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Uncle and Father


'Cheating' in the exams
Benoît Mandelbrot Mathematician
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The war went on; liberation in the north, liberation in the south, and in the fall of 1944 there was a lull. We moved back to Paris. Again I prefer to skip the main events in the summer, they are irrelevant, I think, to my story as a scientist. I was accepted by the Lycée Legrand (1944), which is the biggest, most prestigious high school in Paris, and took the exams as such, as a student of Lycée Legrand. But I didn't really attend the classes. The professor told us the exams of '44 had been postponed, again the world was very unstable, and we would take them in December and January. In December and January we took these absolutely hellish exams. You take the written paper for one exam, the written for the other and the oral of yet another. For a very long time I was doing nothing else except going from exam to exam. At one point, I was walking down the Latin Quarter and Monsieur Ponce, who was, I would say, my host and my teacher but really my host in that high school, hailed me in the street and said, "May I speak to you?", I answered "Yes, sir." "The examiners tell me that one student in my class did the math problem from end to end - in fact only one student in France did it and he's in my class. I don't understand it. I couldn't do it myself. And I know the students in my class, and not one of them could do it remotely. Did you do it?" I said, "Yes, sir, I did it." "How did you do this triple integral in the middle of the problem? It took me hours to get it." I said, "But that triple integral is the volume of a sphere if you don't work in x, y, z co-ordinates, but in u, v, w, which are natural to the problem." "Of course, of course, of course, of course, of course." So again, I'd gone through the moves of this terrifying exam by cheating. I didn't reduce that integral, I didn't think of cute ways of replacing this by that. I had no repertory of tricks of calculation, but I had an innate intimacy with shapes, and that whole problem, instead of doing it as a problem of calculation, I had done it as a problem of describing shapes.

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: Daniel Zajdenweber Bernard Sapoval

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

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.

Duration: 2 minutes, 31 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008