If a shape has equal sides with 90 degree angles between them then it's a square, right? Well, not quite...

So easy to describe, yet so hard to prove.

Why there are only three regular polygons you can tile a wall with.

Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem.