What was announced
On 26 October OpenAI said that an unreleased internal model had produced a 67-page manuscript titled The Exponential Time Hypothesis is False, dated 17 October and revised on the 25th. The claim is a deterministic algorithm that counts the satisfying assignments of any k-CNF formula in polynomial space and in time on the order of 2^(n/(log n)^(1/2)). That is subexponential, and therefore would falsify the Exponential Time Hypothesis — the 2001 conjecture of Russell Impagliazzo and Ramamohan Paturi that deciding 3-SAT on n variables requires 2^Ω(n) time in the worst case — and, the paper argues, the Strong Exponential Time Hypothesis along with it.
The paper is explicit about its limits: it does not claim that NP problems in general admit subexponential algorithms, and it does not settle P versus NP.
How it was produced
The only listed author is "OpenAI". The repository's README states that the "vast majority of results were obtained" with the same internal model, at an average of "three hours of ChatGPT Pro thinking compute" per result, and that the manuscripts are "best understood as a form of raw research data, rather than polished academic papers". OpenAI says the natural-language disproof appeared on 16 October and was formalized in Lean the following day.
A machine check is not a validation. Lean confirms that the formal statement follows from its assumptions; whether that formal statement captures what the paper actually claims remains a question for experts. OpenAI's own Lean notes record a time bound slightly weaker than the sharpest one in the manuscript — a gap that matters precisely because the whole argument rests on squeezing under an exponential.
The review arrangement, and why it is contested
OpenAI says the work will be "verified and shepherded" by a group led by Impagliazzo and Paturi at UC San Diego and Ryan Williams at MIT. The three signed an open letter stating: "Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny." OpenAI has committed to funding a conference and says participants will not be asked to sign non-disclosure agreements.
The process is still disputed. A panel of mathematics advisers that OpenAI convened after earlier proof releases recommended that AI companies not adopt the practice of granting selected researchers first access — a practice this announcement repeats.
Two more claims, thinner evidence
The same announcement asserts a proof of the local smoothing conjecture in every dimension, which OpenAI says resolves the Kakeya conjecture, proved in three dimensions by Hong Wang and Joshua Zahl in 2025. It also claims an existence proof for quantum chromodynamics — the Yang–Mills problem that is half of a Clay Millennium Prize. The materials for the QCD claim have not been released, which makes it the least checkable of the three.
Why it matters
If the ETH result holds, an assumption load-bearing for hundreds of fine-grained complexity papers collapses, and the hardness of exact SAT counting has to be re-derived. If it fails, the episode still marks a shift in how frontier labs publish mathematics: preprint by press release, formalization as credibility, peer review as an afterthought.
The practical consequences are close to zero for now. One self-described SAT specialist on Hacker News called the bounds "galactic" — no immediate applications, but possibly ideas that snowball into faster solvers years later. OpenAI itself says turning the result into practical improvements "will require significant further research".
The real test is the independent check now under way, not the Lean build that passed.
