Anthropic model advances a lower bound tied to the Riemann hypothesis

Anthropic says an unreleased AI model has made significant progress on the Riemann hypothesis, a 150-year-old unsolved problem concerning the distribution of prime numbers. Rather than producing a general proof, the system increased the lower bound of solutions for which the hypothesis holds true. A valid general proof still carries an unclaimed $1 million prize.

The reported work began with an Anthropic staff member who did not have significant mathematical training asking the model to “take a real stab” at the problem. The model then coordinated the task over roughly a day and a half, testing 650 possible approaches through 60 sub-agents and using 31 million total tokens.

A multi-agent search for mathematical ideas

Anthropic’s paper describes a division of labour among the sub-agents. Two developed the key mathematical ideas, while 13 contributed ideas to those agents. Thirty tried but did not manage to develop new ideas; 13 acted as validators checking the arguments; and two helped prepare the initial paper.

Two in-house Anthropic mathematicians confirmed the finding. The result was also formalized with Lean, the open-source proof assistant, providing a machine-checkable representation of the argument. That distinction matters: the work is presented as progress on a lower bound, not as a resolution of the Riemann hypothesis itself.

Part of a wider debate over AI mathematics

The announcement follows a series of AI-assisted mathematical results. AI models have solved a number of Erdős problems this year, while OpenAI recently released ten major results attributed to its internal Astra model. A separate Anthropic effort also disproved the long-standing Jacobian conjecture.

These developments are intensifying a debate over how mathematical research should use AI. In a public declaration signed in June, prominent mathematicians warned that AI could weaken a central norm of the discipline: proofs should be attributable to authors who receive credit and accept responsibility for correctness. Fields Medal winner Timothy Gowers, responding in a blog post, suggested that a future in which theorems are not associated with individual mathematicians might not necessarily be harmful.

Anthropic’s broader position in the AI market has also been shaped by competing approaches to model access; Anthropic’s two-scenario AI market frames that split as two market scenarios, while this result illustrates how unreleased systems can still be used in tightly controlled research workflows.

Implications for research teams

For businesses and research organizations, the case highlights a practical model for using advanced AI on difficult technical tasks: broad exploration by many agents, explicit validation roles, domain-expert review, and formal checking where suitable. The reported advance does not show that AI can settle every open problem, but it shows why governance and verification must accompany AI-generated research results before they are relied upon.