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PreprintCC BYarXiv (Cornell University)

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
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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.

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Cite

BibTeXRIS
BibTeX
@misc{alon2026remarks,
  title = {{Remarks on the disproof of the unit distance conjecture}},
  author = {Noga Alon and Thomas F. Bloom and W. T. Gowers and Daniel Litt and Will Sawin and Arul Shankar and Jacob Tsimerman and Victor Wang and Melanie Matchett Wood},
  howpublished = {arXiv (Cornell University)},
  year = {2026},
  month = may,
  doi = {10.48550/arxiv.2605.20695},
  url = {https://arxiv.org/abs/2605.20695},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Remarks on the disproof of the unit distance conjecture
AU  - Noga Alon
AU  - Thomas F. Bloom
AU  - W. T. Gowers
AU  - Daniel Litt
AU  - Will Sawin
AU  - Arul Shankar
AU  - Jacob Tsimerman
AU  - Victor Wang
AU  - Melanie Matchett Wood
PY  - 2026
DA  - 2026/05/20
PB  - arXiv (Cornell University)
DO  - 10.48550/arxiv.2605.20695
UR  - https://arxiv.org/abs/2605.20695
AB  - 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.
SN  - 2331-8422
ER  -