The Side Most Don't See

Topology is the mathematics of morphing surfaces. It asks whether objects which look very different are actually the same: whether one can be turned into the other by way of a little twisting and stretching, or, on the other hand, if morphing one object into the other requires its surface to be cut.

To a topologist, it is obvious that a circle can be swelled out at the sides to make an ellipse, but that you can't get the twist out of a Mobius strip without tearing it. Because a torus can easily deform into a cylinder with a handle, a classic math joke is to say that topologists can't tell their donuts from their coffee cups.

Topology is a strange field, but one that appears all over the math and physics landscape; it has applications in general relativity, group theory, string theory, and a huge range of other areas. Though a rigorous understanding of topology requires years of training on top of a generous dose of inherent spatial awareness, anyone can get a sense of how it might be to think topologically by watching this wonderful video:

It's 20 minutes long but I found I couldn't stop watching. The clip demonstrates why a circle can't be turned inside out but why a sphere can - and how. Incidentally, the topologist Bernard Morin, who was key in developing this method of sphere eversion, was blind.