Glimpses of All of It

The four-color theorem, you will be glad to reflect, has been proved; that is one irreversible accomplishment of the past quarter-century. It was posed by a man who died in 1868, Augustus Ferdinand Möbius, he of the strip, and amounts to the statement that on a map of any complexity, where any number of countries meet along common frontiers, four colors will suffice to keep them distinct, no two adjacent countries colored alike.

The proof, a topologists’ White Whale for more than a century, yielded just a few years ago to ingenuity abetted by an American Midwestern computer, and it has this vaguely unsatisfactory feature, that in detail no human mind can follow it. Euclid’s beautiful proof that there is no largest prime number can be written out in full on a sheet of notepaper; but the proof of the four-color theorem entails disposing of special cases so numerous and so tedious a tireless machine is all that we can trust for the whole middle part.

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Hugh Kenner

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Aleksandr Solzhenitsyn

The four-color theorem, you will be glad to reflect, has been proved; that is one irreversible accomplishment of the past quarter-century. It was posed by a man who died in 1868, Augustus Ferdinand Möbius, he of the strip, and amounts to the statement that on a map of any complexity, where any number of countries meet along common frontiers, four colors will suffice to keep them distinct, no two adjacent countries colored alike.

The proof, a topologists’ White Whale for more than a century, yielded just a few years ago to ingenuity abetted by an American Midwestern computer, and it has this vaguely unsatisfactory feature, that in detail no human mind can follow it. Euclid’s beautiful proof that there is no largest prime number can be written out in full on a sheet of notepaper; but the proof of the four-color theorem entails disposing of special cases so numerous and so tedious a tireless machine is all that we can trust for the whole middle part.