## four colour map theorem

Synonyms

## four colour theorem

(Or "four colour theorem") The theorem stating that if the plane is divided into connected regions which are to be coloured so that no two adjacent regions have the same colour (as when colouring countries on a map of the world), it is never necessary to use more than four colours.

The proof, due to Appel and Haken, attained notoriety by using a computer to check tens of thousands of cases and is thus not humanly checkable, even in principle. Some thought that this brought the philosophical status of the proof into doubt.

There are now rumours of a simpler proof, not requiring the use of a computer.

See also chromatic number