# OpenAI claims AI models prove 1991 math conjecture in all dimensions

Digest AI · Research · published 2026-10-26T14:49:00Z · updated 2026-10-26T22:17:01Z

Canonical: https://digestai.news/story/openai-claims-ai-models-prove-1991-math-conjecture-in-all-dimensions

## Summary

OpenAI announced on October 26, 2026, that its AI models proved the **local smoothing conjecture**, an unsolved math problem since 1991. The company says the proof also resolves the **Kakeya conjecture** and **Stein’s restriction conjecture** across all dimensions. OpenAI’s models generated the proof on October 18, which was formalized in **Lean**, a theorem prover, and published on GitHub alongside a human-readable explanation.

The breakthrough relies on a new **partial differential equation** introduced by OpenAI. While prior progress addressed specific cases—like the 2D local smoothing proof in 2019 and the 3D Kakeya conjecture in 2025—this marks the first time all dimensions were resolved simultaneously. The Lean formalization shifts scrutiny from AI errors to whether the proof aligns with mathematicians’ original intent. Over **700 AI-generated math preprints** accompanied the announcement, though the conjecture’s proof stands out for its potential impact on harmonic analysis and Fourier theory.

## Key points

- OpenAI claims its models proved the **local smoothing conjecture** (1991) and linked conjectures in all dimensions using a new PDE
- Proof was generated on **October 18, 2026**, formalized in **Lean**, and published on **GitHub** with a natural-language summary
- Over **700 AI-generated math preprints** were released alongside, but the conjecture’s proof is the most significant claim

## Why it matters

A machine-generated proof of long-standing conjectures could accelerate trust in AI’s mathematical reasoning, though experts must verify the formalization’s alignment with original problems. The work may redefine how AI contributes to pure math and inspire further formalized breakthroughs.

## Sources

1. [OpenAI says its models proved the local smoothing conjecture in every dimension](https://cryptobriefing.com/openai-proves-local-smoothing-conjecture) (cryptobriefing.com, 2026-10-26)
2. [OpenAI Says Its Models Produced Three Proofs in Math, CS, and Physics](https://unite.ai/openai-says-its-models-produced-three-proofs-in-math-cs-and-physics) (Unite.AI, 2026-10-26)

## Cite

Digest AI, "OpenAI claims AI models prove 1991 math conjecture in all dimensions", 26 October 2026, https://digestai.news/story/openai-claims-ai-models-prove-1991-math-conjecture-in-all-dimensions

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