AI — and yet it thinks!

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I watched the OpenAI video last night and had to pause for a moment to decide whether to take it seriously. When it comes to OpenAI and math, you now instinctively think of October 2025 — when Kevin Weil announced on X that GPT-5 had "solved ten open Erdős problems," and Thomas Bloom, who maintains the website that catalogs Erdős problems, had to publicly explain to them that those problems were only marked "open" on his site because he hadn't yet tracked down the existing papers. GPT-5 hadn't done any mathematics. It had googled. Weil deleted the post and left OpenAI half a year later. That was embarrassing.

This time is different. It's about the unit distance problem, posed by Erdős in 1946: if you place n points in the plane, what is the maximum number of pairs that can be exactly distance 1 apart? For decades, the best known construction was a plain square grid, and the belief was that you couldn't do better. The OpenAI model has found an infinite family of constructions that beats the square grid — and it does so using tools from algebraic number theory that no human would have tried in this combination on this problem.

What makes the difference from last year isn't just the result. It's the staging. OpenAI didn't headline the blog post with the model's name, but with quotes from Tim Gowers (Fields medalist), Noga Alon, and two other mathematicians who checked the proof. It's a small gesture, but it says: "Don't believe us. Believe these people." Exactly what was missing last year.

And it gets better. One of the verifiers, who wrote a companion note, is Thomas Bloom himself — the same Bloom who publicly took OpenAI apart in October 2025. This time he writes that the result shows "that there is a lot more that number theoretic constructions have to say about these sorts of questions than we suspected." When your harshest critic becomes a co-author because he's convinced, that's the strongest possible proof of credibility. OpenAI couldn't have staged it better.

I find it remarkable because it shows that OpenAI has learned. Not just the model — the company too. In October they delivered what was good for tweeting. Now they deliver what is good for verifying. That's a step toward maturity I wasn't sure would come.

The second thing that strikes me: it isn't a math-specialized model. No AlphaProof, no Lean training stack, no formal-proof system. It's a general-purpose reasoner that does math on the side. If that's true, and if it transfers to other problems, then that is more interesting than the solution itself. It means that the "reasoning models" which have been the main story at OpenAI and Anthropic for about two years are now at a point where they aren't just solving olympiad-style problems but tackling real open ones.

I'm staying cautious. A cracked construction isn't cracked mathematics — the upper bound on the problem still stands; the model only improved the lower one. And Erdős apparently left hundreds of open problems behind. Beating one doesn't mean the others fall. But for the first time since the GPT-5 debacle, I have the feeling that the story OpenAI is telling matches what the mathematicians confirm. And that's not a given.

Sources: - OpenAI: "An OpenAI model has disproved a central conjecture in discrete geometry" (May 20, 2026) - Companion paper by Noga Alon, Tim Gowers, Arul Shankar, Jacob Tsimerman - Companion note by Thomas Bloom - TechCrunch: "Kevin Weil and Bill Peebles exit OpenAI" (April 17, 2026) - eWeek: "GPT-5's Math 'Breakthrough' Gets F-Minus for Hype" (Oct. 2025) - TechTimes: "OpenAI Model Cracks 80-Year Erdős Conjecture, Verified by Its Harshest Previous Critic" (May 21, 2026)

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