AI Claims It Broke a 27-Year-Old Computer Science Rule. Here Is What That Really Means
OpenAI says one of its AI models disproved the Exponential Time Hypothesis, a long-held belief about how fast computers can solve hard logic puzzles. Anthropic claims a similar result. Expert review is still underway.
What Is the Exponential Time Hypothesis?
Computer scientists Russell Impagliazzo, Ramamohan Paturi and Francis Zane proposed the Exponential Time Hypothesis (ETH) in 1999. It says a famous puzzle called 3-SAT, which asks whether a set of logical conditions can all be true at once, cannot be solved in subexponential time. Put simply, every extra variable multiplies the work, and no clever trick escapes that. Hundreds of research papers build on this belief.
What OpenAI Says It Found
OpenAI announced on Monday, Oct. 26, 2026, that an internal model produced a proof that ETH is false. The company says the model found the core idea on Oct. 16, and the proof was then verified in Lean, software that checks mathematical logic step by step. OpenAI published the AI-written proof and the Lean files and agreed to make its raw data public, The Washington Times reported.
Anthropic Says It Found One Too
Hours later, Anthropic posted its own claimed refutation, credited to Claude. It says an internal Claude model found the core algorithm without human input on the same date, Oct. 16. Both companies used Lean, but Lean only confirms that a proof follows from a stated claim. Humans must still check that the claim matches the paper, and Anthropic’s own notes say no machine does that for its file.
Who Is Checking the Work?
OpenAI asked Impagliazzo and Paturi of UC San Diego, plus Ryan Williams of MIT, to organize an open review. They say their involvement is not certification. As of Oct. 29, no flaw had been publicly identified in either proof, according to Dataconomy. Williams said parts of OpenAI’s proof looked routine, while a few unusual sections need wider scrutiny.
What It Does Not Mean
- No faster everyday software. The algorithms would not improve practical 3-SAT solving for ordinary inputs.
- Not a solution to P vs. NP. Anthropic said its result does not directly address that question, and OpenAI said its speedup does not extend to NP problems in general.
- No known break of encryption. One researcher said the result does not directly affect cryptography, though designers should watch closely.
Why It Still Matters
If confirmed, researchers must revisit work that assumed ETH was true. Computer scientist Thore Husfeldt said AI-generated results now arrive every week or two, disrupting projects researchers are still pursuing. For a visual walkthrough, this AI Paper Slop video explains the algorithm’s core idea: split the variables into groups that share only a few numbers, then rebuild the count by interpolation. It also stresses that none of the results has been formally refereed.
Frequently Asked Questions
Has the Exponential Time Hypothesis officially been disproved?
Not yet. OpenAI and Anthropic claim it, but independent review is ongoing. As of Oct. 29, no flaw had been publicly identified.
Will this change everyday software or security?
No immediate change is expected. The algorithms do not speed up ordinary 3-SAT problems, and one researcher said they do not directly affect cryptography.
What is Lean, and does it prove the result is correct?
Lean is software that checks proofs step by step. It confirms a proof follows from a stated claim, but humans must confirm that claim matches the paper’s conclusion.
For now, ETH is a hypothesis under serious challenge, not a discarded one. Treat the claim as promising but unconfirmed until independent experts report back. For broader context, read our look at the innovations driving the future of computing.
Elena Rostova
B2B Operations Consultant & Business Editor
Elena Rostova is a B2B strategy consultant specializing in digital operations, regulatory risk management, and scaling business models. She writes on corporate licensing, operational frameworks, and enterprise growth.
