Two AI-assisted papers claim to resolve the KLS conjecture

The Kannan–Lovász–Simonovits (KLS) conjecture, open for nearly 30 years, may have been cracked: on October 6, two papers claiming to solve it appeared on arXiv the same day, both noting they used large language model assistance, sparking wide discussion.

Confirmed

The arXiv paper "Presenting a proof of the Kannan-Lovasz-Simonovits conjecture" (arXiv:2610.05474) was published by Pierre Bizeul and Boaz Klartag; according to a Reddit post, the paper says ChatGPT provided most of the ideas and reasoning behind the proof, while the authors' work was mainly understanding and exposition.
Zhao Song and Xinzhi Zhang (Microsoft Research) published a 140-page arXiv paper, "An O(1) Bound for the KLS Constant…" (arXiv:2610.01447), proving that the KLS constant for isotropic log-concave measures has an O(1) upper bound.
@michaelchchoi relayed a post by mathematician Guanyang Wang saying the KLS conjecture had been proven by AI, with links to the papers.
@IgorCarron noted that both papers are LLM-assisted, mentioning that GPT-6 and Claude participated in the proofs.
@DrSingularity added links to the papers under his tweet for verification.

Unconfirmed

Both papers are researcher announcements and have not been peer reviewed; @DrSingularity explicitly flagged the claims as unconfirmed.
The actual extent of ChatGPT/LLM contribution to the proofs (the authors state "most of the ideas came from ChatGPT") awaits community verification.

Why it matters

The KLS conjecture, posed in 1995, is a famous open problem in convex geometry and theoretical computer science, with deep connections to probability, optimization, random sampling, and efficient computational search.
If the proofs hold and the LLM contribution is genuine, it would be a landmark in AI-assisted mathematical research, potentially reshaping how top applied-math problems are tackled.

2026-10-06 ~ 2026-10-06 · 7 related posts

Primary sources

KLS conjecture proved after decades; arXiv paper notes AI was used in the proof — felpix_ · 2026-10-06 16:59 (UTC+08:00)
KLS conjecture finally solved: Zhao Song and Xinzhi Zhang post 140-page O(1) bound proof — basedjensen · 2026-10-06 18:08 (UTC+08:00)
Reddit: new KLS proof paper credits ChatGPT with most of the ideas and proofs — 141_1337 · 2026-10-06 16:35 (UTC+08:00)

Mathematician Claims AI Has Proven the KLS Conjecture — michaelchchoi · 2026-10-06
[source] Reddit: new KLS proof paper credits ChatGPT with most of the ideas and proofs — 141_1337 · 2026-10-06
[source] KLS conjecture proved after decades; arXiv paper notes AI was used in the proof — felpix_ · 2026-10-06
LLM-assisted papers claim to resolve the KLS conjecture, a top open math problem — IgorCarron · 2026-10-06
Researchers Claim ChatGPT-Driven Proof of 30-Year-Old KLS Conjecture — Dr_Singularity · 2026-10-06
Paper Link Shared for Claimed ChatGPT-Assisted KLS Proof — Dr_Singularity · 2026-10-06
[source] KLS conjecture finally solved: Zhao Song and Xinzhi Zhang post 140-page O(1) bound proof — basedjensen · 2026-10-06