OpenAI announced last week that one of its general-purpose reasoning models, working without any task-specific training or human guidance, disproved the Erdős unit distance conjecture. This is an 80-year-old open problem in discrete geometry that asks how many pairs of points in a plane can be exactly distance one apart, and Paul Erdős conjectured in 1946 that the right answer was roughly what you get from a square grid. The OpenAI model said no, the answer is bigger, and produced a 125-page argument involving Golod-Shafarevich theory and infinite class field towers to prove it.
The reason this one matters and the previous “AI just solved math” stories did not is the verification chain. OpenAI handed the proof to nine independent mathematicians, including Noga Alon, Thomas Bloom, Tim Gowers, Daniel Litt, Will Sawin, Jacob Tsimerman, and Melanie Matchett Wood. Those mathematicians, without OpenAI’s involvement, sat down and wrote their own 19-page companion paper titled “Remarks on the disproof of the unit distance conjecture.” It checks out. Tim Gowers, who has a Fields Medal and is therefore allowed to use the phrase, called the result “a milestone in AI mathematics.”
The shape of the proof is the part to pay attention to. It is not a long messy computational search. It is a structural argument that uses deep machinery from algebraic number theory, applied to a geometry problem, in a way that no published human proof had previously tried. The model identified the right tool from a different field, brought it across, and used it correctly. That is something math research culture treats as a separate cognitive act from generating valid steps inside a chosen framework, and it is the part that has historically been the hardest for AI systems to do.
Worth keeping the celebration calibrated. One disproof of one conjecture is not the moment large language models start writing publishable math by themselves. It is, however, the first case where the verification chain happened in public and survived contact with the people whose job is to find the bug. The “AI doing real math” goalposts moved this week, and they moved because the math department picked them up and walked them somewhere new.