An internal OpenAI general reasoning model has produced a proof that resolves the planar unit distance problem, a conjecture first posed by mathematician Paul Erdős in 1946. The proof, spanning roughly 125 pages, establishes an infinite family of planar configurations with more unit-distance pairs than the traditionally assumed optimal arrangements.
The AI found geometric patterns that break a limit mathematicians believed held for eight decades. Rather than iterating on known grid arrangements, it approached the problem through algebraic number theory, connecting it to advanced mathematical structures called infinite class field towers. The improvement has been quantified with an exponent of approximately 0.014.
Fields Medalist Tim Gowers and Princeton mathematician Will Sawin both validated the proof's correctness. The announcement came around May 20, 2026, and has immediately reshaped the conversation about what AI reasoning systems can do in pure research contexts.
The techniques involved, particularly the algebraic number theory and the construction of novel mathematical objects, have direct relevance to formal verification and zero-knowledge proof systems. If AI reasoning models can generate and validate proofs at this level, the cost and timeline for formally verifying complex protocols could drop dramatically.