Fermat's Theorem: Did Fermat Have a Proof?

Click For Summary

Discussion Overview

The discussion revolves around whether Pierre de Fermat had a valid proof for his famous theorem, particularly in light of the lack of a complete proof found among his writings. Participants explore the implications of Fermat's claims and the nature of mathematical proof in this context.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that Fermat may have believed he had a simple proof but later found it did not work, as indicated by his subsequent publication of proofs for specific cases (n=3 and n=5).
  • Others argue that if Fermat had a proof, he would have documented it, implying that the absence of such a proof suggests he did not have one.
  • There is a viewpoint that the complexity of the problem raises doubts about the existence of a more elementary solution, with some suggesting that if a simpler proof existed, it likely would have been discovered by later mathematicians.
  • One participant expresses curiosity about what Fermat's proof might have entailed, indicating interest in the historical context of the theorem.

Areas of Agreement / Disagreement

Participants generally express skepticism about Fermat having a valid proof that would hold up, but there is no consensus on the specifics of what he may have thought or attempted.

Contextual Notes

Participants acknowledge the historical significance of Fermat's theorem and the efforts of mathematicians over the centuries to resolve it, which may influence their views on the existence of a proof.

Fermat1
Messages
180
Reaction score
0
In your opinion did Fermat have a proof for his theorem?
 
Mathematics news on Phys.org
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.
 
HallsofIvy said:
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
 
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
 
Fermat said:
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
 
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.

 

Similar threads

Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
9K
Undergrad Fermat point for quadrilaterals
  • · Replies 7 ·
Replies
7
Views
3K
High School Have I proved some part of Fermat's last theorem?
  • · Replies 15 ·
Replies
15
Views
2K
Graduate Prime Number Powers of Integers and Fermat's Last Theorem
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad On Fermat’s last theorem and others....
  • · Replies 13 ·
Replies
13
Views
2K
High School Fermat's Last Theorem; unacceptable proof, why?
  • · Replies 12 ·
Replies
12
Views
3K
MHB Why isn't {0}^{3}+{0}^{3}={0}^{3} a proof for Fermat's Last Theorem?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How to motivate the study of Fermat's Little Theorem
  • · Replies 5 ·
Replies
5
Views
2K
MHB Why certain topics in elementary number theory?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why certain topics in elementary number theory?
  • · Replies 5 ·
Replies
5
Views
2K