Anthropic announced that an unreleased AI model made significant progress on the Riemann hypothesis, a famous unsolved problem in mathematics. The model increased the lower bound of solutions for which the hypothesis holds true.

The progress was achieved with minimal human guidance. An Anthropic staff member prompted the model to attempt a proof, and the model then coordinated the task over a day and a half. It tested 650 ideas, using 60 sub-agents and spending $31 million in total.

The results were confirmed by two of Anthropic’s in-house mathematicians and formalized using the open-source proof assistant Lean. This work adds to a growing list of mathematical breakthroughs by AI models, including solutions to several Erdős problems and the disproof of the Jacobian conjecture.

The developments have sparked debate among mathematicians. Some have raised concerns about AI’s impact on the field’s values, while Fields Medal winner Timothy Gowers has questioned whether AI might change mathematics in a positive way.

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