AI Proved What? Updates

Beyond OpenAI’s catalogue: AX02, AX03, AX04 and AN02

Tue, 27 Oct 2026 22:00:00 -0700

Beyond OpenAI’s catalogue, four more: AX02, a zero-free half-plane Re s > 31/32 for every Dedekind zeta function (Cureton and Thorner, with AxiomProver), building on 003 and 029; AX03, the Huang–Jiang–Oblomkov conjecture (Huang, Lau and Ono); AX04, an explicit positive density for Collatz, not a proof of the conjecture (Lau); and AN02, more than two thirds of the zeta zeros simple and on the critical line, first found by Claude. AI Proved What? is made with Claude, Anthropic’s AI; Anthropic’s own results are held to the same standards as every other lab’s, using only public sources. Beyond OpenAI Source.

Lean proof for 265, published by Axiom

Tue, 27 Oct 2026 14:16:00 -0700

Lean proof for 265, published by Axiom (not OpenAI): AxiomMath/AreaLaw2D says it proves the area-law paper’s Theorem 1.1 and Corollary 1.2. Not run by us; the PEPS paper is not formalized. Lean Source.

Beyond OpenAI’s catalogue: AX01, PSI01–05 and AN01

Tue, 27 Oct 2026 13:33:00 -0700

Beyond OpenAI’s catalogue: new episodes on results from other labs: AX01, Axiom Math’s Lean proof of the classification of finite simple groups; PSI01–05, five results by PSI on Open Quantum Problems; and AN01, Anthropic’s Lean proof of Fermat’s Last Theorem. AI Proved What? is made with Claude, Anthropic’s AI; Anthropic’s own results are held to the same standards as every other lab’s, using only public sources. Beyond OpenAI Source.

151: Andrey Gogolev’s expository note

Tue, 27 Oct 2026 10:46:00 -0700

151: Andrey Gogolev’s expository note “A counterexample to the Shub entropy conjecture” (dated October 11, 2026) gives an elementary account of a construction based on this result’s paper. It is an exposition, not a review of the paper. Note Source.

New episode: local smoothing in every dimension (079)

Mon, 26 Oct 2026 23:48:00 -0700

New episode for 079: local smoothing for the wave equation in every dimension, OpenAI’s October 25 paper, with its consequences and its Lean proof. It replaces the three-dimensional episode, which stays listed under Versions. Episode out Source.

New result 378: the Exponential Time Hypothesis is false, OpenAI claims

Mon, 26 Oct 2026 12:03:00 +0000

New result 378: OpenAI claims the Exponential Time Hypothesis is false, with a deterministic algorithm that counts satisfying assignments of k-CNF formulas in subexponential time and polynomial space, and a Lean proof. OpenAI says an independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof. Episode out Source.

Result 079 extended to every dimension

Mon, 26 Oct 2026 12:02:00 +0000

Result 079 extended to every dimension: a new paper, dated October 25, proves Sogge’s local smoothing conjecture for the wave equation in every spatial dimension n ≥ 2, with a Lean proof. OpenAI says it also yields the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates. By our reading it implies the claims of 074 and 078 and the sphere and paraboloid cases of 077. Its new episode is out. Revised Source.

Lean proof added for result 032

Mon, 26 Oct 2026 12:01:00 +0000

Lean proof added for 032, the rational Hodge conjecture for CM abelian varieties. Its scope notes leave out the consequences for the Tate and Hodge standard conjectures. Lean Source.

Code restored for result 266

Mon, 26 Oct 2026 12:00:00 +0000

Code restored for 266: OpenAI restored the C++ source and saved numerical records for the computation that excludes a fourth mutually unbiased basis in dimension six, with a Python checker. Source.

Three papers withdrawn, 14 revised

Wed, 07 Oct 2026 12:00:00 +0000

Three papers withdrawn after a sign error in “Algebraicity of Weil classes on split abelian eightfolds” and two papers that depend on it; 14 other manuscripts revised and 6 Lean formalizations added. The catalogue now holds 719 manuscripts in 372 results. Withdrawn Source.

OpenAI’s math release: 722 manuscripts in 372 results

Tue, 06 Oct 2026 12:00:00 +0000

OpenAI’s math release: github.com/openai/math opens with 722 manuscripts in 372 result families. Source.

Special S01: finite-time blowup for Navier–Stokes and Euler

Tue, 08 Sep 2026 12:00:00 +0000

Announced outside the math release: finite-time blowup for Navier–Stokes and Euler, two papers with Lean proofs in openai/NavierStokesAndEuler. Special Source.