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Old 2005-08-22, 12:49   #1
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Default 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
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Old 2005-08-22, 12:58   #2
R.D. Silverman
 
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Quote:
Originally Posted by ET_
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
I am sure that it is horses**t.

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???
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Old 2005-08-22, 13:19   #3
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Quote:
Originally Posted by R.D. Silverman
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.
I suspect the main reason is that Fermat claimed to have a proof. IFhe had a proof, it was almost certainly elementary and could be rediscovered.

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
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Old 2005-08-22, 13:32   #4
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Quote:
Originally Posted by xilman
I suspect the main reason is that Fermat claimed to have a proof. IFhe had a proof, it was almost certainly elementary and could be rediscovered.

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

(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.
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Old 2005-08-22, 13:44   #5
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Quote:
Originally Posted by R.D. Silverman
I am sure that it is horses**t.

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"?
"A new hope" is the original title of one of the movies from Star Wars' endless saga My intention was to point out the continuous and hopeless claim of cranks...

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:
Originally Posted by R.D. Silverman
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.
I was just looking for information. After Wiles' discoveries I accepted the idea that no elementary proof could exist.

I would have (eventually) been fascinated by finding out the error in the claimed demonstration.

Quote:
Originally Posted by R.D. Silverman
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???
Now, that IS fascinating!

Luigi

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Old 2005-08-22, 13:54   #6
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Quote:
Originally Posted by ET_
"A new hope" is the original title of one of the movies from Star Wars' endless saga My intention was to point out the continuous and hopeless claim of cranks...

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.



I was just looking for information. After Wiles' discoveries I accepted the idea that no elementary proof could exist.

I would have (eventually) been fascinated by finding out the error in the claimed demonstration.



Now, that IS fascinating!

Luigi
"I accepted the idea that no elementary proof could exist."

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*.
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Old 2005-08-22, 14:02   #7
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>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
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Old 2005-08-24, 09:09   #8
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Default 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
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Old 2005-08-24, 09:35   #9
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Default very strange

I have search in all the web and the only web-site that talk about the russian Aleksandr Ilin and and his proof on the newspaper Novaya Gazeta are italian.
Summer news?

ciao

Fabiano
Torino - Italia
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Old 2005-08-24, 09:41   #10
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Quote:
Originally Posted by Unregistered
I have search in all the web and the only web-site that talk about the russian Aleksandr Ilin and and his proof on the newspaper Novaya Gazeta are italian.
Summer news?

ciao

Fabiano
Torino - Italia
Maybe! I'll try to look further. I read the news on Repubblica and then visited Novaye Gazeta. If I find something I'll post.


Ciao

Ivan
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Old 2005-08-24, 10:43   #11
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Default 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 ninth-grader 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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