Claude Improves a Key Bound in Number Theory While Failing at the Riemann Hypothesis

Learning more about Claude's mathematical capabilities

An unreleased research version of Claude, prompted to take a real stab at the Riemann hypothesis, unexpectedly improved a longstanding lower bound for the proportion of zeros of the Riemann zeta function on the critical line from 41.6% to 67.2%. The result, which combines prior work by Baluyot, Goldston, Suriajaya, Turnage-Butterbaugh, and Bombieri, was validated by Anthropic's mathematicians and formalized in Lean. This showcases AI's growing ability to extend mathematical research in surprising ways.