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.
One of the greatest concerns of my life as scientist has been with economics, more precisely with the twin notions of inequality in all its forms and of financial variability. I must immediately say that I prefer to speak of them separately, after the mathematics and the physics, but in fact my interest in these topics started well before I became interested in either of the other activities I carried on. In fact in late '50s and early '60s this was my principal centre of interest, and I interrupted it for many years and came back to them only several years ago with very great intensity, I must say. The word 'fractal' did not figure in the first half. As a matter of fact, the tools of fractal thinking were developed very much in the context of economics, finance, inequality in general, and then, enriched, came back to be applied to these fields. Two names come to mind in this context, both of them contemporaries, or nearly contemporaries of the other great men mentioned in earlier segments of this interview. The names are Pareto and Bachelier. Pareto was a famous Italian professor of economics at Lausanne, and had a long career after that. In the late 1900s he wrote down an empirical law for distribution of income that had a very interesting history after that. Bachelier was, quite the contrary was quite a person of no social standing whatsoever, who presented a Ph.D. in 1900, at the University of Paris, and whose work was not at all understood except by very few until the '60s when he became very influential and, I would argue, after a while too influential to be beneficial. The same period as Hadamard and Poincaré, Cantor, Peano, Sierpinski and other names mentioned- was the time of these two men.
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.