Anthropic announced on Monday that an unreleased AI model has made significant progress on the Riemann hypothesis, one of mathematics' major unsolved problems for over 150 years. The model notably increased the lower bound of solutions for which the hypothesis holds true.
The progress was achieved after an Anthropic staff member, without significant mathematical training, prompted the model to "take a real stab" at proving the hypothesis. The model then coordinated the task over a day and a half, testing 650 different ideas and spending 31 million in total across 60 sub-agents.
Two of the 60 sub-agents were responsible for developing key mathematical ideas, with 13 contributing to these agents. The finding was confirmed by two of Anthropic’s in-house mathematicians and formalised using the open-source proof assistant Lean.
This development is the latest in a series of mathematical breakthroughs by Large Language Models (LLMs), including the solution of several Erdos problems and OpenAI's "Astra" model proving ten major results. Anthropic also previously disproved the Jacobian conjecture.
The growing influence of AI in mathematics has led to both excitement and concern within the field. Some mathematicians have raised concerns that AI could undermine the standard of attributing proofs to specific authors, while others question whether AI might change mathematics in a more complex and positive way.