Anthropic’s Unreleased Claude Model Makes Progress on Riemann Hypothesis

An unreleased Anthropic AI model has made progress on research connected to the Riemann hypothesis, one of mathematics’ most famous unsolved problems, without solving the hypothesis itself.

Anthropic said Monday that the model improved a longstanding lower bound related to the Riemann hypothesis from 41.6% to 67.2%. The result adds to growing evidence that advanced AI systems can contribute to mathematical research beyond solving established problems.

Claude model tackles the Riemann hypothesis

The Riemann hypothesis has remained unsolved for more than 150 years and concerns the distribution of prime numbers. A valid general proof carries a $1 million prize as one of the Clay MathematicsInstitute’ss Millennium Prize Problems.

The Anthropic experiment began when an employee without significant mathematical training asked the unreleased model to “take a real stab” at the problem. The system was then allowed to coordinate its work for roughly a day and a half.

During that process, the model explored 650 different ideas using 60 subagents and generated 31 million output tokens. Anthropic said two subagents developed the central mathematical ideas, while others contributed suggestions, attempted alternative approaches, checked the arguments and helped prepare the initial paper.

Two Anthropic mathematicians reviewed the result, and the work was also formalised using Lean, an open-source proof assistant used to verify mathematical reasoning.

AI models make deeper moves into mathematics

The result follows a series of examples in which large language models have contributed to advanced mathematics. AI systems have worked on several Erdos problems, while increasingly capable models have produced results on other longstanding mathematical questions.

OpenAI recently disclosed 10 mathematical results produced by its internal Astra model. Anthropic has also reported work involving the Jacobian conjecture, adding to interest in whether frontier AI systems can generate genuinely useful mathematical ideas.

The progress has also intensified debate among mathematicians about how AI-generated discoveries should be treated. A public declaration signed by prominent mathematicians in June raised concerns about preserving standards around authorship and responsibility for the correctness of proofs.

AI raises questions about mathematical authorship

Not everyone sees AI’s growing role in mathematics as inherently harmful. Fields Medal winner Timothy Gowers has argued that the technology could reshape how mathematical discoveries are understood and attributed.

“If we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that won't be any more problematic than the fact that stars aren't named after astronomers and most aren't named at all,” Gowers wrote.

Anthropic’s result does not resolve the Riemann hypothesis or claim its $1 million prize. It does, however, provide another example of advanced AI systems contributing to research on mathematical problems that have challenged specialists for generations.