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École Normale and thought in mathematics

Benoît Mandelbrot
Mathematician

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The first decision I took was to go to the École Normale. Frankly, I don't quite remember why I decided, but I wasn't very sure. So I entered the École Normale. After two days I couldn't stand it and I left, and I would like to explain why. Mathematics at that time was entering a new phase; more precisely it was entering into a hard second-half of its middle-twentieth century life. To make things very rough: the first quarter of the century was very mixed with many influences; the second quarter was a growing tendency towards abstraction; the third quarter, total domination of abstraction; and the fourth quarter of the century - the fourth was very mixed- again returned to what I view myself as a more normal situation. My uncle was very much a man of the first and second quarter, that is, he was not very abstract, but he was himself on the defensive. He was not a mathematician according to what was the ideal. In 1945 one must remember that the world was run by several very deeply felt movements, which knew profoundly in themselves that they represented the future and that it was not something that man could change. 'The March of History' led towards communism, led towards this and that, anti-colonialism; it led towards a structure in science. It was not a mild liberal kind of situation, but a very rough one. My uncle knew very well about it, and again, even though he wasn't defensive, he did not hold a strong position to try to stop it. And for me this kind of mathematics was simply horrendous. I did not succeed in mathematics because of an ability to do algebra; I succeeded because I could think in pictures. They felt that pictures were sort of- the devil! I had this, because of my father and because of just my reading, which was perhaps also from my father, and because of other reasons, I had a very deep curiosity about how the world was put together. For them, that didn't count at all. In a certain sense, a very deep sense, they were Platonists who said that the sensations and the world round us have no importance; mathematics was a thing itself; pure notions, pure categories. It was then that I increasingly realised that first of all, I didn't like it. Secondly, I was just not one of them: I would not succeed, I would not be happy there. I could not change myself. After two days I simply decided to break and to leave. I was very aware of the consequences. I knew, as I was very widely read, of many historical cases where someone had been given a certain very high opportunity and spurned it. That person was treated much more harshly than a person who was not given that opportunity. For a long time it was very, very difficult for the École Normale to recognise that one could do well while spurning it, and the École Normale in a kind of broad sense, French mathematics and world mathematics. And also for me, to realise, that, in a certain sense, I have succeeded in helping to break their stranglehold.

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.

**Title: **École Normale and thought in mathematics

**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, 35 seconds

**Date story recorded:**
May 1998

**Date story went live:**
24 January 2008