AI has proven the Riemann hypothesis – false

But then he spotted a paper that offered progress on one of his favorite pastimes: the Riemann hypothesis, a puzzle about prime numbers and one of seven famed Millennium Prize Problems, often considered the most formidable in all of math. “I was like a kid at Christmas,” Maynard says. “Even if it was some scary monster giving me a gift, I was just so excited.” · The release comes less than 1 month after OpenAI announced a solution to the Navier-Stokes equations, another Millennium Prize Problem. OpenAI’s latest proof solves only a weaker version of the Riemann hypothesis.

AI Proved the Quasi-Riemann Hypothesis. What Happens Now? ... Unlike other recent AI proofs, this one has been unpacked by human experts.

Let’s start here: math’s most famous problem is no closer to being solved than it was a week ago. Neither humans nor artificial intelligence have made progress on the Riemann hypothesis.

OpenAI announced that its AI produced proofs for parts of the Riemann hypothesis.

An unreleased research version of Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis. Drawing on extensive prior research by mathematicians over the past decades, it has increased this bound from 41.6% to 67.2%. Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely.

Parmi les centaines de résultats annoncés par OpenAI, l’un a particulièrement retenu l’attention des mathématiciens : une démonstration assistée par l’IA de la quasi-hypothèse de Riemann, une version affaiblie de l’un des problèmes ouverts les plus célèbres des mathématiques.

Here's the gap that headlines keep skipping: the Riemann Hypothesis needs 100% of zeros on the critical line, not 67.2%. Scientific American was blunt about that distance in its own breakdown of the result, and Anthropic itself doesn't claim otherwise — the lab's statement says plainly it doesn't expect this technique to eventually prove the full hypothesis.

An attempt by Anthropic's Claude failed to prove the Riemann hypothesis, but it did produce something genuinely useful: inspiration.

The Riemann Hypothesis remains unproven. What an unreleased Anthropic research version of Claude did was push forward a specific numerical bound tied to the problem, moving the zero-free region estimate from 41.6 to 67.2, a threshold that had ...