TITLE: Why bother with Mathematics, if Gödel's Incompleteness Theorem is true?
QUESTION [20 upvotes]: OK, maybe the title is exaggerated, but is it true that the rest of math is just "good enough", or a good approximation of absolute truth - like Newtonian physics compared to general relativity? How do we know that our "approximation" is the right one? Another analogy: Fundamental physics is also not  well-fundamented (where is the Higgs boson?) but most of the rest of the physics is on top of it, and it does its job well (it's a good-enough approximation).
Summary: According to the responses, math is indeed an imperfect domain, but can be seen as perfect for all practical purposes. In this case I wonder if math is indeed pure and identical across all possible universes. Maybe another universe comes up with a different set of axioms, more or less consistent than what we have now.

REPLY [2 votes]: Godel's theorem says what we should expect anyways, namely that one cannot simply write down some simple rules, and mechanically derive the deepest mysteries of our Universe.
Godel's theorem is only a limitation of what mechanical non-thinking beeings can figure out about math, truth and the Universe, it does not represent an ending of reasoning.