Godel's Incompleteness Theorem (first one)
Any logical system cannot be both consistent and complete. In particular, for any consistent, logical system that proves certain truths, there will always be a statement that is true, but not provable in the theory.
Mainly, I am fond of this, because while we know of this result, we also tend to ignore it and keep plodding away at math, acting like it doesn't exist.
