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
TL;DR
This paper discusses a verified counterexample to the Erdős unit distance conjecture, reflecting on its implications and historical ideas from notable mathematicians.
Contribution
It provides a human-verified summary of a recent counterexample to a longstanding mathematical conjecture, connecting it to prior influential ideas.
Findings
Counterexample to the Erdős unit distance conjecture verified by humans
Reflects on the mathematical ideas underlying the counterexample
Connects recent results to historical mathematical concepts
Abstract
We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erd\H{o}s 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.
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