Bizeul, Klartag, and Lehec present an arXiv proof of the ~31-year-old Kannan-Lovász-Simonovits conjecture and — per the Reddit relay — credit ChatGPT with most of the ideas and proofs; expert validation of the proof and confirmation of the AI-credit attribution would establish chatbot models as originators of the core of a decades-open mathematics result, while a flaw in the proof or an unsupported credit claim closes it.

Open article · Retrieved 2026-10-06T09:27:27.224798+00:00

# Mathematics > Functional Analysis

**arXiv:2610.05474** (math)

[Submitted on 4 Oct 2026]

# Title:Presenting a proof of the Kannan-Lovasz-Simonovits conjecture

Authors:[Pierre Bizeul](https://arxiv.org/search/math?searchtype=author&query=Bizeul,+P), [Boaz Klartag](https://arxiv.org/search/math?searchtype=author&query=Klartag,+B), [Joseph Lehec](https://arxiv.org/search/math?searchtype=author&query=Lehec,+J)

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> Abstract:Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lovász-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high dimensional geometry in recent decades. We present here a proof of this conjecture. The crucial step in the proof is the very recent criterion from Song and Zhang involving high-order derivatives of tilt averages.

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| Comments: |
| Subjects: | Functional Analysis (math.FA); Metric Geometry (math.MG); Probability (math.PR) |
| Cite as: | [arXiv:2610.05474](https://arxiv.org/abs/2610.05474) [math.FA] |
|  | (or  [arXiv:2610.05474v1](https://arxiv.org/abs/2610.05474v1) [math.FA] for this version) |
|  | <https://doi.org/10.48550/arXiv.2610.05474> Focus to learn more  arXiv-issued DOI via DataCite (pending registration) |

## Submission history

From: Pierre Bizeul [[view email](https://arxiv.org/show-email/daebf8c6/2610.05474)]   
 **[v1]**
Sun, 4 Oct 2026 19:30:34 UTC (28 KB)

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