Consider Gödel's incompleteness theorems (specifically the second one)

"For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent."

Gödel's second incompleteness theorem proves that your theory, which assumes math is valid (aka "including basic arithmetical truths") and assumes itself to also be true, is inherently inconsistent. Math has been proven to be incomplete.

"any consistent effective formal system that includes enough of the theory of the natural numbers is incomplete: there are true statements expressible in its language that are unprovable within the system" (Gödel's first incompleteness theorem). It does, however, mean that it's impossible to prove mathematicians have nothing left to prove, so maybe its good for job security for them.

What about Bitcoin Proof Of Work Algorithm and Other Consensus rules

Thanks