Born in Warsaw, Poland, he has lived in France for much of his life. Mandelbrot was born into a family with a strong academic tradition - his mother was a doctor and his uncle, Szolem Mandelbrot, was a famous Parisian mathematician. His father, however, made his living buying and selling clothes. His family left Poland for Paris in the 1930s to escape Hitler's regime. There, Mandelbrot was introduced to mathematics by his two uncles.

Educated in France, he developed the mathematics of Gaston Julia, and began the (now common) graphing of equations on a computer. Mandelbrot originated what is now known as fractal geometry and the fractal called the Mandelbrot set is named after him. His work on fractals as a mathematician at IBM earned him an Emeritus Fellowship at the T.J. Watson Research Laboratories.

In addition to the discovery of fractals in mathematics, he showed that fractals can be found in many places in nature, leading to entire new fields of exploration in chaos theory.

He joined the faculty of Yale in 1987.