Mandelbrot was born into a family with a very academic tradition. As a young boy, Mandelbrot was introduced to mathematics by his two uncles. Mandelbrot's family emigrated from Poland to France in 1936 and one of his uncles took responsibility for his education. Mandelbrot attended the Lycée Rolin in Paris up to the start of World War II, when his family moved to Tulle in central France. Mandelbrot now attributes much of his success to this unconventional education.

After studying at Lyon, Mandelbrot entered the Ecole Normale in Parisbut he left after just one day. After a very successful performance in the entrance examinations of the Ecole Polytechnique, Mandelbrot began his studies there in 1944. There he studied under the direction of Paul Lévy who was another to strongly influence Mandelbrot.

After completing his studies, Mandelbrot went to the United States where he visited the California Institute of Technology. From there he went to the Institute for Advanced Study in Princeton where he was sponsored by John von Neumann. Mandelbrot returned to France briefly, but in 1958 he returned permanently, and began his long standing and most fruitful collaboration with IBM as a Research Fellow and Research Professor.

With the aid of computer graphics, Mandelbrot was able to show how Julia's work is a source of some of the most beautiful fractals known today. To do this he had to develop not only new mathematical ideas, but also he had to develop some of the first computer programs to print graphics. Mandelbrot discovered the Mandelbrot set, the most famous fractal. His work was first put elaborated in a 1975 book, and more fully in The fractal geometry of nature in 1982.

As well as IBM Fellow, Mandelbrot was Professor of the Practice of Mathematics at Harvard University. He also held appointments as Professor of Engineering at Yale, of Professor of Mathematics at the Ecole Polytechnique, of Professor of Economics at Harvard, and of Professor of Physiology at the Einstein College of Medicine. Mandelbrot's excursions into so many different branches of science was no accident but a very deliberate decision on his part. It was the fact that fractals were so widely found which in many cases provided the route into other areas.

Mandelbrot has received numerous honours and prizes in recognition of his remarkable achievements. For example, in 1985 Mandelbrot was awarded the Barnard Medal for Meritorious Service to Science. The following year he received the Franklin Medal. In 1987, he was honoured with the Alexander von Humboldt Prize. He received the Steinmetz Medal in 1988, and many more awards including the Nevada Medal in 1991, and the Wolf prize for physics in 1993.