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Drawing; the ability to think in pictures and its continued influence


Preparation for exams - Monsieur Croissal
Benoît Mandelbrot Mathematician
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In a few months - because that whole event lasted only a few months - the professor of mathematics saw a few of my classmates and friends and told them about forecasts for the exams. War was raging, France was occupied, but this thing was going on as if nothing was happening. I don't know what would have happened without the landing, but that is how these events proceeded, as I found. The professor told almost every one of his students that he could very reliably say: this one's going to get in, for example, to the École Polytechnique, which was taking 200 students and was the easiest to enter. He felt nobody was going to get into the École Normale, and others would just barely make it, others probably would not make it at all. But one student, for him, was a totally open book: I was that student. He said either I would end up first, or among the first, if I guessed the geometry; or I'd be miserably behind because there was no way that if I didn't get the geometry I could do the algebra in time. Well, I may add more about this. French schooling at the time was clearly quite archaic: that is, these programmes had not been changed for fifty years and more - actually very similar to the tripos at Cambridge, they'd remained for a long time in a very steady state. If it had been unfolded later, geometry probably would have played a lesser role and this kind of game, which saved my life, would not have been possible. But that's how it was. Many years later, I may add, I had the opportunity of revisiting this professor. I was in Grenoble and had to go near Chamonix to give a lecture and learned that this man had retired and was living near Chamonix. I called him and he remembered me instantly. He asked me to come over for supper, which I did. He brought his successor from that school in Lyon to visit, and his wife was there, whom I'd never met before. He told his wife "This is the man I was telling you about in the winter of 44; the student which forced me". His father lived with them and had also been a professor in the same kind of Preparatoire, and they had spent nights, weekends, trying to find problems of algebra which would baffle me and almost completely failed. They looked at all problems in examinations, found the driest, the most incomprehensible ones and for each of them I instantly found some kind of geometric interpretation. Do you recall his name? Yes, of course. Monsieur Croissal was a major figure. It must be said that his preparation was intense to the point of being - amazing. I think we spent twelve or sixteen hours a week with that professor; that is, for him it was an enormous job. He had nothing else - his full teaching load was one class of preparation. There was also a professor of physics whose name I do not remember; the physics was very stereotyped and quite boring and I could guess nothing. I have no recollection of chemistry. There was a professor of French and philosophy, who was professor of the literary students who were preparing for the literary exam of the École Normale, and his name I do remember: de Bideur. I recall when in particular handing in French or philosophy papers to de Bideur who said, "I think this a practical joke happening, because there's one paper more than I expected, and this paper is so good it doesn't look like any one of you people could have written it. Is there an extra student since last time?", I was the extra student. I said, "It's my paper." Well, he was surprised. It was due to the work of Mademoiselle Trancher, who was my teacher in French at high school a few years before and who had taught me to write, in a certain sense, eighteenth century pastiche if I wanted to, which I did on that occasion, it was just a fun story.

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: 4 minutes, 48 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008