The western states of America
Let’s look at the map of the western states of America. If only blue, green and
red were available we could start off by colouring Nevada and Idaho. It does not
matter which colour we begin with so we’ll choose blue for Nevada and green for
Idaho. So far so good. This choice would mean that Utah must be coloured red,
and in turn Arizona green, California red, and Oregon green. This means that
both Oregon and Idaho are coloured green so cannot be distinguished. But if we
had four colours, with a yellow as well, we could use this to colour Oregon and
everything would be satisfactory. Would these four colours – blue, green, red
and yellow be sufficient for any map? This question is known as the four-colour
problem.
The spread of the problem
Within 20 years of De Morgan recognizing the problem as one of significance,
it became known within the mathematical community of Europe and America. In
the 1860s, Charles Sanders Peirce, an American mathematician and philosopher,
thought he had proved it but there is no trace of his argument.
The problem gained greater prominence through the intercession of the
Victorian man of science Francis Galton. He saw publicity value in it and inveigled