😸 OpenAI solved an 80-year math problem by... disproving it
The Neuron · Grant Harvey · 2026-05-22
OpenAI's unreleased general-purpose reasoning model disproved the Erdős unit distance conjecture, an 80-year-old discrete geometry problem, by constructing a counterexample that was subsequently verified and sharpened by external mathematicians including Princeton's Will Sawin.
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Topics: ai-reasoningmathematical-proofopenaidiscrete-geometryai-capabilities
Claims
- OpenAI's unreleased general-purpose reasoning model produced a counterexample disproving the Erdős unit distance conjecture, a problem open since 1946.
- The proof was generated by a general-purpose reasoning model with no special training, scaffolding, or targeting for mathematical problems.
- External mathematicians, including some who had previously criticized a failed OpenAI math claim, co-signed companion remarks verifying the result.
- Princeton mathematician Will Sawin sharpened the result to demonstrate more than n^1.014 unit-distance pairs for arbitrarily large point sets.
- Mathematical proofs constitute a stronger test of AI reasoning than standard benchmarks because they require line-by-line expert verification rather than rewarding pattern-matched guesses.
Key quotes
This is a cleaner test of AI reasoning than a benchmark (a standardized model test). Benchmarks can reward lucky guesses. A proof has to survive expert review, line by line.
OpenAI turned their haters into benchmarks, basically.
AI may surface answers humans could have found, but didn't have time (or the will) to go after because it didn't seem worth finding.