Anthropic未公開モデルがリーマン予想で数学的進展を達成
Original: An unreleased Anthropic model made progress on one of math’s biggest unsolved problems
Why This Matters
AI-driven mathematical discovery is accelerating, challenging traditional research norms and authorship standards across the field.
Anthropic announced on August 11, 2026 that an unreleased AI model made significant progress on the Riemann hypothesis, a 150-year-old unsolved math problem with a $1 million prize, by testing 650 ideas across 60 subagents over 36 hours using 31 million output tokens.
Anthropic revealed on Monday that an unreleased AI model achieved a notable advance on the Riemann hypothesis — one of mathematics' most famous unsolved problems concerning the distribution of prime numbers, which carries a $1 million prize for a verified general proof. The model significantly increased the lower bound of solutions for which the hypothesis holds. Notably, the process was initiated by an Anthropic staff member without advanced math training, who simply prompted the model to 'take a real stab' at the problem and left it running for approximately 36 hours. The model autonomously coordinated 60 subagents, testing 650 distinct approaches and consuming 31 million output tokens. Of those subagents, two developed the key mathematical ideas, 13 contributed supporting concepts, 30 failed to generate new ideas, 13 served as validators, and two helped write the initial paper. The findings were verified by two in-house Anthropic mathematicians and formalized using the open-source proof assistant Lean. This follows a broader trend of LLM-driven math breakthroughs in 2026, including OpenAI's 'Astra' model proving 10 major results and a separate Anthropic effort disproving the Jacobian conjecture. The developments have sparked debate: a June declaration by prominent mathematicians warned AI could undermine authorship norms, while Fields Medal winner Timothy Gowers argued the impact could ultimately be more complex and positive.