Mathematicians Checked the AI's Riemann Breakthrough

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Two weeks ago, OpenAI's model claimed the quasi-Riemann hypothesis: a straight wall at 7/8 in Riemann's strip that no zero ever crosses. On release night, the number theorist Alex Kontorovich made two guesses about how a machine could have done it. Now the mathematicians who took the proof apart have given their verdict in Quanta Magazine: Maksym Radziwiłł calls the consequences "staggering" and the papers "horribly written". The proof needed no new idea. It found the family of functions Peter Sarnak had argued for decades should exist, using obscure metaplectic forms and a 2021 formula proved by two of the very people now checking it. This video follows the two papers (the one a computer checked, and the one the experts are actually reading), the three guesses, and which one was right.

⏱ Chapters
0:00 Intro
0:56 The wall at 7/8
2:20 Two papers
4:03 Three guesses
4:40 The family nobody found
6:30 The verdict
7:37 Outro

🔗 Sources
Quanta Magazine, Konstantin Kakaes, "AI Proved the Quasi-Riemann Hypothesis. What Happens Now?" (19 Oct 2026): https://www.quantamagazine.org/ai-proved-the-quasi-riemann-hypothesis-what-happens-now-20261019/
OpenAI, "The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane Re(s) greater than 7/8" (30 Sep 2026, 199 pp., Lean-verified): https://github.com/openai/math/tree/main/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026
OpenAI, "The Quasi-Riemann Hypothesis" (5 Oct 2026, 49 pp., the 11/12 version): https://github.com/openai/math/tree/main/preprints/The-Quasi-Riemann-Hypothesis-October-5-2026
National Museum of Mathematics, "When AI Solves Major Open Problems" (gala panel, 6 Oct 2026): https://www.youtube.com/watch?v=voDtZqijetw
Our earlier video on the release, "722 Math Papers in One Night. One of Them Is About Riemann.": https://www.youtube.com/watch?v=HO5MefNJh3Y

About the details: this is the quasi-Riemann hypothesis, not the Riemann hypothesis itself; the wall is at 7/8 (or 11/12 in the second paper), not at 1/2. The experts "largely agree that the result is correct", in Quanta's words, but Sarnak won't call it a theorem until humans have checked every detail, and the 11/12 paper has not been formally verified. The 2021 Dunn–Radziwiłł formula was one key ingredient "along with the work of numerous other mathematicians", not the whole proof. The 11/12 paper is the only one of the 722 that a person edited; OpenAI has not said who. The family-in-depth and the bridge are our pictures of the idea: they do not show the actual L-functions or the formula. Bhargava's "not that badly" is what colleagues texted him on release night, two weeks before Radziwiłł's verdict.

🎙 Credits
Voices of Alex Kontorovich, Stephen Wolfram and Manjul Bhargava: short excerpts for commentary from the National Museum of Mathematics gala panel (6 Oct 2026): https://www.youtube.com/watch?v=voDtZqijetw
Photos via Wikimedia Commons: Alex Kontorovich (Katrin Schmid) and Maksym Radziwiłł (Petra Lein), CC BY-SA 2.0 de; Stephen Wolfram (Stephen Wolfram's PR team / Stephen Faust), CC BY-SA 3.0; Manjul Bhargava (IMU), Free Art License; Peter Sarnak (ICM 2018), Henryk Iwaniec (Justas Kalpokas) and Bernhard Riemann, public domain.
Page screenshots: Quanta Magazine and OpenAI's papers (Apache-2.0), quoted for commentary.
Music: "Hitman", "Volatile Reaction" and "Wholesome" by Kevin MacLeod (incompetech.com), licensed under Creative Commons: By Attribution 4.0, http://creativecommons.org/licenses/by/4.0/
Everything else is our drawing.

#Math #RiemannHypothesis #OpenAI #AI #NumberTheory