‘This is what happened with Claude and me’: AI’s failed attempt to crack the Riemann hypothesis led mathematician to a breakthrough

October 5, 2026 thedigitalsolutioncentre@gmail.com

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An artificial intelligence (AI) model’s failed attempt to crack one of math’s most notorious unsolved problems has helped a human mathematician make progress on a related puzzle.

Earlier this summer, Claude — Anthropic’s AI model — attempted to find a solution to what’s widely considered one of the most important unsolved math problems. Known as the Riemann hypothesis, it proposes a hidden order behind the apparently random distribution of prime numbers.

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When Anthropic human operator Jarred Sumner first prompted Claude to solve the Riemann hypothesis in late July, Claude attempted over 600 lines of attack. At the beginning of the next session, in August, Sumner offered the AI some words of encouragement: “Take a big leap of faith in your capabilities.” Claude’s response was curt: “That’s not a confidence problem I can fix by believing harder.”

Feeling like they’d hit a brick wall, the human-AI team set sights on a more realistic objective. “When you find a huge mountain, like the Riemann hypothesis, and you cannot prove it, then you settle on lower objectives,” Lamzouri said. In this case, the more attainable peak was figuring out the minimum proportion of zeroes that sit on the vertical line. Since 1989, mathematicians have known that at least 40% of the zeroes are on the line. Claude achieved 67.25%.

This is why for James Maynard, a professor of mathematics at the University of Oxford who was a co-winner of the 2022 Fields Medal (math’s equivalent of a Nobel Prize) for critical breakthroughs in areas related to the Riemann hypothesis, it is not the “headline percentage” that excites him. “The thing that I am very positive about is that there’s new ideas in the Claude proof that are more directly interacting with the problem,” he told Live Science.

In contrast, when Lamzouri read the paper, he was disappointed. “After a couple of hours, I gave up,” he said. “There was something in there, but it was too complicated — it was not human.” So, instead of continuing to grapple with the paper, Lamzouri decided to read all of the published articles that the Anthropic team stated that Claude had heavily drawn from in its proof. He then spotted something Claude hadn’t.

Lamzouri realized that a lot of the proof’s complicated mathematics could be bypassed by adding a certain constraint on the equations. From this, he produced a different proof that delivered the same proportion of zeroes on the line, 67.25%, but in a much more straightforward way. What’s more, his approach allowed him to prove additional facts, such as that the percentage of zeroes that are no good at all (not simple and not on the line) is at most 11%.

On this point, Lamzouri agrees with Maynard. “The good thing is that once I discovered this new way of looking at things — which was, of course, inspired by Claude — it gave me ideas that I hope to develop in related areas,” he said. “I think it’s going to be a similar thing in other areas of math: that AI discovers things, puts people on the path to looking at concepts from a different perspective, and hopefully, humans will continue pushing for understanding.”

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