Unreleased Anthropic Model Advances 150-Year-Old Riemann Hypothesis

An Anthropic staff member with little mathematical background gave an unreleased model a single prompt: attempt the Riemann hypothesis. Left to run autonomously for about a day and a half, the system returned a result that Anthropic's own mathematicians have since confirmed as genuine progress on one of mathematics' oldest open problems.

The model did not solve the 150-year-old conjecture, first posed in 1859 and still carrying a $1 million bounty for a full proof. Instead, it substantially raised the lower bound of values for which the hypothesis has been verified to hold, a narrower but still meaningful contribution to a problem that has resisted the field's best human minds for over a century.

How the model worked

The system explored 650 distinct approaches before converging on a viable path, burning through 31 million output tokens in the process. It orchestrated 60 subagents in parallel, each assigned a specific role in the investigation.

Of those 60, only two ended up generating the key mathematical ideas that led to the breakthrough. Thirteen contributed supporting ideas, thirty attempted the problem without producing anything new, thirteen acted as validators checking proposed steps, and a final two helped draft the paper describing the results.

The findings were then formalized in Lean, the open source proof assistant increasingly used to machine-check mathematical arguments before humans stake their reputations on them. Two of Anthropic's in-house mathematicians reviewed and confirmed the work independently.

Part of a broader pattern

This is not an isolated case. Anthropic separately ran an effort that disproved the Jacobian conjecture, and 2026 has already seen several Erdos problems fall to AI systems. OpenAI, for its part, published 10 major results attributed to its internal model, Astra.

The pace of these results has unsettled parts of the mathematical community. In June, a group of prominent mathematicians signed a public declaration warning that AI-generated proofs could erode a core norm of the field: that proofs should be attributable to a named author who takes responsibility for their correctness.

Fields Medal winner Timothy Gowers offered a more measured take in a blog post, suggesting the shift might reshape mathematics in a more nuanced and even positive way. He compared the anonymity of AI-assisted discovery to the fact that most stars in the sky remain unnamed, framing authorship as less central to progress than the field currently assumes.

Gowers suggested the change might be "more complex and positive" than critics fear, likening AI's contributions to how most stars remain unnamed.

Anthropic has not said when, or whether, the model behind this result will be released publicly. For now, the episode adds to a growing body of evidence that frontier AI systems, working with minimal human guidance, are becoming genuine contributors to open problems in pure mathematics rather than just tools for computation.