What we call mathematics actually exists as a single point in a space of an infinite number of sets of axioms and inference rules. We like this particular set

What we call mathematics actually exists as a single point in a space of an infinite number of sets of axioms and inference rules. We like this particular set of axioms and rules because they can answer questions about physics, but they were stumbled upon almost by accident when we started using the concept of numbers and asking "What does it mean to prove something?". One could imagine other points in this space though, which define, say, the game of chess, or perhaps something as complex as English grammar. It just so happened that the point we naturally settled on for mathematics is one that was powerful enough to lead to the rules of algebra and geometry etc., and also consistent/deterministic in the same way that most physics seems to be (which is convenient for humans, whose brains are limited by physics). So, mathematics doesn't "underlie" physics in the sense of being more real than it, but merely is a point we have chosen because of its similarity to physics. I suppose the real question, then, is why should such a useful point exist in this infinite space at all.