Lichtman: "absolutely historic" output, but "not the Millennium problem rumor"
Jared Duker Lichtman @jdlichtman · x · 2026-10-06 · ★★★ · archived
Analytic number theorist's thread reading the proofs: zero-free strip, Hodge for CM abelian varieties, the role of cubic L-functions, Kakeya 4D, Chowla.
Summary
Thread by Jared Duker Lichtman (analytic number theorist), Oct 6–7 UTC:
- 23:09 UTC (this post, ~55k views): "floodgates for 300+ solutions", including a zero-free strip for ζ and a proof of the Hodge conjecture for CM abelian varieties.
- 23:37 UTC (https://x.com/jdlichtman/status/2107616346850927090, ~12k): "The cubic family of L-functions appear to be essential for the proof, even for the corollary to the Riemann zeta function".
- 23:42 UTC (https://x.com/jdlichtman/status/2107617476712575153, ~9k): "This output is absolutely historic by any objective metric. However, it is not the Millenium problem rumor that was buzzing around in past weeks."
- 00:35 UTC (https://x.com/jdlichtman/status/2107630987370983698): four-dimensional Kakeya, after Hong Wang's 2026 Fields Medal for 3D.
- 01:41 UTC (https://x.com/jdlichtman/status/2107647445404635480): "the most important day in the history of combinatorics".
- 02:08 UTC (https://x.com/jdlichtman/status/2107654368350834917): May 1 proof, August 10, October hundreds; "Next up in a few months: 1000's of proofs!"
- 02:48 UTC (https://x.com/jdlichtman/status/2107664263225749565): full two-point Chowla with quantitative savings is "of a different order", though the paper seems to stay within "the convex hull of existing methods".
Sentiment: enthusiastic, with a caution against the Millennium-problem rumour.
Archived text
OpenAI has just released floodgates for 300+ solutions to math problems.
Among them include a proof of:
-- a zero-free strip for the Riemann Zeta function
-- a proof of the Hodge conjecture for CM abelian varieties
Quoting @OpenAI: We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and
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Archived 2026-10-07 via syndication.
Related events
- OpenAI releases 722 AI-written math manuscripts (372 result families) claiming hundreds of open problems, incl. quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors 2026-10-06
- OpenAI model claims the quasi-Riemann hypothesis: no zeta or Dirichlet L-function zeros with Re s > 7/8, and no Landau–Siegel zeros (Lean-formalized) 2026-10-06
- OpenAI release claims the rational Hodge conjecture for all CM abelian varieties, which would give the Tate conjecture for abelian varieties over finite fields (no Lean proof) 2026-10-06
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