OpenAI Finds Counterexample to Unit Distance Conjecture

OpenAI announced that a general-purpose reasoning model found a counterexample to the existing upper-bound conjecture for the classical Erdős planar unit distance problem.

• The construction produced by the model suggests that point sets exhibiting a number of unit distances of the form n^(1+δ) are possible for infinitely many n.
• This means the previously expected near-linear upper bound does not hold.
• OpenAI released the results via an official announcement, a proof PDF, and a brief reasoning writeup.
• In terms of process, OpenAI explained that the model's output was verified through an AI grading pipeline, followed by review and correction by mathematicians.
• However, the model name used, sampling method, number of attempts, compute used, system prompt, and detailed grading procedure were not disclosed.

Beyond the core mathematical result, this is also drawing attention as a case demonstrating whether general-purpose reasoning models can go beyond merely assisting mathematical research to actually finding new counterexamples.