Registered: Dec 2004
Short proof of FLT
If you are serious, you should certainly typeset your brief proof and send it as required to Library of Congress for your copyright. Don't share it with anyone until you copyright it. You can also self-mail the manuscript in a sealed envelope (sealed officially by the post office). The manuscript needs to be dated by the post office and then when you receive the manuscript, put it in a very secure location. This is supposedly a method of self-copyright that is widely accepted as valid.
My Fermat manuscript is in limbo after having been published by WSEAS in July 2004. I am not sure that many readers understood my method, but I believe it is workable if carried out rigorously in accordance with the legal stipulations.
I recently submitted the Fermat (FLT) paper and my 2005 paper on Goldbach to a research journal in Sept. 2006, but have had no response yet. The papers were acknowledged as having been received by the journal editor, but I do not yet even have verification that the papers were then forwarded to any math referee(s). Because of this 6 month delay without any reply I may be forced to give up on the journal and try to submit elsewhere. However I would prefer to allow plenty of time for editors and referees to look at these papers.
As readers of NKS Forum may know, it is a bit difficult to publish a paper that has already been published and withdrawn from another journal without the slightest math critique forwarded to the author! In fact this is a gray area from hell, which I hadn't even considered as a remote possibility.
The Collatz paper is still not published and not critiqued in any mathematical sense because the referee who previously looked at it simply stated that my proof was not a proof. He or she stated that my proof of the Collatz conjecture is simply a drawing and a proof claim without verification. However, the drawing is more than just a drawing in that it is "fully generalized," i.e., applicable to any and all true cases of the conjecture.
This full generalization combined with a logical argument is in itself the proof argument; yet this argument and method was not explored or "deconstructed" as they say, in the "critique" provided by the math editor. Therefore, I can say that my Collatz paper has not yet received any math critique, whatsoever.
It is not surprising that my papers are treated contemptuously. Certainly if I were a highly trained and qualified mathematician, I would most likely give little credence and take little time with anyone who claimed a short proof of Fermat's Last Theorem, the Goldbach Conjecture, and the Collatz Conjecture. (This is "blasphemy" in mathematics, and the word is not overly dramatic to use when one experiences this difficult situation.) However, having published a paper, I would have hoped for a math critique from one or all of the papers I had submitted, especially the one which was published and then withdrawn under threats of boycott by library subscribers. (Apparently there were secret or sneaky critiques, but none of the critiques were shared with me.) I fully understand this. People have disdain for my paper on Fermat's Last Theorem, and I simply want to see the arguments against my method and see if I can improve my work. I do not doubt that I can be wrong.
Similarly, in a brief comment regarding my paper on the Goldbach Conjecture, a referee said that my paper stated the method is fully generalized, but did not prove that the method is generalized. In fact that referee said that I had provided a proof for only one number, an even more blatant insult. But the method is indeed generalized, was clearly designed as a fully generalized method, as stated in the abstract, and that is exactly what it is. I can show this full generalization, and did show it, in an addendum provided in June 2005; and via the full generalization we proceed directly to a simple proof! This is astounding to me as well as to anyone who reads the paper. I don't blame people for being puzzled by the impossible.. However the editors of that journal had by then precluded any further consideration of my Goldbach paper, and I was not allowed to have my rebuttal read by the referee. (My rebuttal was criticized for being confusingly written.) But every step of my rebuttal is, or should be, very easy to develop from the method given in the full manuscript. Here's the problem: The ease and clarity of any proof of an ancient mathematical problem is the terrifying mental block which the referees face. They must work around it or just avoid it by rejecting the manuscript without critique. So this is a common problem in math, and partly explains why more and more complex proofs in mathematics are developed even for "simple" or "simply stated" problems. The "simple" or simply developed arguments and methods to prove such problems, are then "the problem" that must be destroyed or ridiculed "by any means necessary." I don't know if this is clear to NKS readers, but "simplicity" on what is acknowledged to be a fiendishly difficult problem in number theory, is simply "blasphemous," and is aggressively treated as such.
An attempt to finalize a proof on the Beal Conjecture hit a real snag, because I was very hasty and neglected to test my method completely and use proper diagramming techniques. However, I believe my general approach was initially sound but not adequately developed through all the stages necessary for full generalization and for a full proof. So in that case, the referee(s) were completely correct, and I am presently focusing my efforts on the Beal Conjecture, because I view it as the "next" problem that is appropriate for me to attempt, and because I see my work on FLT and Goldbach to be completed unless and until a math critique on those papers arrives for my further consideration. I don't know how to respond to nonexistent math critiques though; this is very painful and difficult. (And I believe other FLT provers out there may have faced the same difficulties in the past; I only know my own method to the extent possible at this time, and only want to complete or improve it, rather than working through "simple" FLT proof attempts by others. This is because I am not really a mathematician, rather, a hobbyist and an amateur, and my FLT proof was developed for the sole purpose of proving FLT, not as a pinnacle of my achievement in the field of number theory, etc.
Interestingly, it was in the case of my Beal paper that the referees provided enough feedback to indicate where the proof broke down; I may have similar embarrassing experiences if referees will show where my other proofs may break down. Anyway, I am still willing to try to improve these papers.
I cannot send out copies of any math papers now because two are submitted to a publisher and the others are in early development.
I seriously doubt that any math experts are even looking at my work. Anyway I will be glad to correspond with amateur mathematicians on these topics, although I may not want to be very detailed at this point.
Copyright everything though, that's one thing you learn as soon as you write anything at all of import, you are surrounded by ripoff artists and scoundrels.
My FLT paper was started in 1980, was submitted to two journals and published in the second one it was submitted to. I never copyrighted or submitted any other math paper previous to this one that I published in July 2004.
Drawing a 2D square area to map or represent a number is all it takes. Try it. Use this on 5^2, 6^2, 5^100, 6^100. Represent these values as 2D square areas. Then start thinking...
A trained mathematician will say, well you cannot draw a square to represent 5^100, because a square would be 5^2. This is "rote learning." This is where the stipulations come in. We stipulate certain facts for certain reasons, in order to generalize and attack a problem.
Furthermore, a mathematician will say, you cannot hold x,y constant in the given equation of FLT, because the diagram sizes change as the exponent increases (when the large terms x^n, y^n, z^n are drawn as or mapped as square areas). Well, a mathematician who cannot allow a simple stipulation in an engineered proof argument, is not a mathematician at all. I can say this: a square area containing 5^2 square units is smaller than a square area containing 5^100 square units, or a square area containing 5^1,000,000,000,000 square units, but the root is the same. The root is 5. This 5 is what we may view as a constant in an array of nested, geometrically equivalent squares with constant vertex at one corner. These overlapping diagrams share the same root of 5 units. So in my paper I presented the stipulation that the x,y values will be held constant; they may be any positive naturals, and may differ "vastly" in value, but they must be held constant in the method of my proof. ("Vastly" is an understatement. Perhaps readers of my paper assumed that I had considered only constants x = 3, y = 4, which I used in my example. However, these values may differ by counts equalling all the grains of sand in the universe. This is the beauty of a "fully generalized approach" in number theory. But none of this was stated in my published paper in WSEAS July 2004 (later withdrawn by the publisher).
Certain aspects of my nested diagram system may be only somewhat clear or developed by myself as author. I do not know if any of the readers understood the implications of the "fully generalized" nested diagram method which I have shown in my paper. For example, with constants x = 3, y = 4, as exponent n approaches positive infinity, the value of z decreases toward min of z = 4 when n = +infinity. This may seem bizarre but it is useful under further stipulated and engineered arguments for this proof. Similarly, if x = 3, and y = 1,000,000,000,000,000,000, then as exponent n increases without limit, the value of z decreases toward min z = 1,000,000,000,000,000,000 which is what y is held constant as. In other words, the generalized proof approach gives a geometrically useful method of proof! I don't know why others don't see this as "interesting." But, this method works only if the two smaller areas of the diagram are averaged! It took me a good 17 years to go from the first diagram to the second, averaged diagram, and then when published in WSEAS, neither diagram printed correctly, because of a color/B&W printing error in typesetting (I take full responsibility.) So the puzzle is one in which the target of full generalization was developed and attacked over a period of roughly 20 years (1980-2000 approx, with a 3 year hiatus 1990-1993 because I started thinking I was getting obsessed with FLT). (I restarted a few months before I heard about Andrew Wiles's proof.)
The use of "full generalization" and holding some values as constants, was emphasized by Polya. I don't claim to know anything about his advanced work, but I did notice that emphasis in one of his books in 1980. Of course my published paper on FLT fully utilizes these two key methods; without them, there is no proof possible whatsoever.
Thank you for reading this.
Last edited by jay dillon on 03-07-2007 at 03:51 AM
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