Mathematicians have been using AI models as tools to make progress on mathematical problems for several years. However, Anthropic published a research note on Monday suggesting that an unreleased version of Claude had improved results on a longstanding problem without a mathematician’s hand guiding it.

The result relates to the Riemann hypothesis, a problem first posed in 1859 and one of seven that carries a $1 million bounty under the Clay Mathematics Institute prize. The hypothesis states that the zeros of the Riemann zeta function that determine the primes all sit on one vertical line, something that has never been proven true in every instance.

Mathematicians have made incremental progress on the hypothesis over the years, raising the minimum bound to 41.6%. Claude’s efforts, according to Anthropic, increased this to 67.2%.

The mathematical capabilities of frontier AI models are becoming one central arena for competing labs, alongside cybersecurity and agentic capabilities. On August 1, OpenAI published solutions to 10 open problems and credited an internal version of its unreleased Astra model.

A non-mathematician ran the Claude session

What distinguishes Anthropic’s report is the fact that no professional mathematician was involved in the process. Instead, Anthropic staff member Jarred Sumner ran the session. His role was reportedly limited to providing the initial prompts and messages of encouragement throughout, with the mathematical decisions themselves left up to the AI model.

The session ran for roughly a day and a half across 60 coordinated copies of the same model called subagents. Only two of these 60 agents produced usable results, from a total of 2,400 shell commands and hundreds of Python scripts.

Altogether, the session consumed 31 million output tokens. Anthropic did not disclose the total cost.

On its own initiative, Claude then had its subagents critique the findings and attempt to replicate them. It also tested its findings against a body of academic literature to ensure they were not already known. The model then recommended that a human mathematician verify the results.

Claude’s Riemann Hypothesis results have not been peer reviewed

Two in-house Anthropic mathematicians, Levent Alpöge and Ralph Furman, validated the result internally. The firm then reached out to Dan Goldston and Brian Conrey - the latter of whom set the 40% boundary on the same problem in 1989 - for an external review. It is worth noting that this does not equate to full peer review.

Claude did, however, produce a machine-readable version of the proof for verification, published as a public repository.