Four Colours Suffice: How The Map Problem Was Solved

On 23 October 1852, Professor Augustus De Morgan sat down to write a letter to a colleague, unaware that it marked the beginning of one of the most famous and controversial conundrums in mathematics - one which would take thousands of puzzlers over a century to answer. This is the story of how it was solved.

The problem posed in the letter came from one of De Morgan's former students and involved the colouring of maps. It asked: what is the least possible number of colours needed to fill in any map (real or invented), so that neighbouring countries are always coloured differently?

It sounded simple, yet amateur problem-solvers and professional mathematicians alike were to spend years colouring maps and developing the necessary theoretical machinery before the result could be established with certainty.

Here Robin Wilson clarifies the problem, explains the proof, introduces the characters behind the mathematics - and shows how they all connect with patterns on footballs, maps on doughnuts and the great rhombicubotahedron.