ABSTRACT
How many colours does it take to do a map so that adjacent countries aredifferent colours? The answer is so well known that hardly more thana sentence or two is needed to remind us of what it says. There are a few conditions: the map must be on a plane or sphere; the number of countries is finite; they must be connected (the USA, for example, isn’t since Alaska and Hawaii are separate from the other states); and countries meeting only at a vertex may be the same colour. This has long been a popular problem, and those who tried their hand at it were usually convinced by experience that four colours suffice. In 1976 Appel and Haken proved what was widely suspected; their celebrated result is now known as the four colour theorem (4CT). Its fame rests partly on the fact that it solved an outstanding problem; but even more, its celebrity resides in the way the theorem was established – a computer played an essential role in the proof.1
