What if the set of all well-formed statements in ZFC formed a kind of pseudo-category where a morphism f between objects A, B represented a formal proof that A implied B? What if that category could be interpreted as a strange topological space, and was proved to be a disjoint union of special path connected subspaces?
The connected subspaces are not ordinary, in that many paths from a given statement to another are not reversible. Then someone shows that since two statements (e.g. Riemann Hypothesis and some other proven conjecture) are in the same connected subspace, there exits a morphism (that is, a correct formal proof) of the Riemann Hypothesis.
No one is any closer to proving RH, but there is some axiom-of-choice-esque argument that a proof exists.
Would everyone accept that the Riemann Hypothesis is true? Is such an approach, to show proofs exist without giving an actual proof, viable?