Given the nature of Wile's proof of FLT, do any of u still think Fermat may have had a proof?

-- DO NOT REPLY TO THIS MESSAGE --

A message has been posted by the user "{user-userName}", who

you are watching.

Author: Pubkeybreaker

Subject: Re: Simple proof of FLT: Why is it impossible?

mike4ty4@yahoo.com wrote:

> Hi.

>

> I have a question. Why does everyone believe that a "simple" proof like

> Fermat claimed to have for his famous theorem, does not exist?

> So, why is it believed that such a proof is impossible?

Not impossible. Merely highly unlikely.

Many excellent mathematicians have tried elementary proofs. All

have failed. A lot of interesting mathematics has been discovered in

the

process.

It is known that certain elementary approaches can not work.

Methods based upon factoring the equation do not work because

unique factorization fails.

It is known that descent arguments (such as the Fermat argument for

exponent = 4) can't work for n > 4. The reason for this is very

deep.

The elliptic curve that is associated with the Fermat equation has a

group associated with it, known as the Selmer group. It is known that

only when this group is trivial can descent arguments work. It is

known

that the group is NOT trivial for n > 4.

It is known that modular approaches (look at the equation mod some set

of

primes, then try to piece together a solution for the integers based on

solutions

mod the primes) can not work. The reason is similar to why descent

won't work.

In this case, the non-trivial Selmer group prevents the Hasse-Minkowski

theorem

from working. This theorem tells us when one can construct solutions

over Z

using known solutions modulo primes.

Most amateurs know nothing about these results, so continue trying

these approaches. Their efforts will always be futile.

Fermat never claimed publicly that he had a proof. He only had a

private

note to himself. The fact that he *later* did make public a proof for

the

special case n=4 suggests he realized that he was wrong. Why publish a

special case if you already have a proof for the general case?

To view and reply to the message please see:

http://mathforum.org/kb/message.jspa?messageID=452...

To view the discussion, see:

http://mathforum.org/kb/forum.jspa?forumID=13

<><><><><><><><><><><><><><><><><><><><>

<><><><>

The Math Forum respects your online time and Internet privacy. To view or cancel

your discussion watches, see

http://mathforum.org/kb/editwatches!default.jspa

-- DO NOT REPLY TO THIS MESSAGE --

Perhaps Fermat was being literal when he said the margin was too small for his proof. :) While I suppose it might have been possible that he had come up with a much more simple proof, it seems difficult to believe nobody has found it after 300+ years. Either way, Fermat's genius is still unquestionable.

Nope, I don't believe he could have worked out a proof with the maths of the time when it took Wiles 7 years using tools like elliptic integrals. There isn't a single instance in the whole history of science of somebody having this much more insight than everybody else. Not even Newton, Einstein or Darwin.

They (mathematical historians) believe that Fermat proved it for a couple of cases, and assumed that he could easily generalize it to all cases. The problem is that even though we don't have his "proof that was too big for the margin", historians have found some of his notes, where he thought he proved it for some of the cases, but it turns out that he made some mistakes. Therefore they (at least the ones who have told me this) believe that he probably thought that he could prove it elementarily, but in actuality, he couldn't, and thus his "proof that was too big for the margin" was probably flawed.

absolutely yes because he knew the fact that any given number having any given power can be expressed as difference of infinite sets of two perfect squares like

3 ^ (4) = 41 ^ (2) - 40 ^ (2).

whoma whatti huh? u must be smart....