MIT physicist David Turturean explains what Claude actually proved with the Riemann Hypothesis yesterday and why it is not solving the hypothesis itself: "What Claude did was basically prove that whatever set of zeros or solutions the zeta function has, at least two-thirds of those sit on this critical line. The goal is that we want to show that all of them sit on this critical line for which the real part is a half." "So far they have gotten it down to 41%, whatever number of zeros this…

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We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis. It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%. https://www.anthropic.com/research/riemann-zeta