Additionally, the well-known four colour problem and elementary geometry theorem-proving problem have been discussed.

同时，也对四色问题与初等几何定理证明作了简单的讨论。

youdao

The idea behind both proofs of the four colour theorem is to suppose that the theorem is violated to assume, in other words, that there is some sort of map that requires five colours to fill in.

ECONOMIST: Just what does it mean to prove something?