Anthropic's Unreleased AI Model Makes Historic Progress on Riemann Hypothesis
An unreleased AI model from Anthropic makes significant progress on the Riemann hypothesis, one of mathematics' most enduring unsolved problems. The 150-year-old conjecture, which concerns the distribution of prime numbers and carries a $1 million bounty for a complete proof, has resisted countless human attempts. Anthropic announced on Monday that its model substantially increases the lower bound of solutions for which the hypothesis holds true, marking a notable step forward in a notoriously difficult mathematical domain.
Perhaps more striking than the result itself is how the model achieves it. An Anthropic staff member with no significant mathematical training prompts the model to attempt the proof and then leaves it to work autonomously for roughly a day and a half. During that time, the model tests 650 different approaches, coordinating across 60 subagents that consume 31 million tokens. Two subagents develop the key mathematical ideas, while others contribute supporting concepts, validate arguments, and help draft the resulting paper. Anthropic's in-house mathematicians confirm the findings, which are formalized using the open-source proof assistant Lean.
This breakthrough joins a rapidly growing list of AI-driven mathematical achievements. AI models already solve several Erdos problems this year, OpenAI releases ten major results from its internal Astra model, and a separate Anthropic effort disproves the longstanding Jacobian conjecture. However, the mounting successes also stir unease within the mathematical community. In June, a group of prominent mathematicians signs a declaration warning that AI could undermine core values of the field, particularly the expectation that proofs should be attributable to specific authors who claim credit and bear responsibility for their correctness.