Hr.Bommel : " Holy smokes, what is now so difficult about that simple cubic root solution of FLT. "

Each FLT solution in Core (FST* : n^p = n mod p^k for n in core |A_k| = p-1) has the EDS property : Exponent Distributes over a Sum, because (a+b)^p = a+b = a^p + b^p (mod p^k), hence cannot hold for the correponding integers < p^k, all k>1, with their p-th powers < p^{kp}. The cubic roots of 1 mod p^k (p=1 mod 6, a^3=1) form such a solution in core: a + a^2 == -1 , so : a+1 == - 1/a (mod p^k, k>1, a = a^p != 1, a^2=1/a=(a^{-p} ). . . So equivalence for residues can imply inequality for integers . . . breaking the Hensel lift after all.

"I have always been slow to learn the ways of mathematicians and, for most of my life, reluctant to be critical of those with substantial reputations for doing research. In the mid-60's, my former colleague Holbrook MacNeille, who worked for the Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society, remarked often that whereas laboratory scientists were mutually supportive in evaluating research proposals, mathematicians were seldom loath to dump on each other."

"I attached little significance to what he said because at that time most worthwhile research in the United States was funded and there seemed to be enough money for all but the most greedy. Perhaps some nastiness existed, but not on a scale that was doing much harm." - - However, . . .

"Certainly, there are large differences in quality of mathematical research, and all of us agree that some problems are substantially more important and/or difficult than others. This does not justify condemning whole fields of mathematics out of ignorance. Defending a negative view on a subject about which one knows hardly anything is not easily done in public.
Like their racial or religious counterparts, mathematical bigots deny that the workers in the fields they regard as inferior are worthy of any kind of recognition or of having their work read.... Like Galileo's inquisitor, they see no need to look in the telescope."

Subject:      Re: JSH: Webpage statistics
Author:       Nico Benschop 
Organization: Amspade Research
Date:         Thu, 6 May 1999 12:36:39 GMT (sci.math)

[**----------------------------------------------------------------
James Harris announced, in part:

To make sure that someone else doesn't take credit, I've emailed the
correct webpage to several people who will keep it for me.  That was
done several days ago.  Due to the very public nature of my search,
I'm not that worried about credit, but you can't be too careful.

Based on all the evidence I have before me now,
 I feel confident in concluding that I have a proof.  ...[*]
Sci.math has played its role well as always. ____JSH
-----------------------------------------------------------------**]

Re[*]:   OK James, go for it then: send it in for publication! ;-)

BTW: But don't forget my Pub_lemma -- on the likelyhood of a
     correct (;-) proof to be accepted by a respectable math-journal:

 Let math-problem MP have age Y years, be well known by WK % of the
 general math community, and let the proof have complexity index CPX
    (somewhat subjective, depending on # pages and method used;-)
 with an extra "Stigma Index" SI (very high for special problems of
 popular & simple definition like FLT, Goldbach; e.g. Riemann_Hyp
 and Cantor_CH have a lower SI), and some scaling constant k,
 then the probabilty P_acc of acceptance of the proof(MP) is:

 P_acc{proof(MP)} =  k. [CPX / (WK.Y)] 2^{-SI}

In other words: the simpler your proof, and the better & longer known
the problem, the lower your chance of acceptance and publication is!
(assuming the proof is correct, of course..).

My estimate of P_acc for a simple proof(FLT) is about zero, due to
its very high denominator: WK = 100%, Y = 360, and high SI value.
Only because of Wiles' extremely high CPX proof did it pass, plus
the fact that he did actualy prove something else [EC = MF] much
more constructive than the FLT inequality:
        after all, *what* can one *do* with an INequality ?
(well, actually more than you think,
 see  FLT is anti-closure of n^p (+) ;-)

That Pacc is proportional to proof complexity CPX requires some
psychological insight: the higher CPX the easier it is for the math
community to admit it was not found earlier (very high CPX is a
perfect excuse) cq: a clear & simple proof is highly suspect and
makes it especially difficult to admit being not found by anyone
in the profession...    Another tip: a simple proof of a difficult
problem almost certainly will not be found inside the establishment,
since some essential concept must be missing in the known attacks;-)

Re: "Euler's trick":
  -------- If a problem is really too hard: generalize it ---------
 (expand it's context, to see a way around it for a better approach)

So good luck James, give it a try anyway ;-)

Ciao, Nico Benschop -- http://www.iae.nl/users/benschop

NB:  Published short and direct proof of FLT, in:
  Acta Mathematica Univ.Bratislava (Nov.2005, p169-184)
  Online at FLT proof 

Re: Beyond residues: the role of 'carry' for integer arithmetic:
                       http://www.iae.nl/users/benschop/carry.htm
                       http://www.iae.nl/users/benschop/ferm.htm
Re: Your open letter to Wiles (june98): modular-forms vs. 'functions':
                       http://www.iae.nl/users/benschop/sgrp-flt.htm

____________ If stuck@closure(mod...), use the carry ______________
                  FST --> FST* --> EDS --> FLT