Anthropic’s Claude AI advances Riemann zeta function lower bound to 67.2%

An unreleased research version of Anthropic’s Claude AI model has achieved a significant breakthrough in a mathematical problem related to the Riemann hypothesis. The model successfully increased the proven lower bound for the proportion of nontrivial zeros of the Riemann zeta function that lie on the critical line from 41.6% to 67.2%.

While this does not constitute a full proof of the Riemann hypothesis—a Millennium Prize Problem that carries a $1 million reward—it represents the largest single improvement to this specific bound in the history of the problem. The Riemann hypothesis, formulated in 1859, posits that all nontrivial zeros of the zeta function have a real part of exactly 1/2.

Anthropic mathematicians validated the AI’s findings, which included both a concise informal note for experts and a formally verifiable proof. This development follows previous mathematical contributions by Claude, including work related to the Jacobian conjecture, highlighting the increasing speed of progress in AI-driven mathematical research.