Fermat's Enigma by Simon Singh

Author:Simon Singh
Language: eng
Format: epub
Publisher: Penguin Random House LLC
Published: 2017-03-01T05:00:00+00:00

The Compulsion of Curiosity

Pierre de Fermat’s casual jotting in the margin of Diophantus’s Arithmetica had led to the most infuriating riddle in history. Despite three centuries of glorious failure and Gödel’s suggestion that they might be hunting for a nonexistent proof, some mathematicians continued to be attracted to the problem. The Last Theorem was a mathematical siren, luring geniuses toward it, only to dash their hopes. Mathematicians who got involved with Fermat’s Last Theorem risked wasting their career, and yet whoever could make the crucial breakthrough would go down in history as having solved the world’s most difficult problem.

Generations of mathematicians were obsessed with Fermat’s Last Theorem for two reasons. First, there was the ruthless sense of one-upmanship. The Last Theorem was the ultimate test and whoever could prove it would succeed where Cauchy, Euler, Kummer, and countless others had failed. Just as Fermat himself took great pleasure in solving problems that baffled his contemporaries, whoever could prove the Last Theorem could enjoy the fact that they had solved a problem that had confounded the entire community of mathematicians for hundreds of years. Second, whoever could meet Fermat’s challenge could enjoy the innocent satisfaction of solving a riddle. The delight derived from solving esoteric questions in number theory is not so different from the simple joy of tackling the trivial riddles of Sam Loyd. A mathematician once said to me that the pleasure he got from solving mathematical problems is similar to that gained by crossword addicts. Filling in the last clue of a particularly tough crossword is always a satisfying experience, but imagine the sense of achievement after spending years on a puzzle, which nobody else in the world has been able to solve, and then figuring out the solution.

These are the same reasons why Andrew Wiles became fascinated by Fermat: “Pure mathematicians just love a challenge. They love unsolved problems. When doing math there’s this great feeling. You start with a problem that just mystifies you. You can’t understand it, it’s so complicated, you just can’t make head nor tail of it. But then, when you finally resolve it, you have this incredible feeling of how beautiful it is, how it all fits together so elegantly. Most deceptive are the problems that look easy and yet turn out to be extremely intricate. Fermat is the most beautiful example of this. It just looked as though it had to have a solution and, of course, it’s very special because Fermat said that he had a solution.”

Mathematics has its applications in science and technology, but that is not what drives mathematicians. They are inspired by the joy of discovery. G. H. Hardy tried to explain and justify his own career in a book entitled A Mathematician’s Apology:

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