An unsolved problem in metric geometry
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The question was posed in 1950 by the American mathematician Edward Nelson (1932–2014), then a student, who was known for his research in logic and nonstandard analysis. It was also introduced independently in a slightly different form by the Swiss mathematician Hugo Hadwiger (1908–1981), hence the name Hadwiger–Nelson problem.
It was one of Paul Erdős's favorite problems, and he often mentioned it in his lectures, lamenting that he had not posed it himself! The problem was also popularized by Martin Gardner in 1960 in his column for Scientific American.
This number c of colors is often called the chromatic number of the plane. It is at least 4, since four colors are required to color the set of points below while respecting the constraint, where a line segment joining two points indicates that they are 1 unit apart (see Tangente 195, 2020).
