OpenAI's quasi-Riemann hypothesis proof draws expert praise and criticism
OpenAI's quasi-Riemann hypothesis proof draws expert praise and criticism: a Lean-verified 199-page version and a 49-page one not yet verified.
OpenAI announced on October 6 that its system had settled the quasi-Riemann hypothesis, and mathematicians have now examined the claim. Quanta Magazine reported on October 19 that the proof comes in two versions. A 199-page paper dated September 30 claims all nontrivial zeros of the zeta function lie between 1/8 and 7/8, and it was formally verified in Lean. A 49-page follow-up, finished almost a week later and not yet formally verified, claims the weaker window of 1/12 to 11/12.
The reaction is large. Stanford's Jared Duker Lichtman called it "the most significant AI-for-math achievement so far, by quite a margin." NYU's Maksym Radziwiłł called the implications "staggering," and Science reported that James Maynard called it the best headline result in analytic number theory in the past 100 years. Radziwiłł also said both papers "are horribly written (in a way that would lead to immediate rejection at any mathematical journal)."
Context: the Riemann hypothesis has been open for over 160 years. The quasi version is weaker, and Scientific American reports mathematicians disagree on whether it is real progress toward the full problem.
My take: trust the Lean-checked paper, wait on the short one, and note that OpenAI did not include full prompts or run-time details, according to Scientific American. Some of its other proofs have already been retracted.
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Sources
- AI proved the quasi-Riemann hypothesis. What happens now?, Quanta Magazine
- The most exciting claims from OpenAI's heap of new proofs, Scientific American
- AI edges closer to solving the Riemann hypothesis, one of math's hardest problems, Science / AAAS
Meanwhile at the anchor desk
The quasi-Riemann hypothesis now has a Lean-verified proof. Darling, that is not a footnote, that is a coronation.
Lean-verified paper: 199 pages, checkable today. The 49-page one is not yet formally verified, and OpenAI left out full prompts and run-time details, so the recipe for generating the proofs is missing.
