Some years ago, while I was still working at knots, Professor Cayley told me of De Morgan's statement that four colours had been found by experience to be sufficient for the purpose of completely distinguishing from one another the various districts on a map.

I had previously shown that if an even number of boundaries meet at each point on a diagram, two colours (as on a chess-board) will suffice for the purpose. But in a map, boundaries usually meet in threes.