VISIONS OF INFINITY: THE GREAT MATHEMATICAL PROBLEM

Dallas Morning News “Anyone who has always loved math for its own sake or for the way it provides new perspectives on important real-world phenomena will find hours of brain-teasing and mind-challenging delight in the British professor's survey of recently answered or still open mathematical questions.... Individual readers will dig deeply into certain chapters and skim others according to personal preference, but every one of them will be captivated by the technical achievements, loose ends and human insights that Stewart shares on his grand mathematical tour.”

New York Journal of Books “Entertaining and accessible.... Ian Stewart belongs to a very small, very exclusive club of popular science and mathematics writers who are worth reading today.” About the Author Ian Stewart is Emeritus Professor of Mathematics and active researcher at the University of Warwick. The author of many books on mathematics, he lives in Coventry, England.

Despite the motivation from coloring political maps of countries, the theorem is not of particular interest to mapmakers. According to an article by the math historian Kenneth May (Wilson 2014, 2), “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of mapmaking do not mention the four-color property.”

Three colors are adequate for simpler maps, but an additional fourth color is required for some maps, such as a map in which one region is surrounded by an odd number of other regions that touch each other in a cycle. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proved in the late 19th century (Heawood 1890); however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852....