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.
In '42 two things happened, quite unrelated of course. On the one hand I finished high school and took this baccalaureate, which in France is the high school graduation degree, and of course the Germans occupied the whole of France. Before that, between '40 and '42, the unoccupied zone was genuinely unoccupied, that is the Germans were very much a presence but not on a daily basis, and particular in a place like Tulle one didn't see a single German, and prewar conditions continued. We had many friends through my uncle and therefore we did not feel as isolated or as lost as many people who had moved to the country from Paris might have felt. From '42 on things became very rough, and for about a year and a half I had a hectic and complicated life that I will not describe in detail, except to say that at different times I had different jobs. I was running around to keep my body and soul together. To go to school again was something which was quite inconceivable. I didn't have the money for it, we were afraid of going to the school and to put ourselves in danger, and in general it was very difficult to imagine that I could maintain any kind of regularity in this life. I may add that during the war in occupied France life was not as perturbed as one might have expected. It's a well known fact that these wars tended to leave large parts of a country more or less the same, then a storm went by, some destroying a little or destroying a lot, and then again a kind of peace came to call again. It was not a matter of horror every day and on a routine basis, far from it. I remember life in Tulle at that time, from '40 to '42 as being more or less normal. In fact, surprisingly normal. But the year and a half after that became very, very rough. I had several very close calls with disaster, which I won't describe because they had, I think, no influence - the details had no influence - on my life. But at the end of '43 after a particularly rough episode, the people I was living with, who belonged to the resistance group and were taking care of the welfare of various people and occupying them properly, decided that I needed a few weeks or months of rest. We didn't know how long the war was going to continue. But what did rest mean? Something instead of being in places where I was completely out of place - I was playing roles, which clearly were taken up- I did not look like an apprentice toolmaker on the railroad, which I was for a number of months, because I just spoke differently, I acted differently. I had strange books in my bags, which was very imprudent, but I carried on regardless. I held books that I had collected in this little town, books of mathematics, most of them very old even by then, which I was reading and trying to understand so as not to completely lose touch with what I was going to be studying.
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.