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An unreleased Anthropic model made progress on one of math’s biggest unsolved problems
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An unreleased Anthropic model advanced work on the Riemann hypothesis by testing many ideas and increasing the lower bound of cases where the hypothesis holds.
The experiment shows that a language model can orchestrate dozens of sub-agents to generate and validate mathematical ideas over a day and a half. It demonstrates that AI can contribute to lowering the bound on a long-standing open problem, which may influence how engineers approach automated theorem proving. The result also highlights ongoing debate about credit and responsibility when AI produces mathematical work.
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The model tested 650 ideas using 60 sub-agents, with two sub-agents producing the core mathematical insights.
The work was validated by Anthropic’s in-house mathematicians and formalized in the Lean proof assistant.
The outcome fuels discussion in the mathematics community about AI’s role in proof attribution and the future of human-led research.
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The unreleased model explored the Riemann hypothesis by generating many candidate ideas via a swarm of sub-agents, leading to a new lower bound on cases where the hypothesis is true.
Achieving this required prompting a non-expert to set the goal, letting the model run for a day and a half, coordinating 60 sub-agents, testing 650 ideas, and consuming 31 million in total, plus subsequent validation by in-house mathematicians and formalization in Lean.
The model did not produce a complete proof; it only improved the bound, leaving the hypothesis unsolved for the remaining cases; the approach depends on human experts to confirm correctness and to translate informal arguments into a proof assistant.
The experiment shows that LLMs can act as a catalyst for mathematical exploration, but it also reignites debate about attribution and responsibility when AI contributes to formal proofs, indicating that adoption will need new workflows and governance.
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