Claude boosts Riemann zeta function bound to 67.2%

Anthropic’s unreleased Claude AI model reportedly raised the proven lower bound for the Riemann zeta function: the share of nontrivial zeros on the critical line increased from 41.6% to 67.2%. This is not a full proof of the Riemann Hypothesis, which would require showing 100% of nontrivial zeros behave as predicted. Still, the jump is described as the largest improvement of its kind in the history of the problem. The Riemann Hypothesis (posed in 1859) asserts that all nontrivial zeros of the Riemann zeta function lie on the critical line (real part 1/2). Since proving 100% has remained out of reach, mathematicians focus on partial “at least X%” results. Claude’s new 67.2% nearly doubles the previous best floor of 41.6%. Anthropic says the AI’s math progress is ongoing: Claude previously contributed to resolving the Jacobian conjecture in 2026. The Riemann Hypothesis is one of the Clay Mathematics Institute’s Millennium Prize Problems (US$1 million for a complete solution), but this result falls short of that standard. For crypto traders, this is mainly an AI/research headline rather than a direct market catalyst. The key figure to watch is the quantified benchmark: 67.2% vs 41.6% for the Riemann zeta function bound.