Anthropic revealed Monday that an internal, as‑yet‑unreleased large‑language model made measurable progress on the Riemann hypothesis, the 150‑year‑old problem that underpins the distribution of prime numbers. The model increased the proven lower bound of numbers for which the hypothesis holds, a step that pushes the frontier of AI‑assisted mathematics.
Anthropic's coordinated AI effort
The experiment began when a staff member who does not hold formal training in mathematics prompted the model to "take a real stab" at the conjecture. The researcher then let the system run for a day and a half, during which it orchestrated 60 sub‑agents to test 650 distinct ideas. In total, the agents produced roughly 31 million output tokens.
According to a footnote in the accompanying paper, two of the sub‑agents generated the core mathematical insights. Thirteen others supplied supporting ideas, while thirty attempted but failed to develop new concepts. Another thirteen acted as validators, checking the logical consistency of arguments, and the final two helped draft the initial manuscript.
Two Anthropic mathematicians reviewed the output and confirmed the findings. The results were formalized in the open‑source proof assistant Lean, providing a machine‑checked record of the progress.
Reactions from the math community
The announcement arrives amid a wave of AI‑driven breakthroughs in pure mathematics. Earlier this year, large‑language models solved several Erdős problems, OpenAI’s Astra model posted ten major theorems, and Anthropic previously disproved the longstanding Jacobian conjecture.
Not everyone is celebrating. In June, a coalition of prominent mathematicians signed a public declaration warning that AI could erode core values of the discipline, especially the principle that proofs should be attributable to identifiable authors who take responsibility for correctness. Fields Medalist Timothy Gowers responded in a blog post, questioning whether the loss of authorial attribution is necessarily detrimental. He wrote, "If we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that won’t be any more problematic than the fact that stars aren’t named after astronomers and most aren’t named at all."
The Riemann hypothesis remains unsolved, and a $1 million bounty offered by the Clay Mathematics Institute still awaits a general proof. While Anthropic’s model has not solved the problem outright, extending the verified lower bound marks a tangible advance that could inspire new lines of inquiry.
Anthropic did not disclose when the model will be publicly released, but the company said the experiment underscores the growing capacity of AI to contribute to high‑level scientific research. As AI systems become more capable of generating and checking complex arguments, the mathematics community may need to revisit how credit, verification, and collaboration are defined in the age of machine intelligence.
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