An unreleased Anthropic model made progress on one of math’s biggest unsolved problems

For more than 150 years, the Riemann hypothesis has sat near the top of math’s unsolved pile, guarding a mystery about how prime numbers are distributed. There’s a $1 million prize for a general proof, and nobody has claimed it. AI still hasn’t solved the thing outright, but Anthropic says one of its unreleased models pushed much farther than expected.

On Monday, the company said the model significantly raised the lower bound for cases where the hypothesis holds. The route there was almost comically improvised: an Anthropic staffer without serious mathematical training asked the model to “take a real stab” at the proof, then let it coordinate the work for a day and a half. In that stretch, the system tested 650 ideas, worked across 60 sub-agents, and spent 31 million in total.

The division of labor was the interesting part. A footnote in the paper says two of the 60 subagents developed the key mathematical ideas. Thirteen helped feed those agents ideas of their own, 30 tried and failed to generate new ones, 13 checked arguments for correctness, and the final two helped write the initial paper. Two in-house Anthropic mathematicians confirmed the result, and the proof was formalized with Lean, the open-source proof assistant.

This is not a one-off. AI models have been racking up mathematical results this year, including work on several Erdos problems. OpenAI recently published ten major results from its internal Astra model, while another Anthropic effort disproved the Jacobian conjecture. That has sharpened the fight over what counts as mathematics when the machine is doing more of the proving and less of the typing.