How far does that carry? What about algorithms? Do they also have have an independent right to existence? Can you invent an algorithm at all or do you in fact discover it?
This is a doorway to a pretty abstract philosophical discussion, not a statement of fact. I don't think that math is actually real in the strictest sense, so I'm on the fence about invent vs discover. While I think that mathematical constructions are idealizations similar to Platonic Ideals, I don't believe like Plato did that there's a perfect Plato-space where these idealizations live.
When an artist arranges common-place paints (or sounds or dance moves or whatever) into a novel combination, he is said to have created rather than discovered a new work of art. Is there a good reason why this should not be true when a mathematician takes common-place axioms and makes a new arrangement of them that validates as a proof?