● Covered by 2 sources · 2 reportsMedium impact2 neutral
Anthropic's Claude AI Improves Riemann Hypothesis Lower Bound to 67.2%
Key points
- Claude AI increased Riemann hypothesis lower bound from 41.6% to 67.2%.
- The AI model tested 650 ideas using 60 subagents and 31 million tokens.
- Anthropic staff prompted the model to address the Riemann hypothesis.
- Two Anthropic mathematicians validated Claude's informal note and formal proof.
- The Riemann hypothesis remains unsolved, with a $1 million bounty.
AI Progress on Mathematical Challenge
Anthropic announced that an unreleased research version of its Claude AI has made progress on the Riemann hypothesis, a mathematical problem dating back to 1859. The AI model increased the known lower bound for the fraction of Riemann zeta function zeros that satisfy the hypothesis from 41.6% to 67.2%.
How Claude Achieved the Result
An Anthropic staff member, reportedly without significant mathematical training, prompted the Claude model to attempt the Riemann hypothesis. Over approximately a day and a half, the model explored 650 different ideas, coordinating across 60 subagents and processing 31 million output tokens.
This process led to the improvement of the lower bound, drawing on extensive prior research by mathematicians.
Validation and Significance
Two mathematicians at Anthropic studied and validated Claude’s findings, producing an informal note for experts and confirming a formally verifiable proof generated by Claude. Brian Conrey and Dan Goldston, experts in the field, were also acknowledged.
While the AI did not solve the Riemann hypothesis, which carries a $1 million bounty, its ability to advance a related problem highlights the growing capabilities of AI models in complex mathematical problem-solving and scientific discovery.
The Riemann Hypothesis
The Riemann hypothesis is one of the major unsolved problems in mathematics, concerning the distribution of prime numbers. Despite the AI's progress on a related bound, the hypothesis itself remains unproven.
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Primary sources
GitHub anthropics/zeta-23-lean GitHub leanprover/comparator arXiv 2306.04799 arXiv 2501.14545How outlets covered it
Anthropic announced that an unreleased AI model made significant progress on the Riemann hypothesis by increasing the lower bound of solutions for which the hypothesis holds true. This development highlights the growing capability of AI models in complex mathematical problem-solving, potentially reopening discussions about AI's role in scientific discovery.
An unreleased research version of Anthropic's Claude AI increased the known lower bound for the fraction of Riemann zeta function zeros satisfying the Riemann hypothesis from 41.6% to 67.2%. This development demonstrates progress in AI models' mathematical capabilities, though it is not expected to lead to a full proof of the Riemann hypothesis.