20050822, 12:49  #1 
Banned
"Luigi"
Aug 2002
Team Italia
29×167 Posts 
Fermat's Last Theorem: a new hope
Today I read that a Russian academic, Aleksandr Ilin, redemostrated FLT using onlu three lines, and published his result on the Novaya Gazeta
Has anybody any news about it? Luigi 
20050822, 12:58  #2  
"Bob Silverman"
Nov 2003
North of Boston
7464_{10} Posts 
Quote:
I'd like to ask you a question: When you write "a New hope", what do you mean? FLT has already been proved. So what is the "new hope"? If you are looking for an elementary proof, allow me to say that I never understood the fascination people had for finding an elementary proof. Please explain the fascination. The connection between the Fermat equation, elliptic curves, and modular forms shows that the unsolvability of the equation has roots buried very deeply within arithmetic. So why do people continue to prattle about what is now a solved problem??? 

20050822, 13:19  #3  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11×1,039 Posts 
Quote:
Fermat made many conjectures (statements he believed to be true but for which he didn't have a proof) and almost without exception they were later shown to be false. He also made many statements for which, although not giving a formal proof, he claimed that he had such a proof. Without exception, I believe, proofs have been found for them. FLT is one such. Whether Fermat actually had a proof of FLT is likely to remain unknown. If he had one I would have expected it to have been rediscovered some time in the last three centuries. My believe is that he had a plausible line of reasoning which contained one or more subtle errors. Paul 

20050822, 13:32  #4  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·3·311 Posts 
Quote:
(1) What is often overlooked is that Fermat actually *published* a valid proof for n=4, *AFTER* he left his note about a general proof in his notebook. Why would he do this for a specific case, if he had a general proof? (2) I do not understand why Fermat's private, unpublished note to himself should stir up so many kooks, loons, cranks, and incompetents. The fact that he never went *public* with his "proof" should tell people that Fermat probably realized himself that he was mistaken. 

20050822, 13:44  #5  
Banned
"Luigi"
Aug 2002
Team Italia
4843_{10} Posts 
Quote:
There was no information on Google, so I suspected it was just another crazy claim; this forum is the best place to be sure about it. Quote:
I would have (eventually) been fascinated by finding out the error in the claimed demonstration. Quote:
Luigi Last fiddled with by ET_ on 20050822 at 13:45 

20050822, 13:54  #6  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×3×311 Posts 
Quote:
I am certainly very skeptical about the existence of an elementary proof, given the large effort already expended, but I make no claim that an elementary proof does not exist. I merely think it highly improbable and *not worth pursuing*. 

20050822, 14:02  #7 
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
>I merely think it highly improbable and *not worth pursuing*.
I don't quite agree with the last statement, at least in its absolute form. I, for one, would very much enjoy reading a proof of the (justly or unjustly is a matter of taste) famous FLT that does not require a lifetime of study of elliptic curves and modular forms to understand. I agree that people should stop devoting their lives to finding proofs of FLT. But if someone comes up with an elementary proof for the rest of us to read, more power to him! Alex 
20050824, 09:09  #8 
Aug 2005
Milan  Italy
5 Posts 
Anyway
I wrote demonstration on the russian gazette, but unfortunately I didn't understand a lot, for translation problem I think. It seems to be a very simple demonstration process, based on trigonometry. Is it possible that alla over the internet there is not yet any comment about it? Has anyone of you found something. Please let me know. Just one line on "elementary or simple demonstration". I have ever thought that mathematics has also an estetical appeal. If you try to think about it, it's quite simple to understand why a simple demonstration can be more satisfactful than an other one...
Ciao! Ivan 
20050824, 09:35  #9 
2·3·1,381 Posts 
very strange
I have search in all the web and the only website that talk about the russian Aleksandr Ilin and and his proof on the newspaper Novaya Gazeta are italian.
Summer news? ciao Fabiano Torino  Italia 
20050824, 09:41  #10  
Aug 2005
Milan  Italy
5_{10} Posts 
Quote:
Ciao Ivan 

20050824, 10:43  #11 
1107_{10} Posts 
Automatic proof translation from Novaya Gazeta
So, it is required to prove, that if X and Y  integers in equation X n + Y n = Z n, Z, at n it is more 2,  always not the whole. Before to undertake for the Farm, we shall repeat theorem Pifagora: " the Square of a hypotenuse is equal to the sum of squares of cathetuses ". We have the right to use any variables for its writing. We shall write down it thus: X 2 + Y 2 = R 2, where X, Y, R  integers, and Z, the Farm,  not approves the whole. We shall try to prove. Clearly, Z it is not equal R at the same X, Y. Legkodokazuemo algebraically, and simply logically, that Z always it is less, than R. When we erect X and Y in higher degree we multiply them by themselves. Then them we put and we receive Z in the same degree n. And at erection in it R each of composed should be increased on R which is more, than X and Y.
For example, R 3 = (X 2 + Y 2) R = X 2 R+Y 2 R. What does Ilyin do? Anything especial. Writes down lengths of the parties of triangle XYR in a trigonometrical kind: X = R sin A, Y = R cos A. So, Z n = X n + Y n = R n (sin A + cos A). What is the root, you have not forgotten? Perfectly. Z = R ?sin A + cos A. Earlier we have proved, that Z always it is less R, so, sin A + cos A <1. Such trigonometrical function can be found in any textbook of mathematics of the senior classes and to be convinced under the schedule or the table, that if value of function <1 corner A is more than 60 and less 90 degrees. And what will occur in this case to a right angle In, being between cathetuses? It more any more will not be to straight lines and it will appear in the same limits: 60 o <B <90 o. Not without reason in fact " ninety, sixty, " it is considered ninety an ideal of harmony. It is a silly joke that you have a little relaxed. Because we are already close to finish. Any ninthgrader at whom on the mathematician above a three, straight off will reproduce to you the formula of a parity of the parties of triangle Z 2 = X 2 + Y 2  2 XY cos B. We shall consider expression. At 60 o <B <90 o cos B  number not the whole. So, and Z inevitably is those at whole values X and Y. As was to be shown. 
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