Seriously - by doing math are we inventing relations that we need/deem useful between abstract concepts (like numbers and functions), or are we simply discovering relations that already exist? This question is a bit philosophical at heart, but answering it could give us a better understanding of math in general. Currently wikipedia deems math a "formal science" (a kind of science that is not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules). It may seem like math shouldnt be correct because it seeks no empirical validation, but somehow it ends up being correct if done right.