Anthropic's Unreleased AI Model Advances Riemann Hypothesis

Anthropic has revealed that an AI model, yet to be released, has made notable strides regarding the Riemann hypothesis, one of the most enduring unsolved issues in mathematics, by enhancing the lower limit of valid solutions. Over a span of a day and a half, the model, guided by a non-expert, explored 650 distinct concepts, collaborating with 60 subagents and generating 31 million output tokens. Key mathematical ideas emerged from two subagents, with contributions from 13 others, while 30 attempted without success, and 13 validated the findings. Two subagents authored the initial paper, which was verified by two in-house mathematicians and formalized using the open-source proof assistant Lean. This milestone follows various AI-led mathematical advancements, including resolutions to several Erdős problems and the refutation of the Jacobian conjecture. The development has ignited discussions within the mathematical community, leading to a declaration signed by notable mathematicians in June, voicing concerns that AI might jeopardize the field's integrity, particularly regarding the attribution of proofs. Conversely, Fields Medal recipient Timothy Gowers has challenged this viewpoint, proposing that AI's impact on mathematics could be more intricate and beneficial, likening it to stars not being named after their discoverers. The Riemann hypothesis, which addresses the distribution of prime numbers, has a $1 million reward for a general proof that remains unclaimed.