What do mathematicians do?

Judging by this they make impressive videos presentations. Credit to: Étienne Ghys of the École Normale Supérieure in Lyon, France. See Science News for a good article on this video.

Dimensions
Great graphics and big maths fit together so well.

Starting with projections of the spherical Earth onto a flat plane, that's 3 dimensions displayed in 2, the video takes you through the steps to visualising 4 dimensional objects by projection into 3.

Later, in part 5, they move on to complex numbers, which are just like normal numbers but with an imaginary bit, a multiple of the square root of -1, this adds extra dimensionality to all numbers (the imaginary part is at 'right angles' to the normal number line, this gives the complex plane).

On to fractals where the easiest way to think of them is in the complex plane.

Through topology, described by intersecting complex planes. Doughnuts seem popular here.

Finally they consider the work of Bernhard Riemann some of whose geometries paved the way for the young upstart, Albert Einstein.

Happy viewing.

via Jim Downey at Unscrewing the Inscrutable.
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I was just recovering from learning overload when I found they are planning 'Dimension II' - whoah!!!

Consider a spherical cow...