Joel Bradford Klammer:
I heard from a friend that Marilyn vos Savant (chick with
ludicrous IQ) attempted to refute the proof of Fermat's Last
Theorem and failed miserably, and that, furthermore, there was
discussion of this in sci.math. Is there a sci.math archive
somewhere where I can read about this? Or can anyone just fill
me in? Much thanks.
David T. Ose:
Savant wrote a book in the summer of 1993, about Fermat's last
theorem and Wiles work (I have forgotten the exact title, sorry).
There is a review of her book in the most recent copy of
The American Mathematical Monthly. Interesting and entertaining
reading. The reviewers say that, while she does a very credible
job explaining some of the ideas of modern mathematics, most
of her book's criticism of Wiles and of modern mathematics result
from her own lack of understanding of both mathematics and
mathematicians. And her deceitful use of several prominent
mathematicians' names to give credibility to her book was highly
unethical at best, say the reviewers. But check out the review.
Tim Chow:
Yes, that should give you a representative view.
There is one thing that I would like to add, though. Vos Savant's most
crucial argument is that "if we reject a hyperbolic method of squaring
the circle, then we should also reject a hyperbolic method of proving
Fermat's Last Theorem." Most mathematicians are content to dismiss this
as nonsense; I prefer to regard it as an argument that *would* be valid
except that it's founded on a fundamental misconception.
More precisely, vos Savant appears to regard Euclidean geometry and
hyperbolic geometry as ALTERNATIVE AXIOMATIC SYSTEMS FOR *ALL* OF
MATHEMATICS. If we accept this (false) premise, her argument runs
approximately as follows. The problem of squaring the circle calls
for a proof of a certain statement from the axioms of Euclidean
geometry. Bolyai found a proof from the axioms of hyperbolic geometry,
but this doesn't count. What Wiles has done is to find a proof of
Fermat's Last Theorem from the axioms of hyperbolic geometry, but this
doesn't count, because the original problem calls for a proof from the
axioms of Euclidean geometry.
This argument is shot through with misconceptions, but it does have a
certain logic to it. I've thrashed this out on sci.math before, and
not everyone agrees with my interpretation of vos Savant, but I'm
convinced that the above is what she was thinking, and it's helped me
understand where she's coming from.
David T. Ose:
I would contest your statement that Wiles found a "proof of Fermat's
Last Theorem from the axioms of hyperbolic geometry." The Shimura-
Tanyama-Weil conjectures have little to do with hyperbolic geometry,
although they can be written in the language of hyperbolic geometry,
they are not dependent upon them. This was Vos Savant's biggest
misunderstanding.
Dik T. Winter:
What I understand of Wiles' proof is that it is even not geometric. (I do
not have a copy, but there was somebody who gave an introduction about it,
so I have a minimal understanding.) Perhaps she was misled by the use of
the term elliptic curves (that has nothing to do with elliptic geometry)?
RKinnamon:
I doubt it if Marilyn was "misled" . . . It is still uncertain that Wiles
proof will hold up. I have vos Savant's book and all she says is that
because of the methods Wiles used there may be errors and it may take a
while to verify. And remember, she wrote the book BEFORE Wiles admitted
his error a year ago December.
Aaron Bergman:
She said that [Wiles's proof] was wrong because he used some hyperbolic
geometry, which shows a complete non-understanding of how the proof works, or
even how axiomatic systems are used. And that error [found by Wiles and later
corrected] was completely unrelated to anything she said.
Benjamin J. Tilly:
I have read the book. That book is a joke. If you check, you will find
that she argues that since:
i) You cannot square the circle, and
ii) In hyperbolic geometry you can square the circle,
that
iii) hyperbolic geometry cannot be valid.
Thereby "overturning" over a century of well-established mathematics.
(The error is that the theorem involved in (i) only related to
EUCLIDEAN geometry, and says nothing about what you can or cannot do
with NON-Euclidean geometry. The situation is like my telling you
something about my dog Bob at one time, then something about my friend
Bob at another, and then having you conclude that I have lied to you
since the two comments do not jive with each other.)
In fact she goes on to argue that there is a possibility of disproving
Einstein's theory of general relativity! All of which is complete hogwash.
Oh, and she has yet to admit any mistake, although a variety of people
have written to her, the mathematicians that she referred to having
disputed her comments, and a number of mathematical publications
(the latest being Math Monthly) having published highly critical articles.
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