The Four Color Theorem is easy to state:  If you have a (nice enough) map of countries, and you want to color them so that no two adjacent countries are the same color, then you never need more than four colors to do it!  This theorem was proved in the 70's, but its proof is controversial among mathematicians due to its heavy use of a computer.  We will discuss the history of this theorem, and then prove the Five Color Theorem, which states you never need more than five colors to color our map, which is much easier than four!