OpenAI model disproves Erdős's 1946 unit distance conjecture, a problem open for nearly 80 years
OpenAI said an internal general-purpose reasoning model produced a proof disproving Paul Erdős's conjecture that square-grid constructions are essentially optimal for the planar unit distance problem. The company said external mathematicians checked the proof and wrote a companion paper, while Scientific American reported that the result would merit publication in a top mathematics journal even if produced by humans. Other sources, including a Google DeepMind team describing its Aletheia agent, report that many earlier AI claims on Erdős problems turned out to restate existing literature.
Bottom line — The counterexample gives at least n^(1+δ) unit-distance pairs; Will Sawin has reportedly refined the exponent to δ = 0.014.
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OpenAI said the proof is the first time a prominent open problem central to a subfield of mathematics was solved autonomously by AI, and that the construction draws on algebraic number theory.
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Tim Gowers, writing in the companion paper, called the result 'a milestone in AI mathematics', according to OpenAI.
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Scientific American quoted Gowers saying 'No previous AI-generated proof has come close' to the standard of a top-journal result, and Daniel Litt calling it 'the unique interesting result produced autonomously by AI so far'.
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Scientific American reported that Melanie Matchett Wood argued experts had spent more effort trying to prove the conjecture than disprove it, and that the AI's search was less constrained by that belief.
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Wood also warned that the AI presented ideas without crediting similar results in the literature, which she called professional malpractice if done by a human.
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Google DeepMind's Aletheia study found that 137 of 200 definitively graded candidate solutions were fundamentally flawed and only 13 were meaningfully correct, and that many 'open' Erdős problems had prior literature solutions.
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The Google DeepMind paper argued the 'open' status of problems it resolved 'can be attributed to obscurity rather than difficulty', and flagged the risk of 'subconscious plagiarism' by AI.
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A personal blog by Zeyu Zheng argued that most earlier claims that AI solved an Erdős problem reduced to rediscovery, clarification, or formalization of human ideas.
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Scientific American quoted Sébastien Bubeck of OpenAI saying the model 'did not invent something fundamentally new', while Tsimerman argued AI can 'play for longer' than mathematicians.