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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.

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.