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There's two catches with that. The first is that "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." (Albert Einstein)
Witness his special relativity, wherein 2 apples plus 2 apples might still be 4 apples but 2 m/s plus 2 m/s turns out to only be 3.9999 (and another dozen or so 9s, admittedly) m/s.
So we can come up with conceptual universes of axioms and prove all sorts of interesting things about them, but we can never be totally sure how completely any of them are really relevant to the actual universe we're in, rather than just amusing games. The fact that we've invented so many pure amusing games that turned out to be good descriptions of the building blocks of reality makes this a surprisingly tricky question.
The second is Gödel's Incompleteness Theorems. Any reasonable (able to handle basic arithmetic, not obviously inconsistent) system of foundational axioms for mathematics is inadequate to prove all statements which are true in that system, and is also unable to prove its own consistency. We can sometimes use a more complex system to prove the consistency of a less complex system, but then at that point it's turtles all the way down.
There are a lot of ways to interpret the unreasonable effectiveness of mathematics. To some extent the discovery of how much complexity can be derived from ridiculously simple rules hints at possible alternatives to theism, though I'm not exactly all on board the Tegmark train myself.
I've always been taken by Godel's theorem's as it really cuts us down to size. But if I'm understanding it properly, it doesn't preclude the idea of a proof itself from a series of other proofs, just we can't prove a system of them all lining up together on the same axiom base. But that's not quite the same as having an ambivalent confusion about everything in mathematics...?
These days I like Iain Mcgilchrist's left-brain, right-brain algorithmic vs gestalt brain thing. A lot of our thinking and limitations are because we mistake the left-brain view of the world for reality. The key scientific insights of the 20th century, Godel, quantum physics, relativity and, yes, postmodernism are all pointing us to somewhere else...
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