One of mathematics’ oldest open questions just got a new challenger. The Riemann hypothesis, which concerns the distribution of prime numbers and carries a $1M prize from the Clay Mathematics Institute, has resisted proof for more than a century and a half. Anthropic says a model that has not been released yet moved the needle further than expected.
The effort started almost casually. A staff member with no real mathematical training told the model to genuinely attempt a proof, then stepped away for roughly a day and a half. What followed was a marathon: the system tested 650 candidate ideas. Coordination happened through 60 subagents, and the whole run burned 31M output tokens. Just two of those agents generated the decisive math, according to the company’s paper. Thirteen supplied supporting ideas, thirty came up empty, thirteen double-checked the reasoning, and two wrote the initial draft.
Two of Anthropic’s own mathematicians verified the outcome, and the proof was encoded with the Lean proof assistant, which is open source. The result improves the known lower bound of values for which the hypothesis holds.
The achievement adds to a busy year for AI in pure mathematics. OpenAI’s Astra model has published ten major results, and a separate Anthropic project disproved the Jacobian conjecture. Mathematicians remain divided on what machine-driven proofs mean for the field, with some signing a June declaration about authorship and accountability and Fields Medal winner Timothy Gowers arguing the shift may prove positive in unexpected ways.
