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For nearly 80 years, mathematicians have studied a deceptively simple question: if you place n points in the plane, how many pairs of points can be exactly distance 11 apart?
This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve. The 2005 book Research Problems in Discrete Geometry, by Brass, Moser, and Pach, calls it “possibly the best known (and simplest to explain) problem in combinatorial geometry.” Noga Alon, a leading combinatorialist at Princeton, describes it as “one of Erdős’ favorite problems.” Erdős even offered a monetary prize for resolving this problem.
The proof is available here(opens in a new window). The companion paper by leading external mathematicians is available here(opens in a new window). You can find an abridged version of the model’s chain of thought here(opens in a new window).
This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve. The 2005 book Research Problems in Discrete Geometry, by Brass, Moser, and Pach, calls it “possibly the best known (and simplest to explain) problem in combinatorial geometry.” Noga Alon, a leading combinatorialist at Princeton, describes it as “one of Erdős’ favorite problems.” Erdős even offered a monetary prize for resolving this problem.
The proof is available here(opens in a new window). The companion paper by leading external mathematicians is available here(opens in a new window). You can find an abridged version of the model’s chain of thought here(opens in a new window).
