The Erdős Breakthrough

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics. The proof came from a general-purpose reasoning model, not a system built specifically to solve math problems or this problem in particular, and represents an important milestone for the math and AI communities. This result points to something larger: AI systems are becoming capable of holding together long, difficult chains of reasoning, connecting ideas across distant fields, and surfacing paths researchers may not have explored. We believe those same abilities will soon accelerate work in biology, physics, engineering, and medicine. That future still depends on human judgment. Expertise becomes more valuable, not less. AI can help search, suggest, and verify. People choose the problems that matter, interpret the results, and decide what questions to pursue next. https://openai.com/index/model-disproves-discrete-geometry-conjecture/