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December 22nd, 2015, 04:32 AM   #1
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Is trying to prove Fermat's last theorem by an elementary technique pointless?

Is it?

Would it be more fulfilling for me to try to understand the proof by Wiles?

I realise this would take a lot of study.
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December 22nd, 2015, 06:44 AM   #2
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"Is trying to prove Fermat's last theorem by
an elementary technique pointless? Is it?"

Only if one fails to make a point.
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December 22nd, 2015, 06:57 AM   #3
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My point of view is that:
  1. We already have a proof, so at the very least you should gain an understanding of that before you attempt to create your own - how better to properly understand the problem?
  2. Many great minds over the centuries have looked into this problem and failed. If you really want to spend time on this, you owe it to yourself to research the reasons why they failed. Again, this is part of properly understanding the problem and will help to avoid repeating errors of the past.
  3. Personally, I don't believe that there is one. If there were, one of the geniuses of the last centuries would have found it. It almost certainly won't be found by some self-taught amateur playing at home without reference to the literature.
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December 22nd, 2015, 10:44 AM   #4
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Quote:
Originally Posted by v8archie View Post
It almost certainly won't be found by some self-taught amateur playing at home ...
Is that an argument against Fermat having found a proof? He was, after all, an amateur playing at home. He was a lawyer by trade.
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December 22nd, 2015, 11:12 AM   #5
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Quote:
Originally Posted by Maschke View Post
Is that an argument against Fermat having found a proof?
No. But he won't find a proof, and probably never did.
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December 22nd, 2015, 11:34 AM   #6
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Quote:
Originally Posted by v8archie View Post
. . . one of the geniuses of the last centuries would have found it.
That's a reasonable point, but we can't know what the initially self-taught Srinivasa Ramanujan would have achieved had he been born later and lived longer.
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December 22nd, 2015, 02:46 PM   #7
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Quote:
Originally Posted by Maschke View Post
Is that an argument against Fermat having found a proof? He was, after all, an amateur playing at home. He was a lawyer by trade.
And there is no reason to think Fermat did find a proof. The only evidence is an off hand reference written in a margin of a book. But it does appear that he published proofs of the theorem for n= 3 and n= 4 after he wrote that reference. If he had a proof for all n, he would not have done that.
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December 22nd, 2015, 04:01 PM   #8
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Quote:
Originally Posted by Country Boy View Post
And there is no reason to think Fermat did find a proof. The only evidence is an off hand reference written in a margin of a book. But it does appear that he published proofs of the theorem for n= 3 and n= 4 after he wrote that reference. If he had a proof for all n, he would not have done that.
That's probably the best argument against Fermat having a proof. It would be interesting if someone came up with a proof that no elementary proof exists.
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December 22nd, 2015, 07:23 PM   #9
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Amateur hour is almost over.
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January 4th, 2016, 08:17 AM   #10
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Quote:
Originally Posted by mathsman1 View Post
Is it?
Would it be more fulfilling for me to try to understand the proof by Wiles?
I realise this would take a lot of study.
If you feel a push inside to do it you may try as a challenge for yourself. But do not hope to end up with generally accepted proof. Nobody would even read it to the point of fatal error unless it will appear at the very beginning.
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