The four color theorem: history, topological foundations, and idea of proof
by Fritsch R. , Fritsch G.

Persian Title: قضیه چهار رنگ: تاریخ، پایه توپولوژیک، و ایده از اثبات

Summary and Info
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 bruteforce approach using a computer. The FourColor 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?
More About the Author
Fritsche (Friedrich) Closener (died before 11 March 1373) was a priest and historian of Strasbourg. His work was one of the first vernacular city chronicles, a type that became very common in Germany in the century that followed.
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