The Incompleteness Theorem

There are people who argue that maybe it's impossible. It doesn't say the universe isn't physical or doesn't make sense, but may be like our mathematical systems, which are based on these axioms, are just not the right language for exploring the universe. So if not mat then what? I don't know. We'll have to meet those alien physicists that developed something else. What's the foundation, which the language of their physical theories? Maybe it's not mathematics, right?