The OpenAI internal model's May 20 disproof of Erdős's 1946 planar unit-distance conjecture has cleared a second public mathematician. Thomas Bloom, the Oxford number theorist who curates the open-Erdős-problems catalogue, called it on X "without doubt the most impressive achievement of AI in mathematics so far" — an independent endorsement from outside the OpenAI-commissioned companion paper. [1] Fields medalist Tim Gowers, lead author of that companion paper, wrote in it that if a human had submitted the manuscript to the Annals of Mathematics and he had been asked for a quick opinion, "I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that." [2]

The paper's Sunday brief on the result named the proof and Jack Clark's Oxford "Nobel within twelve months" prediction in the same news cycle. Day five extends the position on the verification ladder. The construction came from a general-purpose reasoning model, not a math-specialized system; Princeton's Will Sawin has refined the explicit improvement to δ = 0.014; Noga Alon, Arul Shankar, and Jacob Tsimerman are on the companion paper alongside Gowers. The Annals reference is editorial language from a Fields medalist, not a submission — but it is the first time any mathematician of that rank has used the phrase about an AI-generated proof. [2]

The next test is whether any external group submits the proof — or its Sawin refinement — to an actual referee. Magnifica Humanitas publishes Monday with Christopher Olah on the panel; Pope Leo XIV was a math major. The encyclical's reception will sit next to a public-frontier result that two senior mathematicians have now publicly endorsed.

-- KENJI NAKAMURA, Tokyo