AI Proofs Reportedly Disprove Longstanding Computer Science Hypothesis, Leaving Research in Question

Two AI companies, OpenAI and Anthropic, claimed this week to have disproved the exponential time hypothesis (ETH), a 27-year-old premise that much theoretical computer science research has rested on. The claim has not been independently verified, and researchers have not yet had time to fully understand the AI-produced proofs, which both firms published on GitHub in natural language and machine-checkable Lean format.

The hypothesis holds that the effort needed to solve certain problems grows exponentially with the size of the problem. Peter Jonsson, a professor at Linköping University, said much of his work became "dead" as of Monday, and he expects similar reckonings at the IEEE Symposium on Foundations of Computer Science, where a coauthor will present his paper in two weeks.

OpenAI has asked the UC Santa Barbara researchers who originally proposed the hypothesis, along with an MIT academic who refuted a version of ETH, to rally researchers to unpack the proofs. The effort so far includes a Google form seeking volunteers and feedback, and a commitment from OpenAI to fund a conference on the topic. UC Santa Barbara professor Daniel Lokshtanov, who plans to join, estimated the result-if confirmed-would make around 50 of his published papers either pointless or in need of a revisit.

Thore Husfeldt, head of the algorithms research group at the IT University of Copenhagen, said the problem he spent most of this year on is now "all irrelevant" as far as he can tell. He described the finding as "fantastic," saying it was like someone illuminating an entire subfield with floodlights. Others have found the pace taxing; Husfeldt said his department has considered hiring an occupational psychologist.

Victor Lagerkvist, an associate professor at Linköping, plans to return to problems he had abandoned under the assumption ETH was accurate. Lokshtanov said that while the result does not directly affect cryptography, "it should definitely scare some cryptosystem designers." Jonsson said he could only have dreamed of a verdict on ETH before, adding: "I don't care if it's a human-written proof, or it's written by AI, or if an alien transmitted this proof to us. If it's true, then we must simply use it in the future."

Source: Wired science