At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.
Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.
The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.