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/

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

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.