Indeed. That's physics. Based on that kind of math you can demonstrate with absolute certainty that the earth is flat. Based on other kind of math, it is not. Hence, for the same object (earth) or observer (human or particle) the truth cannot be absolute.
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I dispute your contention that physics is identical to math. I understand what you're getting at with the flat earth example but in this case feel you're forcing puzzle pieces to fit which actually don't.
The only point I hope to make here is that absolute truth is indeed possible in very narrow and contrived situations where all factors are specified by humans, such as logic and math. This is nothing to be threatened by. Even if you are committed to the view that no absolute truths exist anywhere, I advise you not to ignore these counterexamples just because they do not fit that view.
No need to force them. We can follow your 'axiom premise' and demonstrate two different truths about a single object (earth). Quantum gravity is suggested to work much the same way.
I don't argue against the tool ("math" and/or "axioms"). I argue about the observation. You can use the same axioms for measuring particle activity and still get different results because you are observing them.