Re: Fermat's Last Theorem simple proof impossible?

In article <1193860859.090052.313210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mike3 <mike4ty4@xxxxxxxxx> wrote:

I'm wondering. Has it been proven that it is impossible to prove
Fermat's Last Theorem using only the mathematics Fermat would have had
available at his time?

No.

Did Fermat himself have a real proof like he
claimed?

Barring a time machine, it seems unlikely that this question can be
given a final, definitive answer.

The general consensus, however, is that it is unlikely. Keep in mind
that the "claim" was a personal note made on the margin of his copy of
the book, a note that he probably never imagined someone else
reading. Years after making the note he did publicly discuss a special
case (he gave the full proof in the case n=4, a rarity for him), and
related problems, but never once even hinted in public at the general
statement. As such, it is not unreasonable to think that he may have
later realized he was mistaken; why not make a correction then?
Because the original statement was not public; it was a note to
himself in a personal book. There was nobody to correct.

Just because we don't know how to do it does not mean it is
impossible to do. Obviously a way to settle one of the questions,
namely that of Fermat having a proof, would be to find what he claimed
to have as a proof and see if it was valid.

Unless you discover previously unknown material written by Fermat
himself, this is impossible. Even if you found an "elementary" proof
that used nothing but the machinery that we know existed at the time
of Fermat, you would have no way of knowing whether Fermat had
considered that proof or not.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

Relevant Pages

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