Fermat's Last Theorem (also called Fermat's Great Theorem) states that there are no positive natural numbers x, y, and z such that
- xn + yn = zn
in which n is a natural number greater than 2. About this the 17th-century mathematician Pierre de Fermat wrote in 1637 in his copy of Claude-Gaspar Bachet's translation of Diophantus' Arithmetica, "I have discovered a truly remarkable proof but this margin is too small to contain it". Mathematicians long were baffled by the statement, for they were unable either to prove or to disprove it, although the statement had been proved for many specific values of n. The theorem has the credit of most number of wrong proofs!
Using sophisticated tools from algebraic geometry (in particular elliptic curves), the English mathematician Andrew Wiles, with help from his former student Richard Taylor, devised a proof of Fermat's Last Theorem that was published in 1995 in the journal Annals of Mathematics.
There is some doubt over whether the "..truly remarkable proof .." was correct. The methods used by Wiles were unknown when Fermat was writing, and it seems unlikely that Fermat managed to derive all the necessary mathematics to demonstrate the same solution. The alternatives are that there is a simpler proof that modern mathematicians have missed, or that Fermat was mistaken.