Claude makes a breakthrough on the Riemann Hypothesis

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We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis.

It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from…

— Anthropic (@AnthropicAI) August 10, 2026

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1974	Norman Levinson	> 34.25% (\approx 1/3)	Introduced the "mollifier method" to bound zero density.
1989	J. Brian Conrey	> 40.77% (\approx 2/5)	Refined mollifiers using higher-degree polynomial choices.
2011–2020	Bui, Conrey, Young / Feng / Pratt et al.	> 41.6%	Extended bounds past 41.28\% - 41.6\% using multi-piece mollifiers.
2026	Anthropic Research	67.2%

Pretty big jump!!!