An unreleased Anthropic model made progress on one of math’s biggest unsolved problems
An unreleased artificial intelligence model from Anthropic has made significant headway on the 150-year-old Riemann hypothesis, directed by a staff member without mathematical training.
Stock photo for illustration only, not from the actual event
- An unreleased Anthropic AI model advanced the Riemann hypothesis.
- A staff member with no math background prompted the model for 1.5 days.
- The system tested 650 ideas using 60 sub-agents and spent 31 million total.
- Results were confirmed by in-house mathematicians and formalized via Lean.
For over 150 years, the Riemann hypothesis has stood as a major unsolved problem in mathematics, focusing on the long-running mystery surrounding the distribution of prime numbers. A $1 million bounty remains unclaimed for any working general proof of the hypothesis.
On Monday, Anthropic announced that an as-yet-unreleased model had made substantial headway on the Riemann hypothesis, significantly increasing the lower bound of solutions where the rule holds true.
Stock photo for illustration only, not from the actual event
Even more striking is the method behind this breakthrough: an Anthropic staffer lacking significant mathematical training instructed the model to tackle the proof, leaving it to coordinate the task independently over a day and a half.
Altogether, the model tested 650 distinct ideas for solving the problem, coordinating across 60 sub-agents and expending 31 million in total resources to accomplish the feat.
The integration of advanced AI into complex mathematical research marks a paradigm shift in how unsolved theorems are approached. By leveraging automated proof assistants alongside large language models, researchers can explore combinatorial spaces far beyond manual human limits while maintaining formal verification standards.
The findings were verified by two of Anthropic's in-house mathematicians and structured formally using the open-source proof assistant tool known as Lean.
"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"
Timothy Gowers
This achievement follows a growing wave of mathematical milestones led by Large Language Models. Several Erdos problems have fallen to AI models this year alongside powerful new releases, including
- OpenAI's disclosure of ten major results proved by its internal "Astra" model
- A separate Anthropic initiative that disproved the long-standing Jacobian conjecture
Source: TechCrunch
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