AI Cracks Erdős’s Decades-Old Math Conjecture for the First Time

A Breakthrough at the Intersection of Mathematics and Artificial Intelligence

According to НВ — Техно: On June 2, 2023, a milestone was reached in both mathematics and artificial intelligence. For the first time, an AI system solved a major open mathematical conjecture first posed by the legendary mathematician Paul Erdős back in 1946. The problem focuses on the maximum number of unit distances that can exist among n points on a plane. The neural network behind this achievement constructed a structure more complex than the Erdős grid, leveraging algebraic integers in a high-dimensional space before projecting them onto a two-dimensional plane.

The achievement sparked an immediate response from the mathematical community. Fields Medal winner Tim Gowers called the event a

“milestone in AI mathematics.”

Professor Daniel Litt also shared his reaction, noting that this was the first time he had seen an autonomous result from a neural network that is

“genuinely interesting in its own right.”

Verification of Results and What Lies Ahead

Mathematician Will Sawin confirmed the validity of the findings by reviewing the model and proving that the growth rate is at least n^{1.014}. This success highlights the vast potential for applying artificial intelligence to mathematics, a topic that was discussed extensively at the Joint Mathematics Meetings in January 2026.

This breakthrough in solving a mathematical conjecture not only opens new avenues for research but also underscores the expanding role of AI in scientific discovery. Expert reactions further affirm the significance of this achievement for the future of both pure and applied mathematics. The adoption of such technologies could lead to novel methods for tackling the complex challenges facing the scientific community.

Ars Technica reported on this development.