four colour map theorem

mathematics, application (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

(1995-03-25)