On Monday, Anthropic announced that an as-yet-unreleased model had made significant progress on the Riemann hypothesis, significantly increasing the lower bound of solutions for which the hypothesis holds true. An Anthropic staff member without significant mathematical training prompted the model to “take a real stab” at proving the hypothesis, then left the model to coordinate the task across the following day and a half. The model tested 650 different ideas, coordinating across 60 subagents and spending 31 million output tokens in total. Out of the 60 subagents, two developed the key mathematical ideas, 13 contributed ideas to these agents, 30 attempted but were unable to develop new ideas, 13 served as validators, and the final two helped write the initial paper. The finding was confirmed by two of Anthropic’s in-house mathematicians and formalized using the open source proof assistant Lean. This is the latest in a string of mathematical breakthroughs led by large language models. A number of Erdos problems have been solved by AI models over the course of this year, and OpenAI recently released a set of 10 major results proved by its internal “Astra” model, while a separate effort from Anthropic disproved the longstanding Jacobian conjecture. In a public declaration signed in June, a group of prominent mathematicians raised concerns that AI could undermine critical values of the field, particularly the standard that proofs should be “attributable to specific authors who take credit for their discovery and assume responsibility for their correctness