What Is the Quasi-Riemann Hypothesis, and Did OpenAI's AI Prove It?
LorenzMath
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What Is the Quasi-Riemann Hypothesis, and Did OpenAI's AI Prove It?
3 084 просмотра · 2 дн. назад
LorenzMath
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3 084 просмотра · 2 дн. назад
In October 2026 OpenAI released hundreds of AI-written math papers, and one of them claims the quasi-Riemann hypothesis: no zero of the Riemann zeta function, or of any Dirichlet L-function, has real part above 7/8. This video explains what that statement means for prime numbers, how the argument builds such a wall from cancellation in the Möbius function, and what has and has not been checked so far. It is not a proof of the Riemann hypothesis, and as of October 21, 2026 the papers have not been peer reviewed.
It is for viewers who know complex numbers, infinite series and a little about primes. Our earlier Riemann zeta video is useful background.
Chapters
0:00 OpenAI's claim: a wall at 7/8
0:51 Primes and the zeros of zeta
3:12 Keeping zeros away from the edge
4:26 The precise claim
5:17 Who wrote it
5:47 A detector for zeros: the Möbius walk
6:39 Why a small walk means no zeros
8:14 The trick: a family and an amplifier
11:26 Counting copies: 11/12
12:18 From 11/12 to 7/8, and the ceiling
12:51 What a wall buys
14:14 Did an AI really prove it?
15:51 The answer
Sources
OpenAI, The Quasi-Riemann Hypothesis (manuscripts of Sep 30 and Oct 5, 2026), github.com/openai/math
P. Hall and J. Howlett, The most exciting claims from OpenAI's heap of new proofs, Scientific American, Oct 8, 2026
B. Liu, Improved zero-free half-planes for the quasi-Riemann hypothesis, arXiv:2610.12234
A later video may look at how a proof assistant like Lean checks a proof.
Narration uses a synthetic voice (IndexTTS2, the channel's usual voice); the script, mathematics and animations are written and checked for this channel.