On the History and Solution of the Four-Color Map Problem
John Mitchem · The Two-Year College Mathematics Journal · 1981
In the summer of 1976, the University of Illinois had the audacity to use their postage meter to print the words Four Colors Suffice on the outgoing mail. The words referred to the recently announced computer-aided of the very famous Four-Color Conjecture by Kenneth Appel and Wolfgang Haken (with a significant contribution by John Koch) at the Urbana campus. Their announcement was originally greeted with a rather large degree of skepticism by the mathematical community. This skepticism was not without cause. For about a century there have been numerous rumors and claims of proofs or counterexamples to the conjecture. In fact, in 1971 a different computer-aided proof by Shimomoto was announced but later withdrawn after it failed to survive close scrutiny. Furthermore Hakin's name had somehow been associated (perhaps unfairly) with this ill-fated work. Despite this initial skepticism the Appel-Haken has withstood over three years of close examination. It has been published by the highly respected Illinois Journal of Mathematics [1] and has been accepted by a number of experts throughout the world. Let us now review the statement and history of the Four-Color Theorem. The conjecture was solely the discovery of Francis Guthrie in the early 1850's. While a student at University College, London, Guthrie discovered that he could color a map of England's counties with only four colors in such a way that each county has exactly one color, and two counties which share a common boundary line will have different colors.. Furthermore he tried to prove that the counties (i.e., regions) of any map on the plane could be so four-colored. Not entirely satisfied with his proof, Francis discussed his four-color problem with his brother Frederick, who communicated it to his teacher Augustus De Morgan. On October 23, 1852, De Morgan discussed the problem in a letter to Sir William Hamilton. Hamilton, perhaps showing more wisdom than many other mathematicians through the decades, refused to become involved with the problem.