Talk:Fermat's Last Theorem/Archive 1

message: Why was this page moved to a lowercase title? Fermat's Last Theorem was not Fermat's last theorem - in fact, it wasn't one of his theorems at all. --Zundark 12:43 Oct 30, 2002 (UTC)
: See Wikipedia talk:Naming conventions (theorems)
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Is it not inconceivable that Fermat was joking about the proof fitting into the margin?  Surely he proposed the equation based on a hunch he had but the proof eluded him - effectively laying down the gauntlet for others to attempt a proof.
Surely, mathematicians have a sense of humour too?
Natalinasmpf: Well, for one, Fermat's notes were in his private copy of the Arithmetica. I do not think he would be laying down the gauntlet when it was kept secret, and thus probably not intended for public display. 
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I agree, FLT should be all uppercase.  No big deal though.
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Fermat may have thought that he had the proof when he wrote the note in the margin--there are ways to "prove" the theroem that are now known to be wrong, and Fermat may have done one of them and later realized his error (which would explain why he never published his proof).
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What does worked "in isolation", regarding Wiles, mean exactly?  It's utterly meaningless and misleading.  Wiles had plenty of human contact during that period.  Not only that, he found time to advise Ph.D. students, interact with other faculty in the department, and publish several important papers!
Certainly he kept his work on FLT secret but is that a sign of isolation? Let's not let the Wikipedia degenerate into recopying exaggerated statements made in the popular media.
:Since nobody has responded to my comments, I am going to adjust the entry.
Theres an excellent book on the subject, called Fermat's last theorem (funnily enough!) by Simon Singh if you want to learn the full history of the subject and Wiles eventual proof.
:Yep, it's great, I've read it mroe than once. And it's listed in the article in the Bibliography section. ✏ Sverdrup 17:12, 12 Oct 2004 (UTC)
replies: text: OK, but I would still add the fact that a short version of the theorem is still the focus of many because the way this section of the article is structured, one gets the impression that the writer(s) disbelieve that Fermat ever did have a short version. If you want, you can modify the sentence I added and take away any reference to Ilyin and merely state that many people are still looking for this shorter proof and that many people still believe it exists. 07:53, 24 August 2005 (UTC)
thread_title:  Old or undated discussion 

message: :Proof claims not coming from within the mathematical establishment traditionally meet with some hostility. Rejection of unsolicited papers without reading is often enough used by leading mathematicians to defend their time.
What does this mean? Does it really have anything to do with FLT, and is it NPOV? --80.3.32.6 22:06, 21 Jan 2005 (UTC)
replies: text: I've noticed this as well, and was about to list it for deletion in this talk page. Seeing that other people are baffled as well, I have removed this sentence. -- Itai 13:16, 24 Jan 2005 (UTC)
thread_title:  Did Fermat Have a Proof (2)

message: In the "Homer in 3D" story from Treehouse of Horror IV, a four-digit disproof of FLT is just one of many mathematical easter eggs in the abstract space Homer discovers behind a bookshelf. counterexample
:a.  Wiles proved Fermat's Last Theorem.  If his proof is correct, no disproof can be found.  As one who is not an expert in the field, I accept that his proof is correct, because hordes of number theorists, group theorists and other assorted mathematical geniusses will have pored over his paper for hours; and because he had to correct an error in it.  So it's been through that rigorous process and had to have changes made already.
:b.  If a disproof could be found that simply, do you not think people would have given up a while ago?
:c.  The claimed disproof is not, because it's false, as a simple check will show.  The identity given (for others' reference) is
::1782^12 + 1841^12 = 1922^12
:Now, the last digit of 1782^12 will be the same as the last digit of 1922^12, as both end in the same digit (in fact, it is 6).  But the last digit of 1841^12 is not zero (in fact, it is 1).  So the left-hand side ends in a different digit from the right-hand side.  Your identity is not.  As for P = NP, well, the jury's still out on that one.  Wooster 11:51, 19 July 2005 (UTC)
thread_title:  The Simpsons 

message: ::Actually, there are only three number theorists who supposedly went through Andrew Wiles "proof", Ribet, Mazur and Zarnak.
::The main problem with Wiles approach is that he jumped into the problem without looking at the status of the underlying fields, namely, foundations, particularly, mathematical reasoning, number theory and the real number system. I have discussed those elsewhere on this page. One requirement for a consistent mathematical space is that every concept must be well-defined, i.e., its existence, properties or behavior and relationship with other concepts are specified by the axioms. In the case of a decimal every digit must be known or computable, i.e., there is some algorithm or rule that determines it uniquely. Most of the real numbers do not satisfy these requirements. There are other defects of the real numbers that I have already discussed elsewhere on this page. Consequently, the real number system is ill-defined and any problem formulated in it including FLT is also ill-defined and nonsense. Therefore, any proof of it does not make sense. 
::The first crucial step in the resolution of FLT is an overhaul of these underlying fields which I did the essential parts of which I have discussed elsewhere on this page. However, interested viewers may look at the original sources listed elsewhere here as well as the relevant articles on my website, http://home.iprimus.com.au/pidro/  . I shall be glad to answer specific questions that I have not answered yet on this page.       E. E. Escultura   
I have removed the following paragraph
:Amazingly enough,  if his original proof had been correct he most certainly would have won the most famous award in mathematics,  the Fields Medal.  However mathematicians must be under 40 years old to receive the award,  which he had passed by the time the successful proof was submitted.
Andrew Wiles was born on 11 April 1953. He presented the original (incorrect) proof June 21-21 1993. Therefore he was over 40 years old when he presented the original proof and hence ineligible for the Fields Medal.  --Etimbo | Talk 13:29, 6 Apr 2005 (UTC)
replies: text: For what it's worth, the Fields medal may be awarded to any mathematician no older than 40 in the year the prize is given: for example, Perelman was 40 this year.  So if the Fields were given in 1993, it would have been fine; however, he would have had to wait a year anyway, so he wouldn't have gotten it. Ryan Reich 21:06, 13 October 2006 (UTC)
thread_title:  [[Fields medal]] 

message: As I understand it, there are thousands of false-proofs for the FLT. I am trying to collect some of them.
They are very interesting, from an educational point of view, because you can see what are the most common deduction errors people make.
In the net I haven't found much information (sites about the real proof are aboundant, and probably not many people cares about false deductions).
Do you have some references?
I will appreciate an email: H. Flores "rotceh1974@yahoo.com.mx"
:Try the sci.math newsgroup. Charles Matthews 16:46, 8 September 2005 (UTC)
thread_title:  Looking for false proofs. 

message: So, what is the connection to Gödel's incompleteness theorem? I lent out Singh's book, so I can't check it there. Our article on Gödel's incompleteness theorem does not mention Fermat, so a link does not seem very useful, even if there is a connection. The only think I can think of is speculation like "wouldn't it be cool if FLT was actually unprovable?" (before Wikes' proof). -- Jitse Niesen (talk) 23:40, 6 December 2005 (UTC)
replies: text: Before Wiles' proof, FLT was often used as an example of a theorem that might be undecidable, in the sense that it might have had neither a counterexample nor a proof. Of course, now we know there is a proof for FLT - and the role of "most popular candidate for an undecidable theorem" seems to have been taken over by Goldbach's conjecture. I can't see any current connection between FLT and Gödel's incompleteness theorem. Gandalf61 09:44, 7 December 2005 (UTC)
replies: text: Douglas Hofstadter connects them in his book Gödel, Escher, Bach.  There, on of his characters (the Tortoise?) states that he has proven the FLT to be undecidable.  I don't suppose Hofstadter actually belived FLT was really undecidable, rather he used it as an example, as you mention above.  Take all this with a grain of salt though as I don't have the book and read it (the translation in fact) long ago. -- B jonas 15:01, 14 December 2005 (UTC)

text: Actually, none of the comments above seems to push for inclusion. And I agree with too, and would just remove it. It can only confuse a reader who will think that there is some link between the two topics. Schutz 18:01, 14 December 2005 (UTC)
replies: text: There is a link, see what is now the bottom of this page. 71.198.169.9 10:26, 29 March 2006 (UTC)
thread_title:  Link to Gödel's incompleteness theorem 

message: I removed the following paragraph (contributed by an anon) from the main article because it is unsupported and difficult to follow. If anyone can find a reference and re-write it in a more intelligible manner, it could be re-inserted ... Gandalf61 14:28, 24 February 2006 (UTC)
replies: text: Probably Fermat studied the powers of integers as sums of adjacent nexus numbers.  If a table of power of n is written in form  1+ (2^n-1^n) + (3^n-2^n) + etc. + [X^n - (X-1)^n],  i.e.  1+ sum of adjacent nexus numbers,  it can be noticed that a difference of the same power of two integers is always a nexus number or a sum of adjacent nexus numbers.  Also it can be noticed, that only in the table of squares (n=2) there exist squares of integers among the nexus numbers and sums of adjacent nexus numbers.  Opposedly, in the table of cubes (n=3) there are never cubes of integers among the nexus numbers and sums of adjacent nexus numbers.  Accordingly, in the power tables higher than cubes (n>3) there are never powers of integers among the the nexus numbers and sums of adjacent nexus numbers, since the powers higher than cubes are actually lines of cubes.  Thus a difference or a sum of the same power of any two integers can not be the same power of third integer, if n>2.
Apparently,  any references can not be found, but FLT seems self-evident if power sequences are compiled as sums of nexus numbers:  Reading of powers always start with 1+ etc. while the differences always consist of only a right end fraction of the nexus sum representing the power of n of  the larger integer.  Can you formulate it more intelligible manner?  The nexus line may really be the "demonstrationem mirabilem" which was too large to be presented on the margin of Diophantus. Demonstration may be presented as shown below:
Powers of n |------------->----------->------------------>------------------------------------->
 X^n  =        1 + (2^n - 1^n) + (3^n - 2^n)+ etc.+ [Y^n - (Y-1)^n] + [(Y+1)^n - Y^n]  +etc. + [X^n - (X-1)^n]
                          |<-------<----------<-------------------<-------------------------------------|  Differences of powers
84.231.37.189 08:53, 26 February 2006 (UTC)
thread_title: Nexus numbers paragraph

message: Shouldn't this be renamed "Wiles's theorem"? —Keenan Pepper 16:31, 24 March 2006 (UTC)
replies: text: The theorem? Sure, if you ask me. But not the article. FLT is the most common name by far. Fredrik Johansson 16:47, 24 March 2006 (UTC)
thread_title:  Name 

message: Essay moved to User:BenCawaling/Essay. Gandalf61 08:26, 14 April 2006 (UTC)
replies: text: It is clear that you are not a learned mathematician nor are you familiar with "proof by contradiction" (in fact, I was merely restating Cantor's theorem's "proof").  It would certainly help if you read and understand what you are commenting on ... [BenCawaling@Yahoo.com]BenCawaling 09:09, 2 June 2006 (UTC)
thread_title:  About the incomplete totality of the set of all prime natural numbers 

message: The article claims that the LHS and RHS are different "within a billionth of each other" - that doesn't sound right. A billion is at most 12 (13) digits, and the numbers differ by more than that. Zyxoas (talk to me - I'll listen) 19:46, 25 April 2006 (UTC)
replies: text: The relative difference 1-1/(x-y) is 3 × 10-10, or one-third part in a billion (109). Count digits from the top. Fredrik Johansson 20:20, 25 April 2006 (UTC)
thread_title:  The first Simpsons counter-example 

message: What? No mention or discussion of Andrew Beal and Beal's Conjecture?
Pariah23 21:44, 11 February 2006 (UTC)
replies: text: Actually, the counterexamples to FLT are also counterexamples to Beal's Conjecture. E. E. Escultura
I think a bigger omission is that it ought to mention somewhere in the first paragraph that Wiles has proven it! If I don't see an objection I will add that.
Gene Ward Smith 22:26, 3 May 2006 (UTC)
thread_title:  Omissions? 

message: I strongly remember reading in a book titled Fermat's Last Theorem many years ago that over the years half a dozen or more mathematicians have commited suicide over the problem. I do not know wether this is true (I always assumed it was), but if any of you pros know more about it I think it should be added. J. Stoever 85.197.25.135 15:26, 23 July 2006 (UTC)
replies: text: I think I've heard that. If it is true then I think it should be added, because work on FLT has had hudge affect on various people and society(unsure). Timothy Clemans 22:25, 23 July 2006 (UTC)
thread_title:  Dead mathematicians ? 

message: Why not just do a section on elementary proofs instead of did the guy who inspired all the work on FLT write an elementary proof that was valid and yet many people just have not rediscovered such a proof. There are more important things to be working on in this article like fixing the references section and math formulas. Timothy Clemans 07:14, 24 July 2006 (UTC)
thread_title:  Fermat's proof stuff is annoying me 

message: a^n-b^n=c^2-d^2 like 
7^3-4^3=48^2-45^2,
x^n=z^2-y^2 like
3^3=14^2-13^2,
a^n-b^n=(a-b)^n+nk(a-b), here when "a" is any natural number "b" is any natural number other then the same value of "a" and "n" is any prime then "k" will always be a natural number.
from the above information we can prove very easily and in an elementary way that it is impossible to write 
                                           a^n-b^n=x^n
                                                 or
                                           a^n=x^n+b^n
                                                for n>2.Bhowmickr 14:32, 26 August 2006 (UTC)
replies: text: If you would like to explain your proof here, I am sure there are many people here who will explain why it fails. Madmath789 13:22, 26 August 2006 (UTC)

text: what if it doesnot fails.Bhowmickr 14:32, 26 August 2006 (UTC)

text: Please, let's not respond to this troll. Ryan Reich 14:05, 26 August 2006 (UTC)
replies: text: Actually I'm mildly interested. Bhowmickr, please supply the missing portion of your proof so we can discuss it. We can take it to my talk page if people object that we're not talking about how to improve the article. —Keenan Pepper 02:05, 30 August 2006 (UTC)
thread_title:  simple and elementary proof of fermats last theorem is possible. 

message: This talk page is now 91KB in size. Please could someone who knows how archive all inactive discussions. Tompw 19:09, 7 October 2006 (UTC)
replies: text: Done.  There are instructions at WP:ARCHIVE. CMummert 00:55, 17 November 2006 (UTC)
thread_title:  Please split talk page up 

message: People worrying about what happened to the original proof by Fermat and what it could have contained can take comfort in that the proof might never have existed. Fermat could have been lying, or his proof could have been erroneous. JIP | Talk 12:00, 23 November 2006 (UTC)
replies: text: I'm not clear on how this would give anyone comfort, or why you think that anyone might not have considered this before you suggested it. -- Jibal 06:03, 29 December 2006 (UTC)
thread_title:  Fermat's original proof