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"Perhaps I could best describe my experience of doing mathematics
in terms of entering a dark mansion. One goes into the first room, and it's
dark, completely dark. One stumbles around bumping into the furniture, and
gradually, you learn where each piece of furniture is, and finally, after six
months or so, you find the light switch. You turn it on, and suddenly, it's
all illuminated. You can see exactly where you were.
Andrew Wiles earned his B.A. at Oxford in 1974, and received his Ph.D. from Cambridge in 1980. In 1981, he took a post at the Institute for Advanced Study in Princeton, and he became a professor at Princeton the following year.
About 350 years ago, Pierre de Fermat used to write in the margins of his math books. He wrote notes to himself, and sketched out ideas. Over time, mathematicians went back through Fermat's notes, and wrote formal "official" proofs for most of Fermat's conjectures (the fancy word for guess). One of Fermat's guesses, however, could not be proved. It became known as Fermat's Last Theorem because it was the last one left to prove. You can read more about number theory and Fermat's Last Theorem in the Den.
Andrew Wiles first learned about Fermat's Last Theorem as a child. "I was a ten year old, and one day I happened to be looking in my local public library and I found a book on math, and it told a bit about the history of this problem and I, a ten year old, could understand it. From that moment I tried to solve it myself, it was such a challenge, such a beautiful problem."
He put aside his work on the theorem when he began his academic career. Fermat's Last Theorem was not fashionable in academic mathematics. (Yes, math has trends and fashions, just like every other human activity.)
Then, in the 1980's, other researchers tied together several other mathematical ideas, and Professor Wiles realized that, based on this recent research, he had a chance to prove, once and for all, this problem that had confounded mathematicians for centuries. He abandoned all his other research. He cut himself off from the rest of the world, and for the next seven years, he concentrated solely on his childhood passion.
"I never use a computer. I sometimes might scribble. I do doodles. I start trying to find patterns, really, so I'm doing calculations which try to explain some little piece of mathematics, and I'm trying to fit it in with some previous broad conceptual understanding of some branch of mathematics. Sometimes, that'll involve going and looking up in a book to see how it's done there. Sometimes, it's a question of modifying things a bit, sometimes, doing a little extra calculation. And sometimes, you realize that nothing that's ever been done before is any use at all, and you just have to find something completely new. And it's a mystery where it comes from."
His proof was published in the Annals of Mathematics in 1995. Dr. Wiles has received many honors for this monumental accomplishment. He was awarded the Schock Prize in Mathematics from the Royal Swedish Academy of Sciences, and the Prox Fermat from the Université Paul Sabatier. In 1996, he received the Wolf Prize, and was elected to the National Academy of Sciences of the United States, and received its mathematics prize.
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