OpenAI model overturns 80-year-old mathematical consensus on its own
The mathematical community's most accepted conjecture about a famous problem - which persisted for 80 years - has just been challenged by an internal model from OpenAI: a general-purpose reasoning AI system, not yet released to the public, of the type used to answer questions and analyze texts.
Known as one of the most famous puzzles in combinatorial geometry, the unit distance problem was formulated by Paul Erdős in 1946. For decades, the mathematical community built a consensus - without formal proof - that the square grid was the optimal configuration for this problem.
The apparently simple question remains without definitive solution: given a set of points on a flat surface, what is the maximum number of pairs separated by exactly the same fixed distance? The challenge is to find a rule that applies to any number of points - two or one million.
To refute the prevailing conjecture, the AI model produced a 125-page proof identifying an infinite family of grid-superior point arrangements - that is, not a single isolated counterexample, but an entire class of more efficient configurations. With that, it overturned the decades-old proposition.
The proof was verified by nine external mathematicians, among them Fields Medal winner (the "Nobel of mathematics") Tim Gowers, who proposed recommending it for publication in the journal Annals of Mathematics - and Thomas Bloom, the same researcher who had publicly exposed OpenAI's own previous false claim about mathematics.
What made this AI achievement special?
The Erdős Breakthrough
What draws the most attention to this mathematical insight is what it reveals about the technology itself. The result did not come from a specialized mathematical system, but from a general-purpose reasoning model - the same one that gives cooking tips, summarizes documents and writes texts. This suggests that sophisticated reasoning capabilities are emerging in these systems.
It wasn't a simple Google search. The model connected lines of reasoning that were scattered in the mathematical literature, and none of them related to Erdős' problem. The works are by Golod-Shafarevich (1964), Ellenberg-Venkatesh (2007/2016) and Hajir-Maire-Ramakrishna (2021).
Hosted in the arXiv preprint repository, the article "Remarks on the refutation of the unit distance conjecture" translates the 125-page AI-generated proof into shorter, clearer, and more verifiable mathematical language.
In the independent verification article - not yet peer-reviewed - the authors simplify and generalize the original argument, contextualize the proof within the existing literature and, at the end, reflect on what this episode means for the relationship between mathematicians and AI systems.
The importance of refuting the 80-year-old conjecture for science
Square grid representation, the arrangement that the OpenAI model proved to be not optimal - OpenAI/Disclosure
Even though science requires a human to sign below and answer for the validity of the argument, it is undeniable that a technical boundary has been crossed: a general-purpose AI has generated a mathematically valid proof for a problem that has withstood human effort for 80 years.
The experts highlighted a detail that adds even more value to the result: the question that generated this response was not an explicit request to refute the conjecture - it was just an open question about whether it could be true or false. In other words, the model alone came to the conclusion that it was false, and proved it.
OpenAI said this is the first time that an AI has autonomously solved an open-ended problem of central relevance to a field of mathematics. Meanwhile, the proof awaits formal publication on arXiv, although the instrument that generated it remains out of public reach, with no one outside the company being able to test, replicate or audit the process.
If AI did this alone and the best experts confirmed it, did it stop being a tool and became a collaborator? For OpenAI mathematician Mark Sellke, "We all expected to see something like this at some point, but not so soon," he told Nature. "It's a big leap from what we were used to seeing a month ago," he concluded.
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Source: CNN