OpenAI Model Reportedly Proves Kakeya and Related Conjectures in Lean, Awaiting Expert Review

A 59-page manuscript attributed to an unnamed OpenAI model claims to prove the Sogge local smoothing conjecture in all dimensions, with the Bochner-Riesz, sphere restriction, and Kakeya conjectures following as consequences. For reference, the three-dimensional case of the Kakeya conjecture was only resolved in 2025 by Wang and Zucker. What makes the manuscript unusual is that its six main propositions have been formalized in Lean and can be verified using the open-source Comparator tool, relying on just three standard axioms, with the trusted statements reading as the standard conjectures. If confirmed, this would be a major breakthrough for AI in proving core mathematical conjectures and deserves attention.

Confirmed

• The manuscript exists, is attributed to an unnamed OpenAI model, runs 59 pages, and includes an illustration of a Kakeya set (needle bundle).
• The core claim covers the local smoothing conjecture in all dimensions plus connected results, deriving the Bochner-Riesz, sphere restriction, and Kakeya conjectures.
• Six main statements have been formalized in Lean and can be verified with the open-source Comparator tool, relying on only three standard axioms; the trusted statements match the standard conjectures.
• OpenAI has officially positioned it as raw research data.

Not yet confirmed

• No domain expert has publicly confirmed that the Lean formalized statements fully correspond to the original conjectures.
• No expert has yet manually reviewed the argument itself.

Why it matters

• Resolving the Kakeya conjecture is a long-standing core problem in harmonic analysis; the 3D case was only cracked in 2025, so an AI proof holding in all dimensions would be hugely significant.
• The path of Lean formalization plus automated tool verification allows correctness checking of core propositions to be partially automated, showcasing a new paradigm for AI-assisted formal mathematics.

2026-10-29 ~ 2026-10-29 · 5 related posts

• [source] OpenAI model's Lean-verified manuscript targets local smoothing and Kakeya conjectures — maier_ak · 2026-10-29
• [source] OpenAI model claims 59-page Lean proof of local smoothing and Kakeya in every dimension — maier_ak · 2026-10-29
• OpenAI's 59-page Lean proof: six statements machine-checkable, no expert review yet — maier_ak · 2026-10-29
• OpenAI's math argument still unverified: no expert has publicly assessed it — maier_ak · 2026-10-29
• OpenAI's Lean-formalized conjectures await expert review; firm calls it raw data — maier_ak · 2026-10-29