A better title is, does math exist outside of our minds.

I doubt the universe cares about numbers.

Indeed, this should be the title. Not clickbait enough, tho.

At that point, a more salient question would be whether anything at all exists outside our minds.

We don't actually know that. Science (especially physics) assumes that the universe can in principle be explained, but there's not actually a way to prove this without assuming some explainable is possible (see: problem of induction). More concretely, we know our current theories and maths can't fully explain our observations, though they are very close.