OK, even if the Hypothesis turns out to be false, that was hilarious, but seriously now ... one promising route to the Riemann Hypothesis is
in fact to show that it is undecidable with the standard axioms. It is hard to imagine how this could be done. Even if the zeta zeroes were completely re-characterised in terms of higher categorical invariants, in a way that seemed utterly natural and compelling, that does not imply that we must
look at the zeta function that way. Well, mathematically that is. Physically speaking, we only care about the zeta function in so much as it can describe measurable quantities.
But the zeta function soon gets swamped by its generalisations, inflating the difficulty of the problem. These are certainly physically relevant. Recall, for example, Brown's paper
for MZVs, which contains a 1-operad computation of Veneziano amplitudes. M Theory cannot avoid considering this construction outside set theory.Update:
Thanks to K. L. Lange for further interesting remarks about the possibility that Pati has
inadvertently made progress on showing that RH is unprovable within standard analysis.