In October 2025, an OpenAI executive went on social media to announce that the company’s reasoning model had cracked ten unsolved problems from the legendary mathematician Paul Erdős. The mathematics community took it apart almost immediately. Thomas Bloom, one of the keepers of Erdős’s open-problem list, called the post a “dramatic misrepresentation”: the model had not solved the problems, it had only located existing solutions in the literature.
Last week, OpenAI tried again. This time the response from those same skeptics — including Bloom — is the one nobody saw coming.
The new claim, reported by TechCrunch on 20 May 2026: a single OpenAI reasoning model produced an original AI mathematical proof that disproves a discrete geometry conjecture Erdős first posed in 1946, by finding an entirely new family of constructions that violates a bound everyone assumed for nearly 80 years was tight.
What the AI actually did
The conjecture sits in combinatorial geometry — a field where progress crawls because it depends on inventing the right object, not deploying a known technique. The AI did not just locate a missing argument. It produced a family of constructions that performs better than the literature thought possible. That construction is what disproves the conjecture.
This is the difference that matters. Generative AI is now well-known to “find” mathematical results that are really sophisticated retrieval — see our piece on the AI silver medal at the Math Olympiad for the cleanly-verifiable version of AI doing real math against known answers. This Erdős result is being treated as a step further: an original idea that didn’t exist anywhere before the model produced it.
Why the skeptics actually signed off
When the October overclaim happened, three mathematicians did most of the public dissecting: Noga Alon, Melanie Wood, and Thomas Bloom. All three have now published companion remarks supporting the new proof. Bloom — whose Erdős-problems site is the canonical reference for what’s open — is on record backing the result. As TechCrunch put it: “the mathematicians who exposed its last embarrassing claim are backing it up.”
That endorsement is doing most of the heavy lifting here. AI labs claim mathematical breakthroughs constantly; the real currency now is which mathematicians believe them. When the people who blew apart your last embarrassment publicly verify your next one, the result clears a much higher bar than a press release ever could.
The first autonomous AI mathematical proof?
OpenAI is calling this “the first time AI has autonomously solved a prominent open problem central to a field of mathematics.” That phrasing is doing some work — what counts as “autonomous” and “prominent” is debatable — but the deeper claim is unusually defensible. The proof is original. The conjecture is real. The verifiers are credible. None of those three things were true for the October claim.
If it holds, this AI mathematical proof sits in a different category from the Olympiad silver-medal result. The Olympiad problems were already solved by humans; the AI was reproducing human-grade reasoning against known answers. The 1946 Erdős conjecture had been unsolved for nearly the entire history of modern combinatorics.
What working mathematicians actually do now
The useful reading of this isn’t “AI replaces mathematicians.” It’s that the boring lemmas just got cheap. For the next year or so, expect a flood of partial AI mathematical proofs in adjacent corners of combinatorics and graph theory: most genuinely incremental, some embarrassing, a few real.
The story arc that took a single point off the gold-medal line at the Olympiad in 2024 has now crossed into open research mathematics in 2026. Whether the curve continues at this slope is the actual question. The single data point in front of us is the cleanest one yet.
For the broader context — and a sense of how AI’s role in mathematics has accelerated in just twelve months — our coverage of the Olympiad result is the natural companion piece to this one.