Remarks on the disproof of the unit distance conjecture

2026/05/20 by Noga Alon, Thomas F. Bloom, W. T. Gowers +6 · 4 voices · 9 citations
#math.CO #math.NT

paper · pdf

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.

Cited by

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• ProofCouncil: An LLM Agent for Solving Open Mathematical Problems
• Unit distance graph [wikipedia]

Discussions

• Je ne suis pas sûr que tu mesures les progrès des LLM : ce ne sont plus de vulgaires chatbots. Je suis très très critique de ces outils mais les derniers modèles ont des résultats spectaculaires. Une [bsky, 1 points, 1 comments]
• Here’s the paper: arxiv.org/abs/2605.206... [bsky, 0 points, 1 comments]
• Because OpenAI is lying and their LLM didn't actually disprove the Erdos Unit Distance conjecture. Why are you believing their press release? [bsky, 0 points, 2 comments]
• ⚬ But wait! there is a follow up paper where nine humans explained their abandon. arxiv.org/abs/2605.20695 [bsky, 0 points, 1 comments]

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• On the Erdős distance problem
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