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

Front Cover
Springer Science & Business Media, 1998 - Mathematics - 260 pages
0 Reviews
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?
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

IV
1
V
43
VI
46
VII
59
VIII
68
IX
73
X
77
XI
81
XXII
134
XXIII
139
XXIV
141
XXV
149
XXVI
152
XXVII
168
XXVIII
171
XXIX
184

XII
85
XIV
87
XV
99
XVI
105
XVII
114
XVIII
118
XIX
125
XX
129
XXI
133
XXX
186
XXXI
187
XXXII
208
XXXIII
219
XXXIV
223
XXXV
231
XXXVI
249
XXXVII
251
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

About the author (1998)

Fritsch of the University of Munich, Germany

Fritsch of the University of Munich, Germany

Bibliographic information