AI and the World's Hard Problems · Mathematics · Anthropic · 2026-09-26
Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis
The Riemann hypothesis, an unsolved problem, states that the zeros of the Riemann zeta function all lie on a certain vertical line. While attempting the problem, an unreleased research version of Claude did not prove it but improved a longstanding lower bound on the fraction of zeros that satisfy it, raising it from 41.6% to 67.2%. Two Anthropic mathematicians validated the paper and wrote an informal expert note, and Claude also produced a formally verifiable proof. The result is not expected to lead to a proof of the hypothesis itself.