Mathematical Weirdness
You Can Hold In Your Hand

Paul Harrison @paulfharrison

Wang Invents Wang Tiles
And Makes A Wrong Conjecture

Wang (1961, section 4.1, A Generalized Game Of Dominos)

Given a set of squares with colored edges, can we tile the plane with copies of these squares so all the edge colors match?
(Rotations and reflections are not allowed.)

Wang's conjecture:
If we can tile the plane, we can do so with a repeating pattern.

Wang's student Berger (1966) showed this is wrong.
There are aperiodic tile-sets.