OpenAI Cracks 80-Year-Old Math Problem

A brainy riddle that's stumped mathematicians since World War II appears to have been cracked via artificial intelligence. OpenAI says one of its AI models has solved the "unit distance problem," a classic question in combinatorial geometry first posed by Hungarian mathematician Paul Erdos in 1946, reports Interesting Engineering. Unlike a similar claim that surfaced seven months ago only to fall short, this one appears to be legit, per TechCrunch. Fields Medalist Tim Gowers, for example, called the work "a milestone in AI mathematics," and other renowned mathematicians also backed the claim.

• The puzzle: Given a bunch of points on a flat surface, how many pairs can be placed exactly one unit apart? Generations of mathematicians thought grid-like layouts were essentially as good as it gets, with the number of such pairs growing only slightly faster than the number of points, per the Interesting Engineering post.
• New thinking: OpenAI's system instead uncovered an infinite collection of point arrangements that produce many more unit-distance pairs than the standard grid. The model pulled in heavy-duty algebraic number theory—tools like infinite class field towers that are rarely seen near a geometry puzzle. "For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids," the OpenAI post reads. "An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better."
• Bigger picture: Axios provides context for non-mathematicians: "The implications are enormous: An AI capable of original mathematical discovery could unlock breakthroughs across science, engineering, and medicine."