Anthropic staff recently challenged an unreleased research version of Claude to attempt the Riemann hypothesis, a famous unsolved mathematics problem dating to 1859. Claude did not succeed, but it unexpectedly improved a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis, increasing the bound from 41.6% to 67.2%. Drawing on prior research by mathematicians including Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh, as well as a 2000 paper by Bombieri, Claude combined these results to surpass the previous constant. Two mathematicians at Anthropic studied and validated Claude’s paper, producing an informal note for experts, and Claude also produced a formally verifiable proof. Experts Brian Conrey and Dan Goldston examined the paper. Anthropic does not expect the techniques to lead to proving the Riemann hypothesis, but views the work as an example of rapid progress in AI mathematical capabilities. The Riemann zeta function describes prime distribution, and the hypothesis posits that all relevant zeros lie on a vertical line; mathematicians have gradually raised the known minimum proportion of zeros on that line to 41.6%.