OpenAI Says Its AI Proved Three Famous Maths Results — But Experts Are Still Checking
On 26 October 2026, OpenAI announced that its internal AI models had produced three results that mathematicians, computer scientists and physicists have chased for decades. The announcement, titled "Working with academic communities to build scientific understanding", is one of the boldest claims any AI company has made — and the honest headline is that these are claims, not yet confirmed findings.
What is claimed
The first result is pure mathematics. In 1991, Christopher Sogge proposed the local smoothing conjecture, which says, roughly, that when waves focus to a sharp point, the most extreme focusing can only last a very short time. OpenAI says its models proved the conjecture in every dimension, which would also settle two other famous problems: the Kakeya conjecture, about sets that contain a line segment in every direction, and Stein's restriction conjecture. The previous record was partial: Larry Guth, Hong Wang and Ruixiang Zhang proved local smoothing in two dimensions in 2019, and Wang and Joshua Zahl proved Kakeya in three dimensions in 2025.
The second result is in computer science. OpenAI says its models disproved the Exponential Time Hypothesis, a widely believed guess — proposed in the late 1990s by Russell Impagliazzo and Ramamohan Paturi — that some logic problems cannot be solved much faster than by trying every possibility. Hundreds of papers have relied on it. The claimed proof, found on 16 October, describes a deterministic algorithm that counts the solutions of a certain kind of logic formula in sub-exponential time.
The third is in physics: a rigorous existence proof for four-dimensional quantum field theories, including quantum chromodynamics, the theory of the strong force. That material has not been released; a working group led by physicist David Gross is studying it first.
What has been checked — and what has not
Two of the three results come with public, machine-checkable evidence: the natural-language write-ups and their formalisations in Lean, a proof assistant that checks every logical step, are in OpenAI's public GitHub repository. A computer checking the steps is a strong signal, but it is not the same as a human expert confirming that the formal statement matches the conjecture as mathematicians understand it. None of the three results has been peer reviewed.
The people examining the computer science result are the ones best placed to judge it: Impagliazzo and Paturi themselves, together with Ryan Williams of MIT. On 6 November, the New York Times reported Impagliazzo calling the claimed disproof "very shocking news" — and adding, "It is also a shock that the work was not done by a human being." That is reaction, not a verdict: the examination is still open.
One thing the announcement does not claim: it is not a claim that P equals NP, the most famous unsolved problem in computer science. OpenAI says practical gains "will require significant further research."
Why it matters for learners
Whatever the final verdict, the episode shows how mathematics is changing. Problems that stood for decades are now being attacked by machines as well as by people — and the checking, done in public with tools like Lean, is part of the story. For a student, the lesson is the same one good maths teaching has always given: a claim is not a proof until every step has been checked, and knowing who checked it matters as much as the result itself.
If your child is working towards GCSE or A-level maths and wants to build the kind of careful, step-by-step reasoning these proofs depend on, booster or mock-exam help in maths can make the difference. Book your first lesson
Sources:
- OpenAI, "Working with academic communities to build scientific understanding", 26 October 2026, as reported by ExplainX: https://www.explainx.ai/blog/openai-exponential-time-hypothesis-false-kakeya-yang-mills-three-results-lean-collaborations-2026
- Liberty Unyielding, "Artificial intelligence is solving longstanding problems in math and challenging established theories", 7 November 2026: https://libertyunyielding.com/2026/11/06/artificial-intelligence-is-solving-longstanding-problems-in-math-and-challenging-established-theories/
London Tutors — post your tutoring request and we will match you with a verified tutor.