four colour theorem

four colour map theorem
four colour 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)