As it stands now, the frontier models can prove theorems where the techniques exist in the literature, which it knows better than anyone who's ever lived and won't quit where a human would. There's no way to know if that's true of the Riemann Hypothesis until it's proven.

For example, even if Claude could prove the statement "100% of the zeroes lie on the critical line", that's strictly weaker than the Riemann Hypothesis, so even the best possible version of this result would fall short. (It's an asymptotic result, so it just means the percentage of counterexamples to the Riemann hypothesis goes to zero as their magnitude gets large.)