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The organisation of École Polytechnique; Paul Levy

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The world of learning how
Benoît Mandelbrot Mathematician
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Why did I go to the École Polytechnique? Well, perhaps again it was a mistake of name. I view that as being the best decision I ever took, that the École Polytechnique was the right place for me precisely because it was rather undefined, very broad, had many, many scientific fields and still had a certain concern with the real world. This was not very well expressed, especially in 1945 when it was barely being rebuilt; one did not know whether to apply the laws that stood before the war, or the new laws. But I could in a very strong way continue to build for myself this combination of everything which otherwise would have been impossible. Now, what happened then? École Normale being extraordinarily small- I would like to say how small it was. Because it is very difficult in present time to realise these matters. In mathematics and physics the École Normale was allowed by law in 1944 to take 25 students. They felt that the level was below historical records. Not counting the effects of the war, they took 15. In other words, for mathematics, 15 students, an extraordinarily small number, and that out of two hundred candidates. The École Polytechnique got two thousand people applying for the exam; two hundred were taken in. They were very, very small schools. Therefore, after I decided to leave the École Normale, I found myself in a very strange situation because the École Normale, being so small, could arrange for the second half, from February to the summer of 45, to have a truncated year for the 15 students. The École Polytechnique could not. It therefore started in the fall of 1945 and my class at the École Polytechnique was called to some kind of military training. I volunteered. I say that I volunteered, because I was actually a foreign student. That was a complication of my birth in Poland and all the laws; I entered as a foreign student. I was very highly ranked but I was not entitled to all the privileges. So they went into military training and I tried to follow them and was told I couldn't. So I stayed at school and asked, "What should I do?", "Well, it's very simple. You are a foreigner, you can volunteer for the Foreign Legion and then in six months we'll do our best to get you out of it." That looked very unpromising because the Foreign Legion did not have the reputation of, how should I say it, leniency and easy manners! So from February or March of 45 the war was winding down, though not quite finished until September and I was, well, I was doing nothing, I was nowhere. I would like to underline the importance of those periods where in a way I was nowhere, I was not in school, because this was once again a period where I was not strictly in a framework where people knew what the purpose at school was, what the requirements were, how to succeed, and how to fail. During that period I learned; I read a great deal; also, after the war was over, I learned English very well because I became a guide in Paris. I know Paris inside out and so I was a guide for the high level people who don't take commercial guides, telling them details about life in those palaces, in Faubourg Saint-Germain when I had never been inside, but I knew everything about them. And then in the fall, École Polytechnique came to life and I was a student there for the two years from 45 to 47.

Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.

Listeners: Bernard Sapoval Daniel Zajdenweber

Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Duration: 3 minutes, 52 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008