Re: JSH: Letting it drop

In article <e85s71lm9urvpalrsnaf3uk2hgbqo5lpe5@xxxxxxx>,
JimS <sorry@xxxxxxx> wrote:

>>http://mathforum.org/kb/message.jspa?messageID=412528&tstart=0
>
>:-)
>
>from http://www.maa.org/pubs/monthly_may05_toc.html
>"Along the way we will discover how wrong proofs of Fermat's Last
>Theorem led in part to these developments"
>
>Do you actually name-check James? :-P I *love* irony.

Alas for James, no. "These developements" refers to the developement
of algebraic integers and ideal numbers/algebraic number theory; to
Euler's "proof" for n=3, and Lame's general argument. They both
highlight the problem of unique factorization; some argue quite
vehemently that it was an attempt at making Lame's argument (which was
really something that Gauss, Euler, and Jacobi had tried already, as
Liouville pointed out just after Lame made his announcement) work that
led Kummer to develop ideal numbers. Edwards presents what I think is
compelling evidence that it was really an attempt at proving higher
reciprocity laws along the lines of the work of Guass on biquadratic
and Eisenstein on cubic reciprocity.

But in the Zahlbericht, Hilbert dedicates the very last section to
Kummer's proof of FLT for regular primes and implies it is one of the
most important applications of the theory. While many argue Kummer
agreed but kept saying otherwise because he had failed (saving face in
public), I think I agree with Edwards. Reciprocity laws were in
general much better appreciated it (though of course proving stuff
Fermat had asserted was always considered a feather in your cap,
quadratic reciprocity was still considered Gauss's greatest theorem,
after all).

--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.