<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.