OpenAI says its models cracked three open problems in math, CS, and physics — reviewers are still checking
OpenAI said on October 27 that its models had produced three results it is calling genuine scientific discoveries: a proof of Sogge's local smoothing conjecture for the wave equation in every spatial dimension, a disproof of the Exponential Time Hypothesis (ETH) in computational complexity theory, and an existence proof for a class of four-dimensional quantum field theories that includes quantum chromodynamics (QCD). Taken together, OpenAI says the math result also resolves the long-standing Kakeya maximal and dimension conjectures and parts of Stein's restriction conjecture, across a field that had previously only been settled in three dimensions.
What's actually being claimed
The math and computer-science papers, titled "Local smoothing for the Euclidean wave equation" and "The Exponential Time Hypothesis is false," come with both natural-language arguments and machine-checked formal proofs in Lean, a proof assistant that verifies a statement follows from its axioms. That's a meaningfully stronger evidentiary bar than a plain English write-up, but outlets covering the release note an important caveat: a Lean verification confirms the formalized statement is internally valid, not that the formalization faithfully captures the informal conjecture mathematicians have been chasing for decades. OpenAI's own materials, cited by Analytics Insight and Tech Insider, show the company dated the underlying proofs internally — a Yang-Mills existence proof on September 9 and the QCD result on September 18 — weeks before going public with any of it.
The physics result is handled differently, and that difference is the most interesting part of the story. Rather than publish the QCD and Yang-Mills proofs directly, OpenAI assembled an external "shepherd" group — led by physicist David Gross and including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov — to examine the work before any public release. As of this week, that group hasn't published an assessment, and the physics proof itself remains undisclosed. OpenAI selected the shepherds itself and has said participation isn't an endorsement, which several outlets flagged as a built-in independence problem: the people checking the work were chosen by the company whose claim is being checked.
Real experts, real hedges
The reactions from named mathematicians and computer scientists are notably more measured than OpenAI's framing. Alex Iosevich of the University of Rochester, whose own PhD adviser originally formulated the local smoothing conjecture, called the apparent resolution a "historic development" and said he expects it to reshape parts of theoretical mathematics — while also describing a personal ambivalence about what that means for the field. Ryan Williams of MIT, a leading complexity theorist, said a confirmed ETH refutation would be a major result precisely because so much of theoretical computer science — databases, computational biology, cryptography-adjacent arguments — has been built on the assumption that ETH holds. But he was explicit that the proof is still being checked by the community, and he does not expect any near-term practical payoff even if it holds up: no production system runs faster tomorrow because of this.
The math framing also turns out to be narrower than the headlines suggest. OpenAI's own account concedes the Kakeya-related consequences hold only "throughout the interior of the conjectured range," not the full range mathematicians have been trying to close. That's a common pattern with frontier-lab science claims: the press release states the maximal version, and the fine print narrows it.
Why this keeps happening
This isn't the first time a frontier lab has made this kind of self-published claim. Last month, Anthropic announced that Claude had found a new CRISPR-like enzyme — and got mixed reactions from scientists, some calling it exciting and others saying the company had overstated its significance. The pattern across both labs is the same: a company controls the announcement, the framing, and in OpenAI's case this week, the reviewers — while independent verification trails behind by weeks or months, if it comes at all.
None of that means the underlying math is wrong. Formal Lean verification is a real and unusually strong form of self-checking, and if the ETH result survives scrutiny it would be a legitimately significant event in theoretical computer science. But the gap between "verified by the people the claimant chose" and "independently reproduced by the field" is exactly where OpenAI's physics result currently sits, and where its math and CS results will sit until outside groups publish their own analysis rather than the company's. Treating this week's announcement as settled science, rather than as a strong but self-refereed claim awaiting outside confirmation, is the mistake worth avoiding.