AI solves 80-year-old geometry puzzle, pushing math boundaries

An artificial intelligence developed by OpenAI has achieved a historic milestone by solving the unsolved problem of unit distances, a complex geometry puzzle first posed in 1946 by the renowned mathematician Paul Erdős. This achievement challenges the long-held belief in the human mind's supremacy in scientific research.

The problem involves arranging points on a plane to maximize the number of pairs separated by an identical distance. Erdős had conjectured that an optimized grid arrangement was unbeatable. For 80 years, mathematicians struggled with this conjecture, considering it beyond reach. However, the AI, designed for general reasoning rather than specialized mathematical tasks, proposed a completely new and unexpected approach.

Without specific mathematical training, the AI generated hundreds of pages of calculations. Its strategy involved constructing a network of points in a higher-dimensional space. This allowed it to maximize symmetries before projecting the complex structure onto a two-dimensional surface, akin to casting a shadow. The resulting pattern is so intricate that it remains impossible to visualize or draw accurately.

This significant discovery underscores the capability of machines to devise novel geometric abstractions. It suggests a potential for dramatically accelerating the pace of scientific discovery, pushing the boundaries of what was previously thought possible through human intellect alone.