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Family pressure


Mathematical disagreements with Uncle
Benoît Mandelbrot Mathematician
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Did you discuss with your uncle your ability to visualize mathematical formulas which for him were always kept separate? Oh, it was a source of endless arguments and fights. He said again and again, "Geometry's for children. You must outgrow it." Much, much later - I am jumping forward now but let me jump because the question is very very relevant- I will tell you how my uncle wanted me to write a Ph.D. thesis to continue the work of Julia, which I didn't want because I saw nothing to do about it. That was in '47. And then, thirty years later, in rough numbers, I did this work that led to the Mandelbrot set, and brought the pictures to him. He was then a very old man. He was not well, and conversation was getting strained. I showed him those pictures regardless and said, "Remember, thirty years ago, you wanted me to take up this problem of Julia sets, of iteration, which you said had been lying completely untouched for thirty years, and to do something with it, and you said that what was lacking was a good new idea?" And he said, "Well, maybe, I vaguely remember, but if I did I had something else in mind than pictures. Where are the theorems?" "Well this conjecture was proven by so and so, and this conjecture is open, and people think it's very difficult and very interesting." "Well," he says, "I prefer theorems to conjectures." That is, his view of mathematics and mine were completely orthogonal. The fact that I was just back from the war, when these very sharp fights occurred, and again had never been caught, never been tortured, never been starved, but had been very roughly bumped around, hardened, and had saved my life on many occasions bothered him. I was able to think very fast on my feet. I had taken sensible decisions, in addition to being very lucky - all these stories are luck, luck, luck, and then some hard thinking on one's feet - I was not going to let my uncle tell me anything different. As a matter of fact, everybody who knew me at twenty or so said I was not an easy person in terms of respecting authority and experts. I've seen authoritarian experts crumble dreadfully during the war in a complete fashion and events occur in ways that were not predicted by them. So my uncle had very little actual effect on me, but those big fights left him exhausted, and me exhausted. They were not, how to say, mild intellectual discussions! First of all he was extraordinarily like my father in terms of physique even though there were sixteen years difference. They got roughly the same genes I suppose, at least significant ones, and so it was a fight between very similar minds, and he was not an easy person either. He was a nice person but he had his clear ideas. Discussions with him were the ones, which sort of trained me far more than any teacher I had in the university and elsewhere. I knew his prejudices. I knew very well how to correct for them after a few years. But there's no question that he and my father were overwhelmingly strong influences on my life then, and I think on my life forever.

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, 17 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008