Four Colors Suffice How the Map Problem Was Solved by Robin Wilson.

A nifty book explaining the history of the four color problem and how it was eventually solved. The book contains several short digressions into other matters related to the four color problem or that where derived from the four color problem, but for the most part the book focuses exclusivly on that one problem.

The book covers the history of the problem in great details, from it's first mention to it's current impact. The book would be hard to follow if you don't know a little advanced math, but anybody that took some college level math should be able to follow most of it.

The only over sight in the book is that it fails to comment on something that would probably seem odd to somebody without a mathmatical background, the fact that the this class of problems was solved for many more 'difficult' cases before the 'simple' one. For example, that a map drawn on a sphere with a hole driven through it requires 7 colors was shown in 1890.

To me the most interesting part of the book was the section that covered the controversy over the proof itself. After the solution was published there was an extended argument over the solutions being proof or not. At it's simplest this was a generational problem among mathematicians that distrusted new fangled contraptions likes computers. But there was also a deeper issue. The solutions didn't so much prove that 4 colors is enough as show that, for no particular reason, there is no map that requires 5. And there where quite a few people that disliked the solution because of that.

All a good read, interesting and detailed, without getting lost in mathamtical theory or spending too much time deriving actual formula.

Jay