OpenAI says its AI disproved the Exponential Time Hypothesis

OpenAI says its models have disproved the Exponential Time Hypothesis, a core assumption in computer science for more than 25 years. The claim ships with a Lean formalization and an expert review panel led by the two researchers who proposed the hypothesis. It is still a claim. The more useful lesson for operators sits in the same repository: three earlier AI-written papers were withdrawn three weeks ago for a sign error.

What actually happened

On October 26, OpenAI added two manuscripts to its public openai/math repository, both with Lean formalizations:

• "The Exponential Time Hypothesis is False." A deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas. Applied to 3-SAT, OpenAI says, it refutes ETH. An independent working group led by Russell Impagliazzo and Ramamohan Paturi (who proposed ETH) and MIT's Ryan Williams will examine the proof.
• Local smoothing for the wave equation. A claimed result that would also settle the Kakeya conjectures.

OpenAI's announcement also names a third result in physics. That one does not appear in the repository's October 26 Lean changelog.

Now the context. On October 7, the same changelog withdrew three papers on the Hodge conjecture because a sign error invalidated a key argument. It revised 14 more. At that point, 300 of 719 top-line results, about 42%, were formalized in Lean.

ETH is not P vs NP. A disproof would not break encryption or change any software you run this year. No expert has endorsed or rejected the proof yet.

Why it matters for your business

Here is the pattern that matters: the AI output that held up is the output a machine could check. Lean verifies every logical step. Prose proofs need humans, and humans missed a sign error until after publication.

Your business runs on the same split. Some AI output can be checked automatically:

• Generated SQL runs against a test database and returns the expected rows.
• Generated code passes the test suite and the type checker.
• Extracted invoice totals add up to the stated total.

Some cannot: a policy summary, a contract read, a customer reply. That output needs a human, or it needs to be reshaped until a machine can check part of it. A support reply can cite order numbers that you verify against the database. A summary can link every claim to a source line.

If OpenAI, with its own frontier models and a public repository, ships results that get withdrawn, your unreviewed AI output will have errors too. Build the checker before you scale the generator.

Sources: OpenAI: openai/math history, OpenAI announcement.