In
1852 British student Frederick Guthrie asked
whether any map drawn on a piece of paper can be colored
with no more than four colors.
Guthrie’s question became the “FourColor
Problem.”
The number of colors
needed for a map drawn on other than flat surfaces was
determined in 1968, eight
years before the FourColor Problem was solved.
In 1890, Heawood determined that it
requires at most seven colors to color any map on a doughnut. 

A. B. Kempe,
a lawyer, published a proof of the FourColor Problem
in 1879, but P. J. Heawood found an error in Kempe’s
proof in 1890. The
problem remained unsolved until 1976 when mathematicians
Kenneth Appel and Wolfgang Haken of the University of
Illinois gave a proof based on more than 1000 hours of
computer calculations. 