OpenAI challenges a key theory in computer science

On October 26, 2026, OpenAI announced that it had refuted the exponential time hypothesis (ETH), a foundational idea in theoretical computer science. The claim, made by AI researcher Sébastien Bubeck, was described as a "perhaps the greatest surprise" in his two decades of following the field, though it requires further independent review by specialists.

Exponential time hypothesis explained

The exponential time hypothesis states that for certain complex problems, even the best possible algorithm would require a time that grows exponentially with the number of variables involved. OpenAI claims to have shown that these problems can be solved in "sub-exponential" time, meaning faster than exponential but still potentially very slow.

Link to the P versus NP problem

The ETH is closely related to the P versus NP problem, one of the seven Millennium Prize problems. However, OpenAI does not claim to have solved P versus NP, as a sub-exponential algorithm is still too slow for practical use. Thus, while the ETH's limit is surpassed, the broader P versus NP question remains unresolved.

AI-generated proof and formal verification

According to OpenAI, its AI system generated the refutation on October 16, 2026. The next day, the result was formalized in the Lean proof assistant, and both the manuscript and proof are now available on GitHub. This step is significant, but experts must confirm that the proof addresses the correct problem as defined.

Expert review and future implications

A team of researchers, including Russell Impagliazzo and Ramamohan Paturi from the University of California, San Diego, and Ryan Williams from MIT, will examine the proof. Even if confirmed, the practical application of the result remains uncertain, as theoretical advancements may not translate into usable algorithms without further research.