Boethius, a medieval philosopher, wrote a very intellectually stimulating proof of the existence of a god.

The proof goes as follows (paraphrased):

1, Definition: A god is that which nothing greater can be thought.
2, Assumption: It is greater to exist in reality than the mind alone.
3, QED: A god exists.

Now, the assumptions may seem perfectly valid but there seems to be some missing steps before the conclusion. Let us explore the proof.

Suppose you can imagine something incredibly wonderful that does not exist, we shall call it x. Now, there must exist something in reality that is not as wonderful as x but has no betters; we shall call it y. Therefore, according to assumption 2, y is greater than x and thus matches the definition in 1. If you were to respond with a thought greater than x, then lather, rinse and repeat

Just a note: I am actually an atheist but I find this proof interesting due to its brevity and elegance. Also, know thy enemy.