OpenAI model challenges a long-standing Erdős conjecture

OpenAI has revealed that one of its internal AI models found a counterexample to a famous conjecture made by Hungarian mathematician Paul Erdős in 1946. The problem, known as the planar unit distance problem or Erdős problem 90, asks how many pairs of points can be placed exactly one unit apart when points are arranged on a plane.

The result overturns the long-held intuition that square grid-like arrangements were close to optimal. OpenAI’s proof uses algebraic number theory to show that some point patterns can produce many more unit-distance pairs than the square grid for infinitely many values of n. US mathematician Will Sawin later followed the same reasoning to produce an improved result, while Google DeepMind used one of its models to resolve nine lesser open problems left by Erdős.

Fields Medallist Timothy Gowers wrote that he would have recommended the paper for publication in Annals of Mathematics “without any hesitation” if it had been submitted by a human researcher. The breakthrough highlights both the growing power of AI in mathematics and the uncertainty around whether current models can generate the deeper conceptual leaps that often drive major discoveries.