Anthropic's unreleased AI cracks key math breakthrough

Anthropic has achieved a notable milestone in mathematics by using an unreleased AI model to make substantial progress on the Riemann hypothesis—a 150-year-old unsolved problem with a $1 million prize for a general proof. The breakthrough involved an Anthropic staff member prompting the model to 'take a real stab' at the problem, after which the model autonomously coordinated a multi-agent system across 36 hours. The system tested 650 different approaches, deploying 60 subagents that collectively generated 31 million output tokens. Two of these subagents developed the key mathematical insights, while others contributed ideas, validated arguments, or assisted with documentation. The results were formally verified by Anthropic's in-house mathematicians using the open-source Lean proof assistant.

This achievement is part of a growing trend where AI models are solving long-standing mathematical problems. Earlier this year, AI models solved several Erdos problems, and OpenAI's internal 'Astra' model recently proved 10 major theorems. Anthropic's work also includes disproving the Jacobian conjecture. However, the rapid progress has sparked debate in the mathematical community. Some, like Fields Medal winner Timothy Gowers, argue that AI could change mathematics in profound but positive ways, while others worry about the erosion of traditional authorship and accountability in mathematical proofs.