The reason that the four-color theorem remains a fascinating problem for so many people and the source of so many cranks is not that the problem is easy to express.

It's that Kempe's proof, though in the end incorrect, is very elegant and digestible. Seeing why it is incorrect is actually really tricky! And once you have seen why it is incorrect it feels like it is just one or two corrections away from being a correct proof.

If you have not read the outline of Kempe's proof (the wikipedia article does a pretty fair job of it) then you definitely should. I promise you that you will waste at least a little bit of time trying to figure out how to fix the proof in two lines and become a world famous mathematician instantly.