Mathematicians Puzzled Over a Famous Problem for 80 Years. Now, They've Used A.I. to Identify a Clever Solution

Ellen Wexler· Jun 3, 2026 · 4:14 PM UTC ·7 min read · 0 reactions · 0 comments · 4 views

#mathematics #artificial intelligence #research #Paul Erdős #OpenAI #Daniel Litt #Noga Alon #University of Toronto #Princeton University

Mathematicians Puzzled Over a Famous Problem for 80 Years. Now, They've Used A.I. to Identify a Clever Solution

⚡ TL;DR · AI summary

Mathematicians have long grappled with the unit distance problem posed by Paul Erdős in 1946. Recently, an artificial intelligence model developed by OpenAI has proposed a more effective strategy than Erdős' original approach. This breakthrough raises questions about the role of AI in solving complex mathematical problems.

Key facts

▪The unit distance problem involves arranging dots on a plane to maximize the number of pairs at the same distance apart.
▪For 80 years, Erdős' grid-like arrangement was believed to be the best solution.
▪OpenAI's AI model has identified a strategy that produces more pairs than Erdős' proposed method.

Original article

Smithsonian Magazine · Ellen Wexler

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Mathematicians Puzzled Over a Famous Problem for 80 Years. Now, They’ve Used A.I. to Identify a Clever Solution In 1946, the mathematician Paul Erdős posed the unit distance problem—and suggested a winning strategy. An A.I. model has now landed on a better one. Why didn’t humans get there first? Ellen Wexler | Writer and Special Projects Editor June 3, 2026 12:14 p.m. ShareCopy linkEmailSMSFacebookXRedditLinkedInBlueskyPrintAdd as preferred source For 80 years, most mathematicians assumed Paul Erdős' strategy was correct. OpenAI Place any number of dots on a two-dimensional plane—say, a piece of paper—and measure the distance between each pair.

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