Fermat Goes Back on the "Unsolved" Pile

[Pangloss]

http://www.manilatimes.net/national/2005/may/05/yehey/top_stories/20050505top4.html

 

Looks like an error was found in Wiles' solution.

[Dapthar]

Looks like an error was found in Wiles' solution.

I'm sorry if this sounds a bit pro-establishment, but I think the guy is a little shady. First, note Wiles's reply:

 

Dear Sir,

 

Your work is incredible, I read all of it just yesterday and let me tell you I respect you. I am going to review all my 'proof' which I am sure is wrong (thanks to you!).

 

Would you like to collaborate with me in this work? I have noticed some imperfections in your perfect proof (that sounds like you), and I'd like to create a perfect proof with you, great professor.

 

Also I'd like to have the address of the guy who let you get a PhD 30 years ago. I'd like to discuss few things with him. . .

 

Very respectfully,

A. Wiles

Sounds a bit sarcastic, don't you think? (Italics and bold are my own.)

 

Also, what tipped me off is that the man found fault with the trichotomy axiom of the real numbers. For those who are a bit rusty, the trichotomy axiom of the real numbers states that all real numbers are either negative, positive, or zero. It's a bit difficult to fault with that.

 

Finally, the whole "The result is a new real number system that is free from defects and contradictions," reeks of pseudoscience, since as Godel proved:

Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory.

Thus, you can't make the real numbers, "free of defects", as it were.

 

Source: http://www.math.hawaii.edu/~dale/godel/godel.html#FirstIncompleteness

 

According to the Mathematics Geneology Project, the Mr. Escultura does have a legit Ph.D., but apparently, something went horribly wrong between 1970 and the present day.

 

I'll reevaluate when some other news sources collaborate the story, but for now, I'm betting on a hoax.

[matt grime]

E E is famous on Usenet for being a crank. I think we can safely say that he's nothing to worry about. He allegedly has also said that the real numbers are "wrong" as they are an infinite set.

[Dave]

I can only say that I hope it's a hoax (as it seems to be). I have to say though, my heart skipped a beat for a second - I feel that the proof of Fermat was probably one of the greatest achievements in the world of mathematics ever, and to have it shot out of the water would be a bit of a catastrophe, to say the least.

[Ollie]

Phew, panic over. He really shouldnt run around scaring people like that.

[Dave]

Wasn't this the same guy that posted the erroneous counter-example whilst the proof was going through the verification process?

[Pangloss]

Yes. I'm a little confused, wasn't this guy a professor of mathematics?

 

Are you guys basically saying he's a crank, but he's a crank at a fairly advanced mathematical level?

 

I'm afraid I really know very little about higher math.

[AL]

Mr. Escultura "refuted" trichotomy using the ol' "1 does not equal 0.999..." argument, which we've seen beaten to death here and elsewhere. He argued that it can be both proven that 0.9_ = 1 and 0.9_ < 1, and so trichotomy fails.

http://www.manilatimes.net/national/2004/jun/18/yehey/opinion/20040618opi7.html

 

Needless to say, I'm skeptical, but I'll await further information to see if this gets published in math journals and not merely in a newspaper that Mr. Escultura himself works for.

[Johnny5]

Mr. Escultura "refuted" trichotomy using the ol' "1 does not equal 0.999..." argument' date=' which we've seen beaten to death here and elsewhere. He argued that it can be both proven that 0.9_ = 1 and 0.9_ < 1, and so trichotomy fails.

http://www.manilatimes.net/national/2004/jun/18/yehey/opinion/20040618opi7.html

 

Needless to say, I'm skeptical, but I'll await further information to see if this gets published in math journals and not merely in a newspaper that Mr. Escultura himself works for.

 

 

Anyone who carries out a logical analysis of anything, should be paid attention to, because what if they are right?

 

I wouldn't call him anything I don't know him, and Andrew Wiles seemed needlessly rude.

 

There is most definitely some confusion going on as regards

 

1=.99999999...

 

But to think you have developed a whole new kind of real number system, is far out there. And it would probably be a help to mr Escultura, to simply show him his error, rather than ridicule him. At least that is my take.

 

You don't call a scientist who finds an error a kook. He simply is aware that it is not the case that 1=.9999999... and well he is right. They freaking aren't equal.

 

The LHS and RHS are different kinds of things.

 

The LHS is a number, and the RHS is an infinite series which doesn't terminate.

 

PS: Also I don't know if this is true, but years ago a friend of mine told me he watched Andrew Wiles on a PBS broadcast, and when asked about the fact that his "proof" contained an error, Mr. Wiles began crying. My friend found it odd that a mathematician would take it so seriously that he would cry over making a mistake.

 

No one is perfect all the time... no one.

[Dave]

PS: Also I don't know if this is true, but years ago a friend of mine told me he watched Andrew Wiles on a PBS broadcast, and when asked about the fact that his "proof" contained an error, Mr. Wiles began crying. My friend found it odd that a mathematician would take it so seriously that he would cry over making a mistake.

 

I don't.

 

I'm assuming you don't know the history behind Wiles and his proof. If you do, you can skip this, but this is just for the record. Proving Fermat was Wiles' childhood dream. He left Cambridge after completing his PhD for Princetown in the US. After Frey's famous lecture (and Barry Mazur's further contributions), Wiles began to prove Taniyama-Shimura. He spent the next 7 years on the proof, which he presented at the Newton Insitute lectures. About 6 months after this in the referee process, the error was announced in the proof, which was consequently resolved (or so we thought).

 

Now, imagine what Wiles must have felt at this stage. He had spent the past 7 years in practical solitary confinement proving a theorem that he had always envisioned solving and that had remained unsolved for 350 years. I think he's perfectly entitled to burst into tears at this point - in fact, I wouldn't have blamed him if he'd just walked out.

 

Also, I would appreciate it if you do not try and sideline the thread by raising the recurring decimal problem. There are already multiple threads on this, and I don't want a good one being spoilt by such repetitive and silly arguments.

[dan19_83]

does anyone have a link to the proof of fermat, by wiles?

or does anyone want to do it themselves?!!

[Dave]

does anyone have a link to the proof of fermat' date=' by wiles?

or does anyone want to do it themselves?!![/quote']

 

As far as I'm aware, you're going to have to buy it - it's published in a book.

 

Also, it's over 150 pages long and extremely complex. I think something like 15-20 people are capable of understanding it cover to cover, so I doubt you'd be able to reproduce it easily.

[Johnny5]

 

Now' date=' imagine what Wiles must have felt at this stage. He had spent the past 7 years in practical solitary confinement proving a theorem that he had always envisioned solving and that had remained unsolved for 350 years. I think he's perfectly entitled to burst into tears at this point - in fact, I wouldn't have blamed him if he'd just walked out.

[/quote']

 

That is actually quite touching.

 

And one more thing...

 

I praise him just for the effort alone.

 

Regards

[dan19_83]

oh right!!

 

didn't realise that. i'd say i'd hardly understand the first page of it!

[Dave]

I have the ebook on my computer; it's very technical and I can barely get my head around any of it. Makes for great reading though from a mathematical standpoint

[Ollie]

Wouldnt he have published it in a journal?

[Sayonara]

I'm not sure many journals would publish 150-page proofs, although you'd think they would make an exception for something as important as that.

[Lyssia]

He did publish it in a journal: the Annals of Mathematics, published by Princeton. Although the two papers involved did take up the entire journal for that edition! Here's a link to the online index. I wonder if my university has access to that

 

EDIT: Oh squeeeeeee! It does indeed and I'm looking at it now. Woah

[Dave]

Pretty much every university has subscriptions to these sites. If you log in from the on-campus computers, then you're pretty likely to get access (they base it on IP addresses).

[Lyssia]

Oh that's right, just go ahead and destroy my happiness, why don't you

 

(Is it also a common thing to be able to access these resources off-campus through a proxy server? Because if so...that was my last vestige of "woo"-ness that I had )

[Dave]

Oh that's right' date=' just go ahead and destroy my happiness, why don't you

 

(Is it also a common thing to be able to access these resources off-campus through a proxy server? Because if so...that was my last vestige of "woo"-ness that I had )[/quote']

 

Yup, I do it all the time

 

RIP "woo"-ness 2005