All proofs have axioms if you chase them all the way down. Given the axiom that the solving the math in the crypto is intractable, the crypto algorithm is prove

All proofs have axioms if you chase them all the way down. Given the axiom that the solving the math in the crypto is intractable, the crypto algorithm is proven secure. But only so long as the axiom holds. For example, quantum computing may break the axiom, and then the proof will be invalidated. It might be more correct to say assumption rather than axiom here.