Anthropic's Unreleased Model Advances on Key Mathematical Problem

The Riemann Hypothesis, one of mathematics' most famous unsolved problems about the distribution of prime numbers, remains unsolved for over 150 years with a $1 million prize for a proof. Anthropic has announced that an unreleased model achieved notable progress, significantly raising the lower bound of solutions for which the hypothesis is known to hold. An employee with limited math background suggested the model attempt the problem and then left it to coordinate the task over the next day and a half. During that time, the model tried 650 solution paths, coordinating 60 subagents and consuming 31 million output tokens. Among the subagents, 2 developed main math solutions, 13 generated new variants for those agents, 30 attempted but failed to produce new ideas, 13 served as validators, and 2 helped write the initial paper. The result was verified by two staff mathematicians and formalized in the Lean proof assistant. Recent years have seen AI models solve several of Pál Erdős's problems, with OpenAI's Astra model solving ten and another Anthropic model disproving a long-standing Jacobian hypothesis. These achievements spark both excitement and concern in the math community regarding authorship and responsibility for correctness, with some arguing theorems need not be associated with specific researchers.