One of the most-cited stepping stones of complexity theory has been nudged by a model nobody outside OpenAI has seen. On October 26, OpenAI committed a preprint titled "The Exponential Time Hypothesis is False" to the open repository openai/math, together with a Lean formalization: an internal model produced a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and the 3-SAT case refutes the Exponential Time Hypothesis (ETH). The preprint is not peer-reviewed, and no third party has confirmed it yet.
The hypothesis behind countless lower bounds
ETH, a complexity conjecture dating to 1999, captures how hard Boolean satisfiability really is: it asserts that no subexponential algorithm exists for problems like 3-SAT, and it anchors a large share of complexity lower bounds. As one report put it, hundreds of computer science papers rest on it. If ETH falls, a whole batch of "assuming ETH" lower-bound results has to queue for re-examination.
Every manuscript came from an internal model
The openai/math repository is not an ordinary paper collection. Its README states that all manuscripts and proof artifacts were produced by an unnamed internal OpenAI model: after existing math evaluations saturated, the company started posing open research problems, with each result consuming about three hours of ChatGPT Pro-tier thinking compute on average, across roughly 4,000 posed problems. The catalogue now holds 721 manuscripts in 373 families, with about 42% (300/719) of top-line results Lean-formalized; the repo is Apache-2.0 licensed and has drawn about 15.9k stars. OpenAI is candid about positioning: the manuscripts are "raw research data" rather than polished papers, unformalized results could have issues, and some outputs build on earlier model results. Added in the same batch as the ETH paper is a manuscript proving Sogge's local smoothing estimates, which also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates; the repo additionally released abridged reasoning summaries for ten result families, including the irrationality exponent of pi and the Mahler conjectures.
Who checks it, and how
The verification plan is the most interesting part of this event. The changelog states that an independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof, and that the materials were made public immediately at the group's request. The repo carries its own errata record: on October 7, a single sign error led to three withdrawn manuscripts and fourteen revised ones — the pipeline makes mistakes, but it corrects them in public version history. Meanwhile, Terence Tao publicly criticized OpenAI's rush to release mathematical results at a UCLA seminar earlier this month, saying it exposed the company's real intentions and that constructive cooperation between the two sides is over.
So what
Beyond the "AI disproves a big conjecture" headline, the real story is the restructuring of verification: Lean makes machine-written, machine-checked proofs possible, yet a strategic-level result still needs a working group of Impagliazzo's caliber to vouch for it. When the throughput of discovery becomes a compute question, the bottleneck of mathematics shifts wholesale to verification — that is a stronger paradigm signal than any single theorem. Next time you see "AI topples conjecture X", ask first: who checked the proof?