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An OpenAI model has disproved a central conjecture in discrete geometry

OpenAI · 2026

OpenAI

OpenAI's announcement that one of its models disproved a central conjecture in discrete geometry. Both papers cite it, with the outside mathematicians' remarks, for an AI model that, working on its own, disproved an 80-year-old conjecture of Erdős on unit distances. It is the main evidence for premise 1 of the long arc (C3), that lineages can do research that compounds.

Cited in
both papers (Flagship: Three conjectures; Companion §11)
Used for
C3C3 premise 1
Strand
Frontier AI capabilities · AI in mathematics & science

Cite

@misc{openai2026unitdistance,
  title = {An OpenAI model has disproved a central conjecture in discrete geometry},
  author = {OpenAI},
  year = {2026},
  howpublished = {OpenAI},
  url = {https://openai.com/index/model-disproves-discrete-geometry-conjecture/},
}