Re: Was Fermat\'s Theorem Really Proven?
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Will anyone ever be able to come up with such a "simple" proof, and perhaps more importantly--was Fermat telling the truth?
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Proofs will get simpler over time. How much simpler is hard to say.
I think "almost everyone" agrees that Fermat thought he had a proof, but that it was, in fact, flawed just like the thousands of alleged proofs that came in the years after his book was published.
For that matter, a great many 17th and 18th century proofs, judged correct at the time, would now be considered flawed because of the increased rigor that came into fashion in the 19th century. For instance, if a student were to follow exactly the same steps that Euler used to "prove" that 1+1/4+1/9+..+1/n^2 = Pi^2/6, his paper would be marked wrong (for playing too fast and loose with factoring a polynomial of infinite degree) - Euler just didn't write down a justification for why he could get away with certain manipulations of infinite series, and now we find it easier to prove it by a different method that to fill in all of the background for why Euler's method worked.
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