OpenAI has announced that its general reasoning model has disproved a central conjecture of the unit distance problem. This problem was posed by Paul Erdős in 1946 and had remained unsolved for approximately 80 years.
OpenAI Model Disproves Central Conjecture of the Unit Distance Problem via General Reasoning
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Conventional understanding held that a square grid configuration was essentially optimal for maximizing unit distance pairs. However, the model provided an example of an infinite sequence that yields a polynomial improvement. The proof has been verified by a group of external mathematicians.
Of particular interest is that this achievement emerged from a general reasoning model rather than a mathematics-specialized system. OpenAI had been evaluating the application of its models to several Erdős problems as part of testing whether advanced models could contribute to frontier research.
Fields Medalist Tim Gowers described this result as a "milestone in AI mathematics." Additionally, number theorist Alul Shankar stated that current AI models possess the ability to move beyond being mere auxiliary tools for humans and can execute their own original ingenuity.
Source: An OpenAI model has disproved a central conjecture in discrete geometry（HN 1429pt・1055コメント） (HN Search (backfill), 2026-05-21)