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Pierre de Fermat was a French lawyer who became interested in mathematics
at the age of 30. Fermat's job as a magistrate left him little time
to write complete proofs of his discoveries, so he often wrote them
in the margin of whatever book he was reading at the time. After his
death, his copy of Diophantus' Arithmetica was found to contain a particularly
tantalizing comment. Where Diophantus discusses cases in which the sum
of two squares is also a square, Fermat states in the margin that there
are no solutions possible for any powers other than squares. In other
words, it's impossible for a cube to equal the sum of two cubes, a fourth
power to equal the sum of two fourth powers, and so on. Fermat writes
"I have discovered a truly wonderful proof for this but the margin is
too small to contain it." All the other margin comments of Arithmetica
have been proved. This one, however, long remained unproved, and it
came to be known as "Fermat's Last Theorem." In 1994 Andrew Wiles of
Princeton University announced a proof of Fermat's Last Theorem, an
astounding 350 years after it was conjectured. His proof is one of the
most widely reported mathematical results in the popular press.
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