Unreleased Anthropic Model Makes Progress on Riemann Hypothesis

Anthropic has announced that an as-yet-unreleased model made significant progress on the Riemann hypothesis, a famous unsolved problem about prime numbers that has stood for over 150 years. An Anthropic staff member without significant mathematical training prompted the model to attempt a proof and then left it to coordinate the task over a day and a half. The model tested 650 different ideas, coordinating across 60 sub-agents and spending a total of 31 million tokens. Two of the sub-agents developed the key mathematical ideas, while others contributed ideas, attempted but failed to develop new ones, served as validators, or helped write the paper. Two of Anthropic's in-house mathematicians confirmed the findings, and the proof was formalized using the open-source proof assistant Lean. This is part of a series of mathematical breakthroughs by large language models, including solved Erdos problems and other results from OpenAI's 'Astra' model and Anthropic's disproving of the Jacobian conjecture. The growing body of results has prompted both excitement and concern, with some mathematicians worried about the attribution and responsibility for proofs, while Fields Medal winner Timothy Gowers suggests that the change might be less problematic than it seems.