Fermat's Last Theorem

Fermat's Last Theorem was suggested by the French mathematician Pierre de Fermat. He said he had proved this problem but that there was not enough room in the margin to state his proof. He then died before anyone could obtain his proof.

This problem has confounded mathematicians for centuries, and there still is no proof for it using elementary techniques. Most doubt that Fermat was able to prove it himself.

The theorem is as follows:

For integers n > 2, there are no non-integral solutions to: xⁿ+yⁿ=zⁿ

In a series of lectures in 1993, mathematician Andrew Wiles claimed to have secretly proved this using non-elementary techniques. Critics pointed out a flaw in his proof, however. Wiles spent a year trying to fix the flaw, and in September 1994 announecd a new version of the proof that was largely accepted by the mathematical community, though it is unclear how much independent verification it received. Many mathematicians accept the proof without fully understanding it, and there has been remarkably little improvements or explanations since 1994.