To what extent mathematics can capture all physical phenomena? Drawing an analogy from computer science: finite automata can handle regular expressions (does "(([a-z]))" match "((h))" ), but for more complex tasks, we need Turing machines (eg. determining if a string has balanced parentheses). There is no way we can physically "blow up" finite automata to where they can solve turing computability problems. In the same vein, is there a limit to where we can "blow up" math to where it won't be able to solve the next complexity of "physical phenomena". Where on the computability hierarchy do physics even falls under.
These limitations could have implications on the current open questions on unifying gravity with qm and other theories of everything suggesting them to be fool's errands.
I've already read this thread (Why is mathematics so fantastically successful at describing the universe?), this is a kind of asking the opposite to see where we stand.