Dispatches from the possibly last days of human relevance

As most readers have presumably heard by now, Paul Erdös’s Unit Distance Problem from 1946—one of the central open problems from the field of discrete geometry—has been solved by GPT5.5Pro. Erdös had conjectured that, given n points in the plane, at most n1+o(1) pairs of them could be unit distance apart. Using high-powered results from algebraic number theory, GPT refuted this, constructing a set with n1+ε unit-distance pairs, for ε ~ 10-38. Shortly afterward, Will Sawin, a human (!), improved GPT’s construction to get ~n1.014 pairs. Meanwhile, the best known upper bound remains n4/3, improving Erdös’s n3/2. The entire process seems have been one-shot: my former student Lijie Chen simply gave GPT the problem, then GPT thought for a while and output a several-page argument that, on analysis by human experts, turned out to be correct. Of course there’s selection bias here; we’re not hearing as much about the hundreds of other problems GPT was given that it didn’t solve (isn’t that the…