Graphs and NetworksMaps

In 1852, the botany student Francis Guthrie had to colour a map of counties in England. He observed that four colours seemed to suffice for any map he tried, but he was not able to find a proof that worked for all maps. This turned out to be an extremely difficult problem, and became known as the four colour theorem.

During the following 100 years, many mathematicians published “proofs” to the four colour theorem, only for mistakes to be found later. Some of these invalid proofs were so convincing that it took more than 10 years to discover errors.

For a long time, mathematicians were unable to either prove that four colours are enough, or to find a map that needed more than four colours.