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OpenAI Says General-Purpose AI Solved Erdős Unit-Distances Problem

Independent verification is needed to confirm the company's claim that a model produced new geometric constructions using algebraic number theory that beat long-standing grid-based bounds.

Overview

  • OpenAI announced Thursday, May 21, 2026, that one of its general-purpose reasoning models autonomously found a new family of point arrangements that yields a polynomial improvement on the unit-distances problem posed by Paul Erdős in 1946.
  • The company says the model also produced a written proof that applies advanced algebraic number-theory tools to an elementary geometric question, a methodological link that surprised specialist commentators.
  • OpenAI emphasized this result follows prior contested claims about GPT-5 and sought outside specialist comment when publicizing the work to address earlier criticism that its models had merely recopied known results.
  • Coverage and OpenAI statements make clear that independent community verification and formal peer-reviewed publication of the proof have not yet occurred and remain the key steps to confirm the claim.
  • If validated, the finding would change how researchers view AI’s role in deep discovery by showing a general model can propose new constructions and proofs, with likely effects on peer review, research practice, and use of AI in other scientific fields.