Claude lifts a key Riemann zeta bound from 41.6% to 67.25%

Anthropic reports that an unreleased research version of Claude found an unconditional proof that at least 67.25% of the Riemann zeta function's zeros lie on the critical line, improving the longstanding published lower bound of 41.6%. The result does not prove the Riemann hypothesis: it combines earlier pair-correlation work with a linear-algebra treatment of zeros away from the line. Anthropic released a 35-page paper and a Lean formalization, and says two staff mathematicians studied the result while external experts examined the paper on short notice. If it holds up to broader scrutiny, it is a concrete example of an AI system extending prior mathematical work, although the model's research process and current validation record are primarily reported by Anthropic.