---
title: Erdos Unit Distance Problem
date: 2026-05-26T22:36:06+08:00
categories:
    - llms
---

An OpenAI model [solved](https://openai.com/index/model-disproves-discrete-geometry-conjecture/) the [Erdos unit distance problem](https://mathworld.wolfram.com/ErdosUnitDistanceProblem.html).

Erdos roughly said, "The number of edges of the same distance between N points can't compound faster than close to 0%."

The model found a method of placing points so that it compounds at about 1.4%.

[This visualization](https://sanand0.github.io/datastories/erdos-planar-unit/) is a crude way of visualizing how that works.

[![](https://sanand0.github.io/datastories/erdos-planar-unit/screenshot.avif)](https://sanand0.github.io/datastories/erdos-planar-unit/)