We are talking about the same thing, but I would actually put this the other way around.
Computation and computability is "the final frontier". Math is a "subset" of that. Doesn't matter if we choose ZFC or in the future discover some "better" subset of core axioms, we will always hit limits where BB will trivially skip over whatever we could prove (let alone Gödel's theorems).
> given fixed input of the statement with no other information sources
Also, this is just trivially avoidable, so not sure if we really should be concerned about this limitation. An LLM in a loop where it can write on a tape can be Turing complete, ergo it can compute anything computable and is "bigger" than math at that point.
We are talking about the same thing, but I would actually put this the other way around.
Computation and computability is "the final frontier". Math is a "subset" of that. Doesn't matter if we choose ZFC or in the future discover some "better" subset of core axioms, we will always hit limits where BB will trivially skip over whatever we could prove (let alone Gödel's theorems).
> given fixed input of the statement with no other information sources
Also, this is just trivially avoidable, so not sure if we really should be concerned about this limitation. An LLM in a loop where it can write on a tape can be Turing complete, ergo it can compute anything computable and is "bigger" than math at that point.