An OpenAI reasoning model has disproved an 80-year-old conjecture in discrete geometry: the planar unit distance problem, first posed by Paul Erdős in 1946. For nearly eight decades, mathematicians assumed optimal constructions resembled square grids. The model found an entirely new family of constructions that outperforms them.
This is the first time an AI has autonomously solved a prominent open problem central to a field of mathematics. The model was general-purpose, not fine-tuned for geometry or this problem specifically. That distinction matters: it suggests the capability is broad, not narrow.
The full writeup at openai.com is worth reading for how the model connected ideas across distant fields and constructed a verifiable proof, not just a conjecture. The harder questions, which problems to pursue, what results mean, remain human work. But the search space just got a lot larger.
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