The Four Colour Theorem

The four-color theorem, also known as the four-color map theorem, is a mathematical theorem that states that any map on a two-dimensional surface can be coloured using at most four colours, in such a way that no two adjacent regions have the same colour.

The theorem was first conjectured by Francis Guthrie, and it was later proven by Kenneth Appel and Wolfgang Haken using a computer-assisted proof. The proof is controversial because it relies on a massive amount of computational power and is not easily verifiable by humans.

The theorem has many practical applications, such as in cartography, where it is used to create maps with as few colours as possible and five-colour theorem, which states that any planar graph can be coloured with at most five colours.