Do you think that Fermat had a genuine proof for his last theorem?

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Discussion Overview

The discussion centers around whether Pierre de Fermat had a genuine proof for his Last Theorem. Participants explore various perspectives on Fermat's beliefs, the nature of his work, and the implications of his lack of published proofs. The conversation includes historical context, interpretations of Fermat's writings, and speculation about his intentions.

Discussion Character

  • Debate/contested
  • Historical
  • Conceptual clarification

Main Points Raised

  • Some participants believe Fermat had a proof he genuinely believed in, though its correctness is uncertain.
  • Others argue that Fermat could not have had a valid proof due to the advanced mathematics required to prove the theorem, which he likely did not know.
  • One participant suggests that the margins of Fermat's book were too small to contain Wiles' proof, implying that Fermat's proof may have been different.
  • Another viewpoint is that Fermat had ample time to publish a proof but chose not to, indicating he may have doubted its validity.
  • Some participants speculate that Fermat might have only proven specific cases of the theorem and that he might not have intended to claim a general proof.
  • There is a suggestion that Fermat's margin note could have been misinterpreted, leading to the belief that he claimed a general proof.
  • One participant recounts a personal misunderstanding of the theorem, highlighting the complexity and confusion surrounding it.

Areas of Agreement / Disagreement

Participants express a range of opinions, with no consensus on whether Fermat had a genuine proof. Multiple competing views remain regarding his intentions and the nature of his claims.

Contextual Notes

Some claims depend on interpretations of Fermat's writings and the historical context of his mathematical knowledge. The discussion reflects uncertainty about Fermat's motivations and the completeness of his proofs.

Do you think Fermat had a Genuine proof for his last "theorem"?

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Georgepowell
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Yes or No?

And why do you think that?
 
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I think he had a proof he believed in. Whether it was correct or not I couldn't say, but I don't doubt Fermat's belief that he had one.
 
No, definitely not. It was barely proved using the latest mathematical achievements that Fermat definitely didn't know. Unless mathematicians overlooked a simpler possibility of proving it, which I doubt. As far as I know, however, mathematics so advanced was required to prove there were no solutions to the theorem, that Fermat with only beginnings of calculus as his tools could not possibly have a proof.
 
The margins of Fermat's book were not large enough to contain Wiles' proof, so it is likely that that was the proof Fermat had in mind.
 
jimmysnyder said:
The margins of Fermat's book were not large enough to contain Wiles' proof, so it is likely that that was the proof Fermat had in mind.

Are you an idiot or are you joking?
 
Georgepowell said:
Are you an idiot or are you joking?

:smile: Do you really have to ask?
 
Kurdt said:
:smile: Do you really have to ask?
Well?
 
jimmysnyder said:
The margins of Fermat's book were not large enough to contain Wiles' proof, so it is likely that that was the proof Fermat had in mind.

:smile::smile::smile:
 
Not a chance. Fermat had plenty of time to publish (or at least write) such a proof, but he didn't. Instead, he proved only a special case of FLT... a good indication he changed his mind about the correctness of the proof he had in mind.
 
  • #10
I don't doubt that he was able to prove it successfully for the first few integers([itex]x^3+y^3 \neq z^3[/itex] etc), but if he believed that he had a general proof, it was probably flawed.
 
  • #11
nooo way unless there's a really simple proof which is unlikly...
 
  • #12
Wouldn't he have published it if he did find out the answer?
 
  • #13
bassplayer142 said:
Wouldn't he have published it if he did find out the answer?

He didn't publish the proofs of his other theorems. And they all turned out to be correct. From what I have heard, he didn't do maths to help the mathematical community. He just did it for fun, and as soon as he got the essence of a problem, he went on to do another one without checking it.

He often told people he had proofs to problems, and then didn't tell them the proof on purpose. Just so he could watch them fail and feel better about himself.

So he wouldn't of published it, he never published his proofs.
 
  • #14
But then why would he publish a proof for a specific case (n= 3?) if he had a "simple" proof that would work for all n?

I think what happened is what happens to all of us- he thought that the had a brilliant, simple, proof that, when he actually started working out the details, turned out not to work.
 
  • #15
I tend to favor the theory that his "truly marvelous proof" alluded to was just a proof for the n=3 case. At least in the common english translation it seems easy to interpret Fermat's famous margin note such that the "or in general..." was just an aside and Fermat was not even trying to say he actually had a proof for the general case. I guess that leaves me voting no.
 
  • #16
The first time i heard about this theorem I was probably 13 or 14 and I mistakenly thought it was saying a^n + b^o cannot equal c^p. for every number bigger than two. I knew that couldn't be true and actually spent a little while proving it wasn't true. Then got into an argument with my teacher telling her she was wrong.
 
  • #17
Was it possible that he never even claimed he had a general proof? And we just misinterpreted him?
 

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