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Remarks on the disproof of the unit distance conjecture

· 2026 · math.CO · arXiv 2605.20695

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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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2026 1

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Split primes and the Elekes-R\'onyai problem

math.NT · 2026-06-11 · unverdicted · novelty 5.0

Constructs sets A subset R with |{x+y+(x-y)^2 : x,y in A}| <= |A|^{2-c} for some c>0, giving a counterexample to the Elekes-Rónyai problem.

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  • Split primes and the Elekes-R\'onyai problem math.NT · 2026-06-11 · unverdicted · none · ref 2 · internal anchor

    Constructs sets A subset R with |{x+y+(x-y)^2 : x,y in A}| <= |A|^{2-c} for some c>0, giving a counterexample to the Elekes-Rónyai problem.