Mathematical primitives, like prime numbers, are discovered. Something that exists independently, like gravity. Mathematics is too big to be captured entirely by rules.
There’s likely an encoded structure underlying all reality and it’s decoded using mathematical models. That decoding is possible given our innate cognitive structures.
We know the incompleteness of proofs don’t imply the incompleteness of truths. That distinction is what keeps, at least in large part, mathematical truths in the realm of discovery.