Four color theorem
The four color theorem requires the "map" to be on a flat surface, what mathematicians call a plane. In 1890, Percy John Heawood created what is called Heawood conjecture today: It asks the same question as the four color theorem, but for any topological object. As an example, a torus can be colored with at most seven colors. The Heawood conjecture gives a formula that works for all such objects, except the Klein bottle.