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Xn + Yn = Zn ?

Looking for intrigue, romance, mystery and fame? Then abandon the pulp fiction aisle and dig deeper through your dusty calculus and algebra books. This weekend I tackled Simon Singh's Fermat's Enigma, which vividly revealed a world far removed from the nerdy stereotypes of mathematics. The book traces almost the entire map of math history in an effort to illuminate the elusive Fermat's Last Theorem, the deceptively simple statement that baffled mathematicians for 350 years. 

There's the story of Paul Wolfskehl, who was prepared to commit suicide over the woman he loved, but decided against it after discovering the wonders of Fermat's Theorem just hours before he was scheduled to shoot himself. There's Evariste Galois, who began a promising math career as a teenage prodigy, only to leave it behind to become a passionate political rebel, and then die in a duel while defending the woman he loved. Singh tells of Galois the night before the duel - confident in the knowledge that he would die - frantically writing every inkling of math he'd discovered in the hopes of salvaging something for a future mathematician to one day prove.  There's Sophie Germain, arguably the finest mathematician of her era, who was forced to communicate with her mathematical peers through letters under an assumed male name, for fear her gender would hinder any constructive discussion.

And finally there's Andrew Wiles, the ultimate prover of Fermat's Theorem, who was entranced by the problem when he was 10 years old. Only through working secretly and passionately on the Theorem for 6 years could he achieve his childhood dream. And when a slight flaw threatened to shatter the proof, Wiles resiliently fought back with a solution that took another year to realize.

Singh tells many more wonderful stories connecting disparate areas of math and history. But what most intrigued me about the book was not Singh’s words, but two pieces the book quoted from G.H. Hardy's memoir, A Mathematician's Apology. Reading these quotes it struck me how similar they were to something I'd read years ago, from Oscar Wilde's Introduction to The Picture of Dorian Gray. We find two scholars applying the term "beauty" to their respective fields, and coming away with a similar analysis. How affirming it is to see seemingly divergent areas of thought intersect so nicely. Through these quotes I discover that though math has its applications in science, math alone is an art.

"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." - G.H. Hardy

"Those who find ugly meanings in beautiful things are corrupt wihout being charming. This is a fault. Those who find beautiful meanings in beautiful things are the cultivated. For these there is hope. They are the elect to whom beautiful things mean only Beauty." - Oscar Wilde

". . . if a chess problem is, in the crude sense, "useless," then that is equally true of most of the best mathematics . . . I have never done anything "useful" . . . I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value." - G.H. Hardy

"We can forgive a man for making a useful thing as long as he does not admire it. The only excuse for making a useless thing is that one admires it intensely. All art is quite useless." - Oscar Wilde

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