OpenAI Claims It Solved an 80-Year-Old Math Problem

An anonymous reader quotes a report from TechCrunch: OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdos in 1946. If this sounds familiar to you, it's because this isn't the first time OpenAI has made such a bold claim. Seven months ago, the AI giant's former VP Kevin Weil posted on X: "GPT-5 found solutions to 10 (!) previously unsolved Erds problems and made progress on 11 others."

It turns out, GPT-5 didn't actually solve those problems; it just found solutions that already existed in the literature. Taunts from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis followed, and Weil promptly took down his premature post. Today, at least, it seems OpenAI didn't make the same mistake twice. Alongside the announcement, the company published companion remarks (PDF) in support of the disproof from mathematicians like Noga Alon, Melanie Wood, and Thomas Bloom, who maintains the Erdos Problems website, and previously called Weil's post "a dramatic misrepresentation."

[...] The proof, per OpenAI, came from a new general-purpose reasoning model, not a system specifically designed to solve math problems or even this problem in particular. OpenAI says this is significant because it means AI systems are now more capable of holding together long, difficult chains of reasoning and connecting ideas across fields in ways researchers may not have previously explored. That has implications for biology, physics, engineering, and medicine.

Mathematician commentary included

[phantomfive]

Here is the paper [openai.com]. It has some really nice commentary from mathematicians at the bottom. I recommend reading (or at least skimming) it. It's not clear exactly what the AI did, since it was "human-digested, somewhat simplified, and somewhat generalized." This quote from Melanie Matchett Wood is clarifying:

"One other concern that directly arises in this development is that there is a history of closely related ideas in the literature,.. which are not appropriately referenced in Chat GPT’s paper. If a human came up with this argument and didn’t cite such previous work, we would assume that they were unfamiliar with the previous work and came up with the ideas independently, since our professional norms require us to cite previous work whose ideas influenced our work. On the other hand, Chat GPT is in some sense “familiar” with all the previous work."

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[Hentes]

To be fair, even just a tool that can search the literature for solutions of similar problems is extremely useful.

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[UnknowingFool]

I am waiting for the paper to be thoroughly reviewed before I would declare that the model proved anything. Andrew Wiles made a mistake in his first attempt proving Fermat's Last Theorem where he relied on logic that had not been proven previously. It was a fundamental problem where he had to rework his proof around that flaw.