When the Four Colour Theorem (FCT) was finally ‘proved’ in 1976, it upset a lot of mathematicians.  It was the first significant mathematical concept to be proved with a good deal of help from a computer and, for many, that didn’t make it a real proof.  Although we’re largely (maybe not entirely) OK with it now, the objections at the time weren’t just theorists’ snobbery.  At the heart of it all were some fundamental questions about the role a computer could or should play in formal logic.

Essentially, the FCT says that the maximum number of different colours needed to colour a map, so that no bordering countries are the same colour, is four.  (Colours can touch at a point but not at an edge.)  It’s easy to show that five will always do the trick and, in fact, most normal maps only need three.  However, certain types of map certainly seemed to need four so was four always enough? Continue reading