The hard part in proving the four color theorem is proving that there aren't any possible maps that can't be colored with four colors. Perhaps there's one out t

The hard part in proving the four color theorem is proving that there aren't any possible maps that can't be colored with four colors. Perhaps there's one out there that needs five and can't be colored with only four. Proving some maps can't be colored with three colors is easy, you only need to find one and enumerate all the three-colorings and find none of them work. It's not really a theorem about colors though, they're just labels.