Remarks on the disproof of the unit distance conjecture

Noga Alon; Thomas F. Bloom; W. T. Gowers; Daniel Litt; Will Sawin; Arul Shankar; Jacob Tsimerman; Victor Wang; Melanie Matchett Wood

doi:10.48550/arxiv.2605.20695

Remarks on the disproof of the unit distance conjecture

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, Melanie Matchett Wood

DOI: 10.48550/arxiv.2605.20695

Cited by: 1

Abstract

We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it. The argument relies crucially on ideas that may, at least in retrospect, be attributed to Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna.

Fields of Study & Subjects

Computability Logic AI Algorithms Limits and Structures in Graph Theory Analytic Number Theory Research

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 20 May 2026
Document type: Preprint