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#37
Sep107, 07:16 AM

P: 107

when x = 0 the equation is 1.
But as far as the purpose of this thread, to explain wiles proof, i don't think many of us on here would get much out of it. when wiles made the error in his proof initially he said "Even explaining it to a mathematician would require the mathematician to spend two or three months studying that part of the manuscript in great detail." 


#38
Sep107, 09:37 AM

P: 83




#39
Sep107, 10:03 AM

P: 107

the theorem has already been proved. are you looking for an alternate proof?



#40
Sep107, 10:08 AM

P: 83

Yes, without referring to what Wiles did and the possible lines along which we could proceed will be the first step.



#41
Sep107, 11:44 AM

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You understand, do you not, that people looked for a proof for almost 500 years before Wiles came up with his! If you are expecting a different proof, "even if it takes years" may not be enough! And certainly, any different proof will be no easier to understand than Wiles'.



#42
Sep107, 03:31 PM

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(I would also hope for such an improved proof of the fourcolor theorem, but that may never happen  somehow I see Wiles' theorem as more fundamental and more worthy of continued effort.) 


#44
Sep107, 09:30 PM

P: 107

what's the difference between proving that a proof exists and proving the theorem? if you prove that a proof exists then assuming the theorem was false would lead to a contradiction. so saying a proof exists is essentially proving it isn't it?



#45
Sep207, 09:16 AM

P: 858




#46
Sep207, 09:31 AM

P: 83

yes,its like a stack of books.If the the lower books hold, then the upper books will also hold .Already established axioms are like the lower books and the newer proofs depend on them.



#47
Sep207, 09:56 AM

P: 107

i thought i understood proofs, i've done many of them (though i am still doing my undergraduate work).
by saying a proof exists, we are saying that the conjecture is valid, are we not? that is what i take it to mean. if there is a proof to a conjecture, then a conjecture is valid. there is a proof to the conjecture therefore the conjecture is valid. so by using that logic we have proved the validity of the conjecture, and yet that is not enough? 


#48
Sep207, 10:07 AM

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Knowing that something exists is different from a construction that demonstrates it. Many things in mathematics are nonconstructive. OK, I can't think of any examples where one knows that a proof exists, but one cannot write it down, but I'm no logician.



#49
Sep207, 10:18 AM

P: 107

so are you agreeing with me that knowledge of a proof would constitute a proof despite there not being a construction? or must the construction exist? if someone proved there was a proof to the Riemann hypothesis, would mathematicians now be justified to say "as we now know R.H. is true..."? this whole thing is really kind of stupid, but i think it would be interesting to see any example where a proof is known to exist and yet has not been found, simply because the idea is so counterintuitive.



#50
Sep207, 10:29 AM

P: 993

You normally "prove the existence of a proof" by writing the proof down. I've never seen a proof a la "suppose a proof does not exist", but I imagine something like that could exist in higher order logic or something.



#51
Sep207, 01:54 PM

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I am neither agreeing nor disagreeing with you, matticus. The question is so ambiguous as to be unanswerable.



#52
Sep307, 06:12 AM

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Here is a proof that comes awfully close to that:
Prove the there exist irrational a, b such that a[sup]b[/sub] is rational. Look at [tex]\sqrt{2}^\sqrt{2}[/itex]. It is not known (last time I checked) if that number is rational or irrational. However: If it is rational, then we are done. If it is irrational, then [tex]\(\sqrt{2}^\sqrt{2}\)^\sqrt{2}\)= \sqrt{2}^2= 2[/tex] is rational. We have proved that there exist irrationals a, b such that a^{b} is rational but are unable to say what a and b are! 


#53
Sep307, 08:08 AM

P: 107

yeah that proof was in my discrete math book, it is cool. the example i was going to use was that given any number we know there is a bigger prime, despite the fact that at some point we won't be able to construct it. neither of these are the same thing, but i think one of the things that attracts me to math is that you can know things exist without having to see them exist. where in science statistical evidence is very important, in math it's almost irrelevant.



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