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École Normale and thought in mathematics

RELATED STORIES

Influences: Father and Uncle
Benoît Mandelbrot Mathematician
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My father and my uncle were extraordinarily strong influences on my life. And I was taught perhaps by my uncle. When I was thirteen my uncle became professor at the Collège de France. Therefore I knew that mathematics was an option, that one could lead a life as a mathematician. On the other hand, the war had intervened, times were very rough, and my father had survived World War I and World War II under very complicated and heroic circumstances. My father had a very deep feeling about the uncertainties of life, and during and after the war he was extraordinarily keen not to allow his sons, my brother and myself, to even think about professions which would depend upon state certification, degrees that would be good in one place and of no value elsewhere and professions that would fill a need in one place and not another. When the war ended in, when my exams ended in the winter of 1945- though the war was not quite finished - it was clear that my father wanted me to choose a profession that would be as independent as possible of whether France would be rebuilt, whether Europe would come back, or whether we may have, once again, to pick up roots and move to the United States or South America. He wanted me to become a kind of engineer, which could find a job anywhere. My uncle on the other hand was a very successful person and he was extraordinarily lucky to be at the right place at the right time. He felt that the only thing I could even consider was pure mathematics. My uncle felt that in a way I should, and I was destined to, live his own life with one thing improved: namely, he did not go the École Normale. I, on the other hand, had entered the École Normale. And so in 1945 I had taken the science exams under heroic conditions and I was faced with a very big choice: should I go to the École Normale or to the École Polytechnique? And a kind of family council got together to, in a certain sense, really fight for my soul. My uncle wanted me to drop every consideration and just go into mathematics - I was very good, I was entering number one at École Normale, - and forget about any other consideration, just take a gamble. My father was very much against gambles. He felt that the life of a professor of mathematics in France was too much linked to a state, which was being rebuilt, but was certainly in very bad shape. A third person entered the story, a cousin of mine named Magar, who was a physical chemist. I would like to mention their ages: Magar was about thirty-five, my uncle was forty-six and my father was sixty-two. Magar felt that France was just about to enter a total change, and that schools such as the École Polytechnique and the École Normale were going to be abolished and that, in a certain sense, a completely new system would occur and my so decision amounted to nothing. He thought I should devote myself to science and forget about everything, forget about school. My uncle said not just any science but mathematics at the École Normale. My father said: anything except professions, which will link you to a certain environment. This fight was extraordinarily rough. It was one of the hardest parts of my life. In a certain sense, before world events decided for me, and except when my parents strongly intervened, as they did, I had to make up my mind alone. Now truly and deeply I can say that I've never made up my mind. My uncle's and my father's influence always fought in me and one of the reasons why my life has been so complicated, with lurches, if you will, towards very pure mathematics at one time, then lurches away from pure mathematics to very practical things, was very much this fight between these two men when I was approximately twenty.

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, 30 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008