Will Sawin got OpenAI’s email on a Friday night. Or Saturday morning. Either way, Sawin, a professional mathematician, spent his entire weekend thinking about that email. By next Monday, he decided to write up a paper that essentially improved what was given to him—an AI’s “proof” of Paul Erdős’s unit-distance problem, an infamous conjecture from 1946. Last week, OpenAI published a blog post on the AI’s proof. The paper came with a companion piece containi