The 'Resolved' category archives questions which have been answered since they were added to the site.

As of Apr. 2019, this entry is now moved to the 'Resolved' section. This theorem is widely regarded as having been solved. See : Formal Proof—The Four-Color Theorem Notices of the AMS Volume 55, Number 11.

For reference, the original text of the Wikenigma article is archived below :

The Four Color Theorem states that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Source : Wikipedia

Computational tests, checking millions of possible configurations, have never found an exception. (note that a formal proof with 5 colors was made in the late 19th century by Percy Heawood, seeWikipedia ).

A 'machine generated proof' was described by Georges Gonthier of Microsoft Research Cambridge England, in 2007. See: Asian Symposium on Computer Mathematics, ASCM 2007 Asian Symposium on Computer Mathematics, ASCM 2007: Computer Mathematics pp 333-333