My favorite theorem is the Pythagorean Theorem. It is much better than EVAN'S FAVORITE THEOREM_MA375Fall2008walther.
(No seriously, I chose it before looking at his page) --
Here it is $ a^2+b^2=c^2 $
It's one of those theorems that is surprising at first. When I saw the proof of it I was pretty amazed. See image here.
If I couldn't choose that one, I would probably choose the four color theorem, ($ \forall $ maps, $ \exists $ a coloring of that map that uses $ \le 4 $ colors.) because I think it's kind of interesting since it's something people can relate to, and it's an interesting graph theory problem.
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