From Hadwiger to de Grey

The Prompt

Explain the Hadwiger-Nelson problem to a reader with no background in graph theory. Define the chromatic number of the plane; explain the Moser spindle and the hexagonal tiling argument that establish the bounds 4 ≤ χ ≤ 7. Cite Hadwiger (1945), Nelson (1950), and de Grey's 2018 result raising the lower bound to 5. Note that de Grey is an amateur mathematician and explain what his contribution illustrates about the accessibility of open problems in combinatorics.

Completion Criteria

A short essay (three or four paragraphs) with at least three citations and a note on de Grey's contribution and its significance.

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