The Four-Color Theorem: History, Topological Foundations, and Idea of Proof

by Rudolf Fritsch, Gerda Fritsch, J.lie Peschke (translator)

This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?

Kindle Edition

First published August 13, 1998

Reviews

[Dina · Rating 3 out of 5]

Very helpful when I was writing a paper on the four color theorem. Also, a nice easy to follow read.

[Sey Dou · Rating 4 out of 5]

Nice exposition on a fascinating theorem that may color our lives in far more many ways than we know or can imagine.