AI Stunned Scientists by Solving an 80-Year-Old Mathematical Problem

OpenAI's artificial intelligence has disproved a hypothesis by legendary mathematician Paul Erdős that had remained unchallenged for nearly 80 years. The result is already being called one of the first truly significant mathematical discoveries made by a machine. This was reported by The Conversation.

OpenAI's internal AI model found a counterexample to the famous unit distance problem on the plane, known as Erdős Problem #90. Formulated back in 1946, it sounds deceptively simple: if a certain number of points are placed on a plane, how many pairs of them can be positioned exactly one unit of distance apart from each other?

For decades, mathematicians were convinced that the best solution was provided by structures resembling a square grid. Erdős himself believed that it was impossible to substantially surpass such a configuration — even with an enormous number of points. However, OpenAI's AI demonstrated that more efficient constructions do in fact exist.

To prove this, the model employed methods from algebraic number theory and constructed point placement schemes that yield more pairs with unit distances than the classical square lattice.

Canadian mathematician Daniel Litt called the result "the first autonomously AI-obtained mathematical result that is genuinely interesting in its own right." Researchers were particularly struck by the fact that the problem was solved not by a specialized mathematical system but by a general-purpose language model.

Following the publication of the work, American mathematician Will Sawin managed to improve upon the obtained result using a similar approach. In parallel, researchers from Google DeepMind reported solving nine other open Erdős problems using their own AI models.

Fields Medal laureate Timothy Gowers stated that if a human had submitted a similar paper, he would "without hesitation" recommend it for publication in the Annals of Mathematics — one of the most prestigious mathematical journals in the world.

However, scientists urge caution: AI is not necessarily yet capable of genuine "eureka moments," which are traditionally considered the most human aspect of mathematics. In the experts' opinion, the model was rather able to effectively combine already existing ideas and test an enormous number of possibilities without any time constraints.