OpenAI announced three results it says its models produced, in harmonic analysis, complexity theory and quantum field theory, and released them differently, Engadget reports. Two manuscripts are on GitHub: one proves Sogge's local smoothing conjecture for waves in every spatial dimension, and one claims the Exponential Time Hypothesis (ETH) is false. The preprint describes a deterministic algorithm that counts the satisfying assignments of any k-CNF formula in subexponential time.

ETH, a widely believed assumption that some problems can't be solved quickly, underpins hundreds of papers; if it is false, better algorithms could exist in fields from databases to computational biology. OpenAI asked outside experts, including the scientists who proposed ETH, to examine and explain the computer-science result; the physics result (on interacting quantum field theories in four dimensions) has been left to a group of physicists that has not yet published. OpenAI says it won't seek academic credit. TechCrunch reports that Anthropic released its own refutation of ETH hours later, after Anthropic mathematician Levent Alpöge suggested OpenAI's solution drew on pre-existing work. The claims have not been peer reviewed; MIT's Ryan Williams, organizing the field's response with ETH's proposers, told TechCrunch parts of the proof look "alien."

Hacker News commenters said the headline "buries the lede," asked whether this shifts the odds on P versus NP, and one questioned the size of OpenAI's donation to academia.