Anthropic AI Makes Significant Progress on 150-Year-Old Riemann Hypothesis

Anthropic has disclosed that one of its yet-to-be-released AI models achieved a notable advance on the Riemann hypothesis, a fundamental unsolved problem in mathematics that has puzzled researchers for over 150 years. The breakthrough involved substantially raising the lower bound for which the hypothesis is verified—a finding that raises profound questions about artificial intelligence's capacity to drive scientific breakthroughs.

How the AI Tackled the Problem#

The approach differed sharply from conventional mathematical research. An Anthropic researcher with limited mathematical background asked the model to make a serious attempt at the proof, then let the system work autonomously for roughly 36 hours. During this period, the AI generated and tested 650 distinct approaches by orchestrating work across 60 specialized sub-agents. The entire computation consumed 31 million tokens.

The labor was strategically distributed: two agents developed the core mathematical insights, thirteen contributed supporting ideas, thirty attempted (unsuccessfully) to develop novel concepts, thirteen validated the logical soundness of arguments, and two prepared the resulting findings for publication. Anthropic mathematicians confirmed the results and formalized them using Lean, an open-source proof verification system.

Broader Context in AI and Mathematics#

This achievement joins a growing constellation of mathematical victories won by large language models in 2026. AI systems have cracked multiple Erdős problems, while OpenAI's internal "Astra" model has produced ten major proofs. Anthropic separately achieved recognition by disproving the longstanding Jacobian conjecture. These successes underscore how increasing model capability translates into more ambitious mathematical contributions.

The Field's Mixed Response#

The flood of AI-driven mathematical advances has sparked tension within mathematics. In June, a coalition of prominent mathematicians signed a public declaration warning that AI threatens a foundational principle: that proofs belong to identifiable human authors who take responsibility for their validity. Yet the community remains divided on how to integrate these new tools.

Fields Medal laureate Timothy Gowers offered a counterpoint in a July blog post, suggesting that the shift may prove constructive rather than corrosive. He proposed that mathematics might evolve productively even if theorems lose their traditional human attribution—comparable, he argued, to how astronomical discoveries no longer bear astronomers' names.