# OpenAI says its models solved three famous problems. Experts have started checking

URL: https://ai-pulse.aglaganova.com/blog/openai-says-its-models-solved-three-famous-problems-experts-have-started-checking
Published: 2026-10-30
Author: Roman Aglaganov, Full-stack developer
Category: Research
Region: Global
Tags: science, reasoning

> OpenAI claims proofs of the Kakeya conjecture in every dimension, a refutation of a key assumption in computer science, and a construction of the theory of quarks and gluons. The maths is public; the physics is not yet. Anthropic posted its own version of one result hours later.

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On 26 October OpenAI said its internal AI models had produced three new results, each on a question that researchers have worked on for decades. They are OpenAI’s claims for now. The company has asked outside experts to review them and says those reviewers are free to publish what they find.

## The three claims

**Maths.** OpenAI says its models proved the local smoothing conjecture, a 1991 problem about how waves concentrate, in every number of dimensions. That would also settle the Kakeya conjecture and Stein’s restriction conjecture. Earlier work had proved local smoothing in two dimensions and Kakeya in three. OpenAI says the proof was generated on 18 October and checked in the Lean proof language the next day.

**Computer science.** OpenAI says its models disproved the Exponential Time Hypothesis, a widely used assumption that a classic logic problem cannot be solved much faster than by brute force. Hundreds of papers rely on it to argue that certain problems are hard. A disproof would not automatically give faster programs for real problems.

**Physics.** OpenAI claims a rigorous mathematical construction of interacting quantum field theories in four dimensions, including quantum chromodynamics, the theory of quarks and gluons, and pure Yang-Mills theory. The Yang-Mills question is part of a million-dollar Millennium Prize problem, but the prize also requires proving a “mass gap”, which this claim does not cover.

## Who is checking

Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT will lead a review of the computer-science claim. In a letter to colleagues they wrote: “If the claim is correct, it will change an important part of theoretical computer science.” They added: “Our involvement should not be taken as certification of the claim.” OpenAI has agreed to fund a conference to examine it. A group led by the physicist David Gross will review the physics.

OpenAI has published the maths and computer-science proofs, with Lean versions, on GitHub. It has not released the physics materials: it says the outside physics group chose to hold them back while it prepares its own account. The independent Advisory Group on Mathematics and Artificial Intelligence has called for them to be released now, saying that “understanding should develop in the open, with everyone given the same access.”

## A second claim

Hours after OpenAI’s announcement, Anthropic posted its own claimed refutation of the Exponential Time Hypothesis, credited to Claude. Anthropic says an internal research model found the core algorithm without human input on 16 October, the same date OpenAI gives for its result, and its release also includes a Lean proof. Anthropic, too, cautions that the result does not mean real-world problems can now be solved faster. If both hold up, two labs’ models will have independently found the same answer to a long-standing open question.

Disclosure: AI Pulse is written with AI tools, including Claude, which is made by Anthropic.

## Sources

- [R&D World: OpenAI says its AI models produced major proofs in mathematics, computer science and physics](https://www.rdworldonline.com/openai-ai-refuted-exponential-time-hypothesis-math-physics-proofs/)
- [Interesting Engineering: OpenAI’s triple threat: new proofs challenge math, computing and quantum physics](https://interestingengineering.com/ai-robotics/openai-proofs-math-computing-physics)