Anthropic announced this week that an unreleased AI model made progress on the Riemann hypothesis. The hypothesis has puzzled mathematicians for more than 150 years.
It deals with how prime numbers are spread out. A working proof would win a $1 million prize that has never been claimed.
The model did not solve the hypothesis. But it pushed forward the lower bound of solutions for which the hypothesis holds true.
An Anthropic staff member with little math training prompted the model to try proving the hypothesis. The person then left the model alone for about a day and a half.
How the Model Worked
During that time, the model coordinated work across 60 subagents. It tested 650 different ideas in total.
The process used 31 million output tokens. That is a large amount of computing power for a single task.
Anthropic shared a breakdown of what each subagent did. Two subagents developed the main mathematical ideas that led to progress.
Thirteen subagents added ideas to support those two. Thirty subagents tried to come up with new ideas but did not succeed.
Another 13 subagents checked the work for errors. The final two subagents helped write up the results in a paper.
Two of Anthropic's own mathematicians reviewed the findings. The result was also checked using Lean, an open source tool used to verify proofs.
Part of a Larger Trend
This is not the first math result tied to AI this year. Several Erdos problems, a set of open math questions, have been solved by AI models in recent months.
OpenAI recently shared 10 math results from its internal model, called Astra. Anthropic separately said it had disproved the Jacobian conjecture, another long-standing math problem.
These results have sparked debate among mathematicians. In June, a group of mathematicians signed a public declaration raising concerns about AI's growing role in the field.
Their worry centers on credit and responsibility. The declaration says proofs should be tied to specific people who can take credit and be held responsible if something is wrong.
Not everyone shares that view. Fields Medal winner Timothy Gowers responded with a blog post questioning whether the shift away from named authorship is a problem.
Gowers compared it to how stars in the sky are not named after the astronomers who study them. Most stars, he pointed out, are not named at all.
The debate over how AI should be used in math research is ongoing. For now, Anthropic's unreleased model remains the latest example of AI making progress on a problem that has stumped humans for over a century.
