Anthropic said in an official research announcement that an unreleased research version of Claude pushed a key Riemann Hypothesis-related lower bound from 41.6% to 67.2%, marking the largest single advance ever recorded for that bound.
A record jump in a long-running mathematical problem
The company said the result concerns a benchmark linked to the Riemann Hypothesis, one of mathematics’ long-unsolved problems for more than a century. A full proof remains extremely difficult, so mathematicians also work on showing what proportion of the zeros of the Riemann zeta function can be proven to satisfy the hypothesis. The higher that lower bound goes, the closer the field gets to the target.
Before this result, the lower bound stood at 41.6%. Claude raised it to 67.2%, according to Anthropic. The company also said this line of work does not prove the full Riemann Hypothesis, describing the outcome as a concrete quantitative gain rather than a final answer.
About 60 subagents and 650 failed ideas
Anthropic said the result was produced by a set of autonomous subagents working over about 36 hours. Roughly 60 subagents generated around 650 unsuccessful ideas before arriving at the crucial insight.
According to the announcement, Claude combined recent results from Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with work by Bombieri. That let a technique proposed by mathematician Montgomery in 1973 be converted into an unconditional lower bound.
Lean-formalized proof reviewed by Anthropic mathematicians
Anthropic said Claude’s final output was a proof formalized in Lean, making it machine-verifiable. The company added that two of its mathematicians reviewed and confirmed the proof.
ABMedia also noted that Chain News had previously reported that OpenAI’s next-generation model Astra solved 10 mathematical problems that had remained unsolved for more than 10 years. As frontier AI begins to contribute to genuinely open problems, the shape of mathematical research is changing.