Unreleased Anthropic model pushed Riemann hypothesis research

31 million tokens for a single proof

During a test of an unreleased model from Anthropic, a developer without a deep mathematical background gave the model a prompt to try proving the Riemann hypothesis (one of the oldest and most complex problems in mathematics, which carries a $1,000,000 bounty). The model worked for a day and a half, coordinating a network of 60 subagents.

During this time, it tested 650 different mathematical concepts. Of the 60 agents, two developed the main ideas, 13 supplied them with supporting materials, 30 tried unsuccessfully to find new paths, 13 functioned as validators, and the final two wrote the scientific paper itself. The result was subsequently formalized in the Lean system and confirmed by Anthropic's in-house mathematicians.

From random attempts to an organized network

Scientific research is transitioning from a phase where the model worked as a clever search engine to a phase of a coordinated laboratory. Anthropic did not use one large model, but let it generate and manage an entire structure of specialized workers.

For research institutions and companies, this changes the perspective on how many resources are needed for scientific projects. Instead of expensive years of research and hundreds of hours of human time, you just pay the bill for 31,000,000 output tokens and run the process over the weekend.

The boundary between discovery and verification

While the model pushed the lower bound for which the Riemann hypothesis holds true, it still hasn't solved it globally. The brute force of agents hits a limit at the moment when a completely new, previously undescribed theoretical framework is needed, rather than just combining existing methods.

Real integration of Lean will show the actual power

The deciding factor will be how the broader mathematical community responds to these proofs. If academic journals are flooded with papers written by agents and formalized via Lean, a debate will emerge about what authorship of a scientific discovery actually means.

Lilith's verdict

Science is transitioning from a brilliant flash in the mind of a single mathematician to a cloud bill. Whoever has the larger budget for tokens will push the boundaries of hypotheses.