Maths lacks the physical grounding, so in that sense, it's less "real", and more "made up", even though of course it's so pure.

its the same... physics hand-waves the 'why' all the same as chemistry or biology...the gap might be wider but its the same

It isn't because you can choose any axioms you want and build an entire mathematical system based on that, but it isn't real in the sense that the universe is. It isn't wrong either - its just not bounded by physical reality.

Physics has a long history of throwing out laws with exceptions in favour of laws that cover larger and larger numbers of observations.

Downvoters are probably misunderstanding this. Mathematical theory is based on axioms and inference. The axioms do not have to be true in any cosmic sense for the math to be correct or even useful. Math is a superset of physical reality.

yet there are problems there too we do not know the "true axioms of math", people disagree (math foundations)

Yes, we've all seen the xkcd[1] but you've misunderstood it. Physics applies mathematics but mathematics cannot derive physics in the way that a complete physics (and a lot of compute) could derive chemistry and biochemistry.

Math isn't attempting to describe a physical universe. It provides the substrate upon which such a description can be expressed and validated - found to be consistent with itself - but many valid descriptions do not describe our universe. Physics is the empirical search for the correct mathematical description of our universe.

[1] https://xkcd.com/435/

> mathematics cannot derive physics

thats just at the current state of the art...doesnt mean a complete maths cannot...its arguably debatable why physics follow some maths and why the specific constrains

I don't think that's true. Mathematics can model every conceivable universe; you cannot derive the values of c or G in our universe from a purely mathematical model. Even if there were a proof that the current values for cosmological constants are the only possible values, that proof would necessarily have to rely on lemmas from physics.

It could be that once we truly understand math in a complete way it would lead inexorably to the definition of one and only one possible universe with only one possible set of rules and c and G would simply fall out naturally. I'd agree it seems unlikely given our current understanding of math and physics (and their relationship to each other). But given both are incomplete it remains a possibility. The one theme that seems to hold true as we dig deeper and deeper into how the world works is that the fundamental rules seem to get more and more unified.

Please tell us more about this. I’m not familiar with any definition of mathematics that would support the idea that it can prove statements about our universe without access to observed facts.

Are there any papers where this possibility is explored? What does it mean to have a complete understanding of mathematics?