Math talks to blow your mind

The world turns on symmetry -- from the spin of subatomic particles to the dizzying beauty of an arabesque. But there's more to it than meets the eye. Here, Oxford mathematician Marcus du Sautoy offers a glimpse of the invisible numbers that marry all symmetrical objects.

Robert Lang is a pioneer of the newest kind of origami -- using math and engineering principles to fold mind-blowingly intricate designs that are beautiful and, sometimes, very useful.

Physicist Geoffrey West has found that simple, mathematical laws govern the properties of cities -- that wealth, crime rate, walking speed and many other aspects of a city can be deduced from a single number: the city's population. In this mind-bending talk from TEDGlobal he shows how it works and how similar laws hold for organisms and corporations.

'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.

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.

What can mathematics say about history? According to TED Fellow Jean-Baptiste Michel, quite a lot. From changes to language to the deadliness of wars, he shows how digitized history is just starting to reveal deep underlying patterns.

Web cartoonist Randall Munroe answers simple what-if questions ("what if you hit a baseball moving at the speed of light?") using math, physics, logic and deadpan humor. In this charming talk, a reader's question about Google's data warehouse leads Munroe down a circuitous path to a hilariously over-detailed answer — in which, shhh, you might actually learn something.