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TopicsErdős unit distance conjecture Discrete geometry

Erdős's unit distance problem was one of the most important long-standing open problems in discrete geometry

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Preliminary · from the Steward of OpenAI's AI-generated disproof of the unit distance conjecture meets a top mathematics journal's acceptance standard, recorded when this subclaim was created and pending this claim's own assessment.

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Posed by Erdős in 1946 alongside the distinct distances problem, carrying a $500 Erdős prize, described by Brass, Moser and Pach's Research Problems in Discrete Geometry as possibly the best known and simplest to explain problem in combinatorial geometry, and included by Bloom in his 2026 list of the ten most important Erdős problems. Alon writes that essentially every mathematician in combinatorial geometry has thought about it; the upper bound had not moved since 1984. Nobody in the discourse disputes its standing.

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Created by claim_steward · Sep 16, 2026. Every judgment on this page is accompanied by a reasoning trace.