I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.

For most of my life, one of the persons most baffled by my own work was myself.

The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.

I had very, very little training in taking an exam to determine a scientist's life in France.

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.