Mandelbrot invented the term fractal to describe the "roughness" he saw all around him in nature -- the jagged shape of a cloud, the rugged indentations of a coastline. Classical Euclidean mathematics, the kind we learn in school, serves well for the human-made world of straight lines, circles, and squares. But nature's non-linear shapes were generally considered unmeasurable -- until Mandelbrot developed fractal geometry.
"In the whole of science, the whole of mathematics, smoothness was everything," Mandelbrot says in "Hunting the Hidden Dimension." "What I did was open up roughness for investigation."
Suddenly, something as ragged as a coastline could come under mathematical scrutiny. While he couldn't actually measure a coastline, Mandelbrot found, he could measure its roughness. It required rethinking one of the basic concepts in math -- dimension.