a story lives forever
Sign in
Form submission failed!

Stay signed in

Recover your password?
Form submission failed!

Web of Stories Ltd would like to keep you informed about our products and services.

Please tick here if you would like us to keep you informed about our products and services.

I have read and accepted the Terms & Conditions.

Please note: Your email and any private information provided at registration will not be passed on to other individuals or organisations without your specific approval.

Video URL

You must be registered to use this feature. Sign in or register.


Return to France and the Air Force - a year of thinking


Leaving Caltech; crisis over future
Benoît Mandelbrot Mathematician
Comments (0) Please sign in or register to add comments
Why had I becoming disenchanted with aeronautics? Again, because some people were doing very practical applied work, which was not doing very well, I felt. For example, I became interested in turbulence and I met several people of great brilliance, very good friends. They were studying turbulence but somehow I did not feel that it was beginning. It was still very hard. The K-5/3, which was everybody's dream, was totally beyond what they could do. It was complicated, in a way, it was a mess that had already been visited unsuccessfully, rather than a fresh mess to order. Furthermore, the mathematics was moving very far away from it. One of the professors I had during my second year was very blunt about it. It took - again, one of the turning points of my life - only a few minutes. He was giving an oral exam in his course. Caltech was on a quarter system so after ten weeks there was an exam, and so we chatted there were questions - I answered them. Then he leaned back and said, "Well, I have some good news for you and some news which may be bad. The good news is you have an A." "Thank you." "Well, you deserve it. The bad news is that I don't think you should write a Ph.D. with me because you do not admire me enough." That was perfectly true, and I was very worried about that. I did not think that this man's work was going in the right direction. He was going too far, too fast, in a rather dry mathematical manner, attacking a problem, which he did not understand in a physical sense to my satisfaction. I was very relieved because somehow the idea of returning, of doing that work, was very repellent to me. But having seen what someone could do - Delbruck having seen what someone could do in turbulence and being turned off by both, I reached a very profound crisis at that point in '47. I thought perhaps I'd made a mistake by not going to the École Normale. Now, if that hadn't happened at all, it would have been a total miracle, because again I was lost. I had been several years in very, very good schools. I was very well regarded personally and given nice fellowships and everything, but I was not even beginning to know what I was going to do. And so in the spring of '49 I applied to many of the maths departments, the new maths departments, which at that time in my mind were Chicago, Princeton and Harvard, also, requesting a fellowship because I couldn't come without it. Chicago accepted me and I was very close to returning, to going back to mathematics and just, well, starting four years later where I could have started before. It was a very tempting solution but I finally didn't take it. And perhaps my luck was that the person I would have been closest to would have been Niederberaist, well-known for his very abstract view of mathematics, and I just felt it was too much. I could go part of the way to mathematics, pure mathematics; I could work hard and get back in this field, but not that far, and this man's algebra was precisely what I was repelled most by.

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: 3 minutes, 57 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008