A Simple "Proof" of Fermat's Last Theorem
- From: contradictions.for.all@xxxxxxxxx
- Date: 9 Apr 2006 05:22:34 -0700
If you go to the website
http://www.oakton.edu/user/~pboisver/fermat.html
you will find a "proof" of Fermat's Last Theorem. Now, I don't know why
Boisvert does not indeed take advantage of the "great generalization"
this remarkable method provides and, in the same manner, settle the
Riemann Hypothesis and the Poincaré Conjecture. (He does point out
that he has another remarkable proof, in this case for the
yet-unsettled Goldbach Conjecture.) In fact, all you need in this
technique is to replace statement III by your favorite one... and
remarkably it will a forteriori be true! Notably, letting III be 0=1
you could just as easily and remarkably settle an arguably more
important issue and show that mathematics is inconsistent.
In case you don't want to leave this forum, here is the "proof",
profession-derogatory comments included:
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A Simple Proof of Fermat's Last Theorem
It is a shame that Andrew Wiles spent so many of the prime years of
his life following such a difficult path to proving Fermat's Last
Theorem, when there exists a much shorter and easier proof. Indeed,
this concise, elegant alternative, reproduced below, is almost
certainly the one that Fermat himself referred to in the margin of his
copy* of Bachet's translation of Diophantus's Arithmetica--how arrogant
of future chroniclers of mathematical history to insinuate that the
garlicky Gallic genius was incapable of formulating the crucial
insight! Why, a child can follow the logic below...however, for the
benefit of those readers who are no longer children, a short set of
notes fleshing out the argument is provided after the proof.
The Theorem: xª + yª = zª has no positive integer solutions
(x, y, z, a) for a > 2. (Pierre De Fermat, 1601-1665)
The Proof:
I) At least one of the following two sentences is true.
II) The preceding sentence is false.
III) xª + yª = zª has no positive integer solutions (x, y,
z, a) for a > 2.
Q.E.D.
The Notes:
A. Statement I is either true or false.
B. Assume I is true. Then so is either II or III. But II is false,
as it denies the truth of I. Hence III must be the true statement of
the two.
C. Assume I is false. Then both II and III must not be true. But
II agrees that I is false, so II is true. This is a contradiction.
D. Since assuming I is false leads to a contradiction, I is true.
E. Since I is true, so is III (see note B.) Thus III, Fermat's
Last Theorem, must hold.
The Aftermath:
It goes without saying that the system employed above is capable of
great generalization. But mathematicians are a stubborn lot, and,
despite the efficiency and aesthetic appeal of the approach, legions of
haunted, driven men and women will continue to pursue arcane
mathematical truths by means of tortuous, convoluted, labyrinthine
arguments--and that's OK, because it keeps them busy and off the
streets, where their generally preoccupied state dramatically increases
their probability of being killed by drivers using cell-phones.
But even I have to admit that an over-used method is a
life-essence-draining method, and have proceeded from proofs utilizing
the algorithm above to even more startling applications of
easily-overlooked syllogistic constructions. In fact, I have
discovered a truly remarkable proof of Goldbach's conjecture which this
web page is too small to contain...
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Now, it seems quite straightforward that the main, self-referencing
argument is not valid, just like "This statement is false". What formal
comments, arguments and references could you provide (me and,
especially, the author)?
Thanks a lot in advance,
CFA
.
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