Posted by Hervé

The Four Color Problem

In the 1850's Francis Guthrie was the first mathematician to formulate the Four Color Problem. He asked whether it is possible to color any map with four or fewer colors so that adjacent regions (those that share a common boundary) are colored differently. At the time when he posed the problem, he was a student at University College in London. He attempted to prove that the countries of any map could be colored in this map with four colors. However, he was not entirely satisfied with his proof, so he mentioned his problem to his brother Frederick, who, in turn, mentioned it to his instructor, the famous Augustus De Morgan (after whom De Morgan's Laws of set theory are named). In a letter dated October 23, 1852, De Morgan mentioned the problem to Sir William Rowan Hamilton (for whom hamiltonian graphs are named). In his response, Hamilton, perhaps displaying his insight into the difficulty of mathematical problems, replied to De Morgan that he did not plan to consider this problem in the near future. Evidently, De Morgan spoke often of this problem with other mathematicians. Indeed, De Morgan is credited with writing an anonymous article in the April 14, 1860, issue of the journal Athenaeum in which he discusses the Four Colour Problem. This is the first known published reference to the problem.