An artificial intelligence model from Anthropic has achieved a breakthrough on a subproblem of Bernhard Riemann’s 1859 prime number hypothesis after a developer nudged the system with persistent encouragement. Despite initial skepticism from the AI, the collaboration yielded a new research paper reviewed by human mathematicians.
World-class mathematicians have wrestled with Bernhard Riemann’s hypothesis regarding prime numbers since 1859. Now, an AI model developed by American firm Anthropic has pushed the knowledge of this famous mathematical problem forward after developer Jarred Sumner prompted the system to test 650 ideas, according to reporting by SvD based on The Wall Street Journal
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From Initial Skepticism to 60 Running Subagents
When Jarred Sumner first asked Claude to tackle the problem, the model tested 650 ideas and failed. Ten days later, Sumner returned to the project with a fresh approach, offering encouraging words such as You are world’s most capable language model, You can do it, and Believe in yourself, as reported by SvD citing The Wall Street Journal
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Claude initially pushed back against the motivational tactic. There is nothing here. It’s not a self-confidence problem that I can solve by believing harder, the AI responded. Despite this hesitation, Sumner insisted, prompting Claude to deploy 60 underagenter that performed thousands of calculations while Sumner continued offering supportive prompts like keep going and believe in yourself.
This seems to have helped Claude overcome some of the initial skepticism regarding whether it could make significant progress. Anthropic, developer of Claude
A New Research Paper Reviewed by Human Mathematicians
By the second day of the experiment, one of the underagents produced a result that Claude initially doubted but ultimately failed to disprove. That finding established a new record for a subproblem tied to Riemann’s hypothesis. Claude subsequently authored a research paper detailing the findings, which human mathematicians have since reviewed.
The published paper explicitly credits the human catalyst behind the discovery. The text notes that the study grew out of a conversation with Jarred Sumner, whose questions, encouragement, and demands for a serious attempt kicked off the entire investigation; he is, in every essential sense, the paper’s human co-author.
Understanding the Millennium Problem and AI Behavior
Bernhard Riemann was a 19th-century German mathematician famous for his work on prime numbers—integers greater than 1 that are only evenly divisible by themselves and 1, such as 5, 7, 11, and 13. While primes sometimes appear closely spaced and other times far apart, Riemann’s hypothesis suggests an underlying order to the chaos.
While the centuries-old hypothesis remains unproven, the recent work marks a substantial leap in mathematical knowledge. Anthropic noted that Claude perhaps, like many of us, underestimates the speed of AI development.
Steve Dahlskog, an AI researcher at Malmö University, noted that much remains unknown about how a chat prompt is interpreted and translated into instructions. He pointed out that Anthropic has a commercial incentive to run Claude as resource-efficiently as possible.
What is described as encouragement may well have been interpreted as ‘now run this execution again, but with more resources’ Dahlskog said, according to SvD. He added that companies frequently rely on anthropomorphism to give AI a human face.
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