AI Proves Mathematicians Wrong
AI has solved the 80-year-old planar unit distance problem, overturning the long-held conjecture that a square grid is optimal.
“How many pairs of points can have exactly the same distance from each other on a surface?” This is the “planar unit distance” problem, for the solution of which the famous Hungarian mathematician Paul Erdős even promised prize money in 1946. However, despite this extra motivation, researchers have not been able to solve the problem in the past 80 years. They had only agreed on a conjecture; that a square grid is essentially the best arrangement to maximize the number of point pairs with the same distance.
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