Anthropic Model Advances Riemann Hypothesis After Testing 650 Ideas
Anthropic says an unreleased AI model raised a verified lower bound for the Riemann hypothesis after testing 650 ideas across 60 subagents in 36 hours.
Summary
On Monday, August 10, 2026, Anthropic said an unreleased model significantly increased the lower bound of cases for which the Riemann hypothesis holds, without producing the general proof needed to claim its $1 million bounty. The hypothesis, unsolved for more than 150 years, concerns the distribution of prime numbers. An Anthropic employee without significant mathematical training asked the model to attempt a proof, then let it coordinate work for a day and a half. It tested 650 ideas through 60 subagents and generated 31 million output tokens. Two subagents developed the key ideas, 13 assisted them, 30 failed to develop new ideas, 13 checked the arguments, and two helped draft the paper. Two Anthropic mathematicians confirmed the result, which was formalized with the open source Lean proof assistant.
The result adds to several 2026 AI mathematics advances, including solutions to multiple Erdős problems, 10 major results from OpenAI’s internal Astra model, and a separate Anthropic effort that disproved the longstanding Jacobian conjecture. More powerful model releases have produced stronger results, intensifying debate over discovery and accountability. A June 2026 declaration signed by prominent mathematicians warned that AI could erode the principle that proofs should be attributed to identifiable authors responsible for their correctness. Fields Medal winner Timothy Gowers responded that mathematics could change more positively and complexly, comparing unattributed theorems with stars that are not named for astronomers.
Positives
- An unreleased Anthropic model significantly increased the verified lower bound of cases where the Riemann hypothesis holds.
- 650 ideas, 60 subagents and 31 million output tokens supported a coordinated search lasting a day and a half.
- Two Anthropic mathematicians confirmed the finding, and the open source Lean proof assistant formalized it.
- OpenAI’s Astra produced 10 major results, while separate Anthropic work disproved the longstanding Jacobian conjecture.
- An employee without significant mathematical training initiated the Riemann hypothesis project with a simple request to attempt a proof.
Risks & concerns
- The Riemann hypothesis remains unsolved after more than 150 years, leaving its $1 million bounty unclaimed.
- 30 of the model’s 60 subagents were unable to develop new mathematical ideas.
- Only two subagents generated the key ideas, despite the system spending 31 million output tokens.
- A June 2026 declaration warned that AI generated mathematics could weaken authorship, attribution and responsibility for proof correctness.