Large Language Models (LLMs) have definitively disproved the Unit Distance Conjecture, a longstanding Erdős problem that human mathematicians struggled with for over 80 years. Unlike previous AI-assisted solutions that relied on traditional probability-theory frameworks, the LLM employed a novel approach, producing a correct proof in under one page. This breakthrough was endorsed by a Fields Medalist who confirmed the AI-generated result equates to the quality of a PhD thesis. The solution marks a significant advancement in AI-driven mathematical problem solving.
Mathematicians specializing in combinatorial geometry, AI researchers focused on automated theorem proving, computational mathematicians, and scholars interested in the intersection of artificial intelligence and advanced mathematical problem solving.
LLMs have solved Erdős problems before, but the one Price chose wasn’t just any Erdős problem. It was one that human mathematicians had worked on for 60 [Ed:80] years without success. The nature of the solution was also unusual. While previous LLM solutions to Erdős problems used standard techniques, this one took an entirely different approach. Rather than starting from Erdős’ original probability-theory-based framing of the problem, as human mathematicians had, the LLM found an alternative route – one that led naturally, in less than a page, to a correct proof.