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The organisation of École Polytechnique; Paul Levy

Benoît Mandelbrot
Mathematician

Views | Duration | ||
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11. 'Cheating' in the exams | 1524 | 02:30 | |

12. Uncle and Father | 644 | 05:40 | |

13. Mathematical disagreements with Uncle | 795 | 04:16 | |

14. Family pressure | 513 | 03:05 | |

15. Influences: should I be an engineer or a mathematician? | 540 | 04:29 | |

16. École Normale and thought in mathematics | 765 | 03:34 | |

17. The world of learning how | 696 | 03:51 | |

18. The organisation of École Polytechnique; Paul Levy | 629 | 05:18 | |

19. Gaston Maurice Julia | 634 | 02:02 | |

20. Leprince-Ringuet and experimental physics | 1 | 485 | 01:27 |

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It was very strangely organised. The main professors gave very few lectures. Then there were, not main professors, but other professors who gave exams and so on. It made for an extraordinarily tight, very tough schedule with work every week and exams at regular and close intervals. Indeed, the fact that it was a military academy was quite apparent. It was not run as an institution of learning, but as a military academy, which had become more and more a school for science and engineering as opposed to anything else. Now the three professors whom I remember best were professors of mathematics, of analysis actually. There was Paul Levy, Gaston Julia who was the professor of geometry, and the professor of Physics who was called Leprince-Ringuet. I first heard of Paul Levy, I remember it very well, was in the courtyard of the Collège de France in March 45. My uncle, having resumed his course at the Collège de France, had two or three people come over, it was an extraordinarily small group, and one of them was a person named Michel Loave, who was not exactly very young, but who was a probablist trying to establish himself at that time, and had learned about my situation from my uncle, who had actually told him, "Please help me save this lost soul. He just went to the École Normale, and left after two days. A terrifying situation." Loeve told me that I would have the privilege of meeting Paul Levy in the École Polytechnique, who was, he said, one of the two great probablists of the day, the other being Kolmogorov. Now, Loev did not tell me much about Paul Levy, but I soon found out. Paul Levy was a very strange person, for reasons that had nothing to do with events, because his life had been rather peaceful, he had taken a path which was also not of his time, and later on he wrote a kind of autobiography, in which he said he always had the impression of being an anachronistic person, that he was a person of the mid-nineteenth century lost in the mid-twentieth century. First of all, he too perhaps thought in pictures, but he didn't express it, he didn't confess it, but it was often very clear that his arguments were very intuitive and not the kind of hard mathematical proof type. Besides, he was making amazing mistakes of a childish nature. He would go through a paper and put the wrong formula for the surfaces here, then find a discrepancy of two somewhere else, and then he was surprised by it. Later somebody pointed out that it was simply in a little algebra mistake. Paul Levy was so brilliant in his youth that everything was forgiven him. Again I must say now I remember a stroke of fate that was not of his choosing, but of the world, which made him change his way. The dean at the École Polytechnique asked him to give a few lectures about gunnery. So he looked at gunnery, about how far guns can shoot and errors in gunnery, and became interested in probability; but instead of just stopping after the duty was performed he went on. Now in that sense Paul Levy did something I was doing, namely when the chances of life came he did not correct for them, he did not resume a straight and narrow, he let himself be directed by events, which I did again and again. Paul Levy had a very weak voice when it was not amplified. I was assigned to the last row in the auditorium, so I barely heard him, but I read his notes; every week we got these notes that were actually hand-written and then produced by a very old-fashioned system and called 'the sheets', the feuilles. The Paul Levy Feuilles were something very odd. Where other people had ten pages of straight algebra, Paul Levy had two pages of motivation, then two lines of algebra, then a few statements which were more or less proven, and then everything became either totally clear for one person, myself, and totally obscure for everybody else. So I was the interpreter of Paul Levy, where I said, 'Well, he says so and so, but what he means is not that. That's the proof, but there is proof behind it.' But in any event he made you understand what was happening. I was very friendly towards Paul Levy, but at the École Polytechnique I barely spoke to him.

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: **The organisation of École Polytechnique; Paul Levy

**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:**
5 minutes, 19 seconds

**Date story recorded:**
May 1998

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