If one is seeking to explain everything, doesn't one run up against Goedel's incompleteness theorem?
Goedel's theorem concerns proof systems that are rich enough to prove arithmetic. Second order propositional calculus is such a proof system, and any system that contains it, such as the popular ZF axioms of set theory, is either undecidable or incomplete, by Goedel's theorem or its successors.
But any mathematical system than does not base itself on such a proof system is not necessarily undecidable or incomplete. Tarski showed that geometry is complete back in 1948, and work in the last ten years or so has shown that a broad class of operations with real numbers is complete, too. So it's not a foregone conclusion that the math of physics will run into Goedel problems.
Physics in not an attempt to prove the completeness of mathematics. Nor has it been proven that you even need a complete math system to prove the completeness of physics. Physics is deliberately using only a subset of math since it's an effort to reduce all things to a brief formula, it does not require every valid mathematical formula for its completeness.
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