At first glance Four Colours Suffice
seems like such an easy thing to prove. However big and complicated the map, four colours are enough to distinguish each country from its neighbours. How do we prove that only four colours are needed? Once we realise that, if four countries all share borders with each other, then one country must be enclosed by the other three (try it), we seem to be most of the way there. But things turned out to be not quite so simple. Robin Wilson might balk at the idea that his sardonic and lively account of the problem and its solution is in any way farcical--as, indeed, might the dedicated mathematicians and keen amateurs whose 150 years of work he describes. But if the way an apparently simple problem throws out poisoned blossoms of complication, confusion and embarrassment is your definition of farce, then this story surely fits the bill. Proving the four-colour conjecture turned out to be heinously difficult, and has at last been achieved--and that in the ugliest way imaginable--only with the aid of a computer.
This, we can see now, was a landmark moment in mathematics: the moment we realised that there are proofs out there so complicated, that publishing them in full is impractical, working through them by hand is impossible, and explaining them to the public requires writers of a very special stamp indeed. (Robin Wilson, I should add, is most definitely one of them.) The publishers, in deciding to make a black-and-white book out of a colour problem, have not only done justice to Wilson's illustrations, but have also created one of the most visually arresting science books around. --Simon Ings
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The four-color conjecture, formulated in 1852, was among the most popular unsolved problems in mathematics. Amateurs and professionals alike succumbed to its allure. It is, simply stated: four colors are all that is needed to fill in any map so that neighboring countries are always colored differently. That the proof, which was completed in 1976, consumed a thousand pages and gobs of computer time hints at the hidden complexity encountered by those attempting to solve it. Recreational mathematicians will find Wilson's history of the conjecture an approachable mix of its technical and human aspects, in part because the math involved is understandable even to able middle-schoolers. The conjecture seemed a snap to its originator, one Francis Guthrie, but his claimed proof has never surfaced; those proofs that did surface, prior to the final breakthrough by Kenneth Appel and Wolfgang Haken, contained fatal errors. Wilson explains all with exemplary clarity and an accent on the eccentricities of the characters, Lewis Carroll among them. Gilbert TaylorCopyright © American Library Association. All rights reserved
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