OpenAI says its AI disproved a famous math conjecture from 1946

In short: OpenAI says one of its AI models produced a proof that disproves the Erdős unit distance conjecture, a well known math claim that stood for about 80 years.

What happened

OpenAI announced in mid May that an internal AI model found a proof about the “unit distance problem.” This problem asks how many pairs of points can be exactly one unit apart when you place a large number of points on a flat surface.

A simple way to picture it is like placing pins on a sheet of paper and counting how many pairs are exactly one inch apart. Mathematician Paul Erdős guessed that the best you can do grows only a tiny bit faster than the number of points as you add more pins.

OpenAI’s model did not confirm Erdős’s guess. It showed a different way to arrange points that creates more “one unit apart” pairs than Erdős expected. Several mathematicians reviewed the result, and OpenAI published some of their reactions, including comments from Fields Medal winner Tim Gowers.

The reporting notes that the AI’s proof mainly combined existing ideas from different areas of math, rather than inventing a totally new method. After OpenAI shared the work, human mathematicians cleaned up the proof and extended it. For example, mathematician Will Sawin showed the count can grow at least like n^1.014, while the best known upper limit is still around n^1.333.

Why it matters

This is one of the clearest cases yet where an AI system seems to have produced a result that changes what mathematicians believe about a major open question. It also suggests a near term pattern where AI can explore many complicated, time consuming approaches, while humans check the work and turn it into a form other people can use.

Source: Arstechnica