Primary evidence
- A proof of the Kannan–Lovász–Simonovits conjectureS1 · Primary research · Paper · 2026-10-04
Bizeul, Klartag and Lehec release a ChatGPT-assisted proof of the KLS conjecture
In the acknowledgements, the authors state that most proofs and mathematical ideas in the paper were found by ChatGPT. They identify the suspension idea as a notable human contribution and describe their role as understanding the model's proofs, checking and organizing the mathematics and improving…
What happened?
Pierre Bizeul, Boaz Klartag and Joseph Lehec claim a dimension-free Poincaré bound for isotropic log-concave probability measures, thereby proving the Kannan–Lovász–Simonovits conjecture. Their paper builds on very recent work of Song and Zhang that reduced the remaining dimension dependence to a slowly growing factor and claims to remove that dependence completely.
In the acknowledgements, the authors state that most proofs and mathematical ideas in the paper were found by ChatGPT. They identify the suspension idea as a notable human contribution and describe their role as understanding the model's proofs, checking and organizing the mathematics and improving the exposition. The paper is currently a very recent preprint; Chronicle has not located a public proof-assistant artifact or independent specialist review sufficient to move the event beyond a paper-released verification state.
Why it matters
KLS connects convex geometry, concentration of measure, Markov-chain mixing and high-dimensional algorithms. A correct dimension-free proof would close a major research programme with broad consequences. The explicit attribution to ChatGPT is historically significant because the model is described not merely as a calculator, proof checker or drafting assistant, but as the source of most of the mathematical ideas and proofs later understood and presented by expert human authors.
Significance rationale: This Event is a Historical Milestone because the paper claims a complete proof of the Kannan–Lovász–Simonovits conjecture, a central long-standing problem in asymptotic convex geometry and high-dimensional probability, and the authors explicitly credit ChatGPT with finding most proofs and mathematical ideas in the manuscript. If the result withstands specialist scrutiny, it is a direct example of a general-purpose conversational AI making primary intellectual contributions to the resolution of a major open conjecture.
Historical context
Earlier developments
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Later developments
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Related milestones
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Evidence & status at a glance
- Significance
- H1 · Historical milestone
- Verification
- Paper released
- Evidence level
- E2 · Research record
- AI role
- AI primary, human verified
- Formal assurance
- No formal assurance
Contribution & verification
- Mathematical novelty
- New result
- Interface
- Informal, Symbolic
- AI contribution
- The authors explicitly state that ChatGPT found most proofs and mathematical ideas in the paper. Human authors supplied important ideas of their own, including the suspension idea, and were responsible for understanding, checking, organizing and presenting the final proof. This classification records the authors' own account and does not imply independent reconstruction of every model interaction.
- Human contribution
- Pierre Bizeul, Boaz Klartag and Joseph Lehec selected and developed the research direction, contributed original ideas, understood and checked the model-produced arguments, integrated them with the recent literature and wrote the final mathematical exposition.
- Verification
- Paper released · E2 · Research record · No formal assurance
- Last reviewed
- 2026-10-07
Technical details
- Systems
- chatgpt
- Organizations
- —
- Problems
- kannan-lovasz-simonovits-conjecture
- Methods
- convex-geometry, localization, stochastic-localization, poincare-inequality, human-ai-collaboration
Sources & artifacts
- A proof of the Kannan–Lovász–Simonovits conjectureS1 · Primary research · Paper · accessed 2026-10-07
Verification history
- 2026-10-04 · Paper released · E2 · Research record
The authors released a public preprint containing the claimed KLS proof and an explicit first-party description of ChatGPT's role. The Event records that publication and attribution; it does not independently certify the mathematical correctness or historical priority of the proof.
Corrections
No corrections recorded.