Tiling the Plane

In May of this year, the French mathematician Michaël Rao announced that he had catalogued all families of convex pentagonal tiles that can be used to tile the plane. This resolves a problem that is nearly 100 years old. It has a really nice history, with some contributions by amateur mathematicians, and some false claims, and it also points the way towards the future of mathematical proofs. This week's pundit is our man with a number for every occassion from Victoria University's School of Mathematics - Dr Dillon Mayhew.