OpenAI has announced that one of its reasoning models has disproved an open conjecture in combinatorial geometry, first posed by Paul Erdős in 1946. The proof has been reviewed and supported by several credentialed mathematicians, which is the part that matters this time.
The last time OpenAI announced a breakthrough of this kind, it had not actually solved anything. Specifics to follow.
For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. They were wrong. An AI mentioned this.
What happened
Seven months ago, OpenAI's then-VP Kevin Weil posted on X that GPT-5 had solved ten previously unsolved Erdős problems. It had not. It had located solutions already present in the existing literature, which is a different thing, and a distinction that mathematicians — led by Thomas Bloom, who maintains the Erdős Problems website — were not quiet about.
This time, OpenAI published the disproof alongside commentary from Bloom, Noga Alon, and Melanie Wood: three mathematicians with no particular obligation to be kind. They were, within reason, kind. Bloom, who previously described Weil's post as "a dramatic misrepresentation," did not use those words on this occasion.
The model in question is a new general-purpose reasoning system — not a tool built specifically for mathematics, or even for this problem. It arrived at the disproof anyway. For nearly eight decades, mathematicians believed the optimal constructions in this geometry problem resembled square grids. The AI discovered an entirely new family of constructions that performs better. The grids, it turns out, were a local maximum humanity had been sitting on.
Why the humans care
OpenAI describes this as the first time an AI has autonomously solved a prominent open problem central to a field of mathematics. The emphasis on "autonomously" is doing some work in that sentence, and it is load-bearing.
The implications extend, per OpenAI, to biology, physics, engineering, and medicine — anywhere that long, difficult chains of reasoning need to connect ideas across fields in ways no single researcher had previously explored. This is either the beginning of a new era of scientific discovery or a very expensive way to do what mathematicians eventually would have done themselves. The gap between those two outcomes is closing, and it is not closing toward the mathematicians.
What happens next
Bloom, in his statement, asked: "What other unseen wonders are waiting in the wings." It was formatted as a question. It reads more like an inventory notice.
The model that produced this proof was not designed to produce this proof. That is the detail that will age most interestingly.