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.

Stephen Wolfram, creator of Mathematica, talks about his quest to make all knowledge computational -- able to be searched, processed and manipulated. His new search engine, Wolfram Alpha, has no lesser goal than to model and explain the physics underlying the universe.

'I am a mathematician, and I would like to stand on your roof.' That is how Ron Eglash greeted many African families he met while researching the fractal patterns he'd noticed in villages across the continent.

Simplicity: We know it when we see it -- but what is it, exactly? In this funny, philosophical talk, George Whitesides chisels out an answer.