My favorite theorem is The Four Color Theorem, which states that the chromatic number of any planar graph is no more than four. It is my favorite theorem for a number of reasons:
1. The theorem was "proven" using a computer program running on physical computer hardware, thus calling into question the correctness of the proof. Being a computer science student, I know that the correctness of an algorithm can be proven, but when a physical machine is involved, the correctness of its computations rests in the hands of a few untrustworthy transistors.
2. This theorem tells one when it is time to get a new box of crayons. If a box has four or more crayons remaining after much use, that is still plenty to color any coloring book on the market without having ugly pictures where two adjacent regions are colored the same. One only needs to start worrying when the number of crayons drops below four.
-Josh Magner
