OpenAI model solves 80-year-old planar unit distance problem
An OpenAI model has successfully solved the planar unit distance problem, a mathematical conjecture that has remained unsolved for 80 years. The AI-generated proof, which spans 125 pages, was validated by leading mathematicians, including a Fields Medalist. This breakthrough reveals new geometric patterns that exceed previously believed limits on the number of unit-distance pairs in a plane.
- ▪The planar unit distance problem was first posed by mathematician Paul Erdős in 1946.
- ▪The AI's proof establishes an infinite family of planar configurations with more unit-distance pairs than previously thought possible.
- ▪For decades, the best-known configurations were grid-like structures that seemed to confirm Erdős's conjecture.
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OpenAI model solves 80-year-old planar unit distance problem An internal reasoning model produced a 125-page proof that refutes a conjecture Paul Erdős posed in 1946, validated by a Fields Medalist and leading mathematicians. Share Add us on Google by Editorial Team May. 21, 2026 window.sevioads = window.sevioads || []; var sevioads_preferences = []; sevioads_preferences[0] = {}; sevioads_preferences[0].zone = "01f21ccf-2092-46b1-9ac7-8c44cc782e0f"; sevioads_preferences[0].adType = "native"; sevioads_preferences[0].inventoryId = "c5700508-581b-472c-8fdd-a931cdbfc8e1"; sevioads_preferences[0].accountId = "1e47efc1-ec2d-4fca-a8b9-354e249e5095"; sevioads.push(sevioads_preferences); For 80 years, one of the most stubborn problems in combinatorial geometry sat on the shelf, occasionally dusted…
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