Do mathematicians create or discover?

The answer to this question will significantly affect the idea of my previous post. I have a feeling that in general they discover. For example, a Tyrannosaurus Rex probably couldn't count, but that doesn't change the fact that it had 2 arms, 2 legs, 1 tail, and "x" razor-sharp teeth. So numbers "existed", but they weren't really being thought about carefully.

If mathematicians always discover (rather than create) mathematics, then my analogy in the previous post becomes quite weak. However, my faulty analogy might not change my acceptance of the (rather unlikely) possibility that an advanced civilization had a hand in the creation of the universe.

I should do some reading on the philosophy of mathematics and then post what I've learned. Stay tuned.