact that the mathematical models are applied way out of their range of validity in the hope that they will still work. We should be damn skeptic towards numbers calculated in that way, especially when they are presented as facts. Often numbers are used to pretend something is sure! Think of the following sentence, which I also learned from a clown: “90% of people believe in a sentence which has percentages in it.” To come back to the prior question, knowing a bit about the underlying models and calculations is an excellent way to appreciate the uncertainty, which is behind them, and to judge when the model is trustable and when it is not. Even if this requires quite an expertise.

JUnQ: Appreciating the uncertainty is not always easy. The predictions for the global warming until 2100 range from 1.1 °C to 6.4 °C, a huge difference. If you ask five differenct scientists you can expect ten different answers. How can we decide which expert to believe in?

Villani: I have more trust in experts which present different results than in experts who present one single result. Giving several results means you have tested several hypotheses, you have been critical, you are humble enough to admit your partial ignorance. Science in general is often criticized for its uncertainty, the climate issue is a good example. Even though they do not always look secure, scientific approaches are still the most reliable, more reliable than other approaches like faith, politics, or feeling at least. Sometimes the precision of results is amazing. The difficulties of scientists just reflect the fact that the world is so complicated.

JUnQ: Do you feel that there is a wall of alienation between the mathematician and the public? Do you have an idea how we could make the public more enthusiastic about math?

Villani: My experience is that the public is always enthusiastic to learn about science. And scientists are among the last heroes in our era, the most trusted experts. The percentages of confidence for scientists are substantially better than for politicians. In all my public lectures, I get the impression that the public has an enormous appetite for science. To make the public enthusiastic, it is sufficient to present science in a pedagogical way, in an incarnated way, with people, adventures, stories, and history.

— Leonie Mueck

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