MHB Fermat's Theorem: Did Fermat Have a Proof?

[Fermat1]

In your opinion did Fermat have a proof for his theorem?

 

[HallsofIvy]

Hey, if Fermat doesn't know!

My opinion (and it is only an opinion) is that what happened is what happens to all of us. Fermat thought that he had a simple proof, wrote a quick note to that effect, then went to bed. And discovered when he tried to carry out the proof, that he it did not work. That is supported by the fact that after he wrote that, he published proofs of the theorem for the cases n= 3 and 5. He wouldn't have done that if he had a proof for all n.

 

[MarkFL]

Hey, if Fermat doesn't know!

My opinion (and it is only an opinion) is that what happened is what happens to all of us. Fermat thought that he had a simple proof, wrote a quick note to that effect, then went to bed. And discovered when he tried to carry out the proof, that he it did not work. That is supported by the fact that after he wrote that, he published proofs of the theorem for the cases n= 3 and 5. He wouldn't have done that if he had a proof for all n.

I share your opinion on this. :D

 

[Fermat1]

To my mind it doesn't really make sense that this kind of problem doesn't have a more elementary (less artificial I mean) solution. Having said that, if Fermat had a proof, he would have written it

 

[MarkFL]

To my mind it doesn't really make sense that this kind of problem doesn't have a more elementary (less artificial I mean) solution. Having said that, if Fermat had a proof, he would have written it

Considering the monumental giants who tackled the problem during the centuries it remained unresolved, I tend to think that if a more elementary proof of the theorem existed, it very likely would have been found. :D

 

[Jameson]

Definitely agree he did not have a proof that would hold up. I would be very curious to see what it was though.

There was an even better video on the subject I saw once, but this one is also interesting.