OpenAI Says New AI Refuted 1998 Exponential Time Hypothesis
Updated
Updated · The New York Times · Nov 6
OpenAI Says New AI Refuted 1998 Exponential Time Hypothesis
3 articles · Updated · The New York Times · Nov 6
Summary
OpenAI said on Oct. 26 that its newest AI system refuted the exponential time hypothesis, a 1998 conjecture long used to argue some problems must stay computationally hard.
The result does not solve the broader P vs. NP problem, but it challenges a key supporting intuition in theoretical computer science: that finding solutions is inherently far harder than checking them.
ETH was proposed by Russell Impagliazzo, Ramamohan Paturi and Francis Zane, and had stood for nearly 30 years as a benchmark assumption about the limits of fast computation.
Because P vs. NP is one of the Clay Mathematics Institute's seven Millennium Prize problems, the claim could widen debate over whether AI can meaningfully reshape core mathematical and computer-science assumptions.
If an AI can disprove a 28-year-old computer science conjecture, could its subexponential algorithm eventually be adapted to crack modern encryption?
Since AI just overturned a foundational assumption of complexity theory, what other impossible mathematical barriers might fall before the decade ends?
Even with a machine-verified proof, how can mathematicians be certain the AI didn't just exploit a translation loophole in the formalized theorem?
October 2026: AI Shatters the Exponential Time Hypothesis with Subexponential 3-SAT Algorithms
Overview
In October 2026, both OpenAI and Anthropic announced that their AI models had independently discovered subexponential algorithms for the 3-SAT problem, refuting the long-standing Exponential Time Hypothesis (ETH). These breakthroughs were formally verified using Lean 4, ensuring logical correctness but highlighting the need for human experts to confirm the proofs matched the original ETH statement. The AI-generated results, which tackled the harder exact counting version of 3-SAT, forced the computer science community to re-examine decades of complexity theory. However, these algorithms only outperform traditional methods at astronomical problem sizes, so real-world software and cryptography remain unaffected.