An unreleased Anthropic model made progress on one of math’s biggest unsolved problems

For over a century and a half, the Riemann hypothesis has remained the "holy grail" of mathematics—a notoriously difficult mystery concerning the distribution of prime numbers. While a $1 million bounty for a definitive proof remains unclaimed, the landscape of mathematical discovery is shifting. Anthropic recently announced that an unreleased AI model has achieved significant progress on the problem, successfully extending the lower bound for which the hypothesis holds true.

A Collaborative AI Breakthrough

What makes this achievement particularly striking is the methodology behind it. An Anthropic staff member, lacking formal advanced mathematical training, prompted the model to attempt a proof. The AI was then left to autonomously coordinate the research effort over the course of 36 hours.

The scale of the operation was immense, involving a complex architecture of subagents:

• Total Ideas Tested: 650 distinct mathematical approaches.
• Agent Coordination: 60 specialized subagents working in tandem.
• Computational Cost: 31 million output tokens.

According to the project’s documentation, the labor was divided strategically: two subagents spearheaded the core mathematical concepts, 13 provided supporting ideas, 30 attempted—though failed—to generate new breakthroughs, 13 acted as validators to ensure logical consistency, and two drafted the final paper. The results were subsequently verified by Anthropic’s internal mathematicians and formalized using Lean, an open-source proof assistant.

The Growing Influence of LLMs in Mathematics

This milestone is the latest in a series of high-profile mathematical successes driven by Large Language Models (LLMs). Throughout the year, AI has successfully tackled various Erdős problems, while OpenAI has showcased 10 major results proved by its internal "Astra" model. Furthermore, Anthropic previously made headlines by disproving the long-standing Jacobian conjecture.

These rapid developments have ignited a fierce debate within the academic community. In June, a group of prominent mathematicians signed a public declaration expressing concern that the rise of AI could erode the field’s core values—specifically the tradition that a proof must be attributable to a human author who takes personal responsibility for its accuracy.

Redefining Mathematical Authorship

The mathematical community remains deeply divided on how to integrate these new research tools. However, some leading voices are urging a shift in perspective. Fields Medal winner Timothy Gowers recently addressed these concerns, suggesting that the integration of AI might fundamentally—and perhaps beneficially—alter the nature of mathematical discovery.

"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," Gowers wrote in a blog post.

As AI models continue to push the boundaries of what is computationally provable, the definition of a "mathematician" is becoming increasingly fluid. Whether these tools are viewed as a threat to academic integrity or as a powerful catalyst for human knowledge, it is clear that the era of AI-assisted mathematical discovery has arrived, and it is moving faster than many experts ever anticipated.