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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

I was just reading about the theorem when i came upon that it was proved. I would like to see the proof. Or an explanation at the least how the Andrew Wiles proved the conjecture and used it prove the theorem. I m still in High School so i might not understand all of it but i cant believe it without seeing it.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

10 Mb??

Fermat was right when he wrote ** "..this space is too short to contain it.."**!!

I am interested to know if the theorem was valid even before it was proved?

Is there any corollary to the theorem?

Which other problems make use of Fermat's Last theorem??

I believe it was the EASIEST problem for anyone TO UNDERSTAND ((in contrast, Reimann's Hypothesis is something which needs a good deal of knowledge of Set Theory)) and yet to be the TOUGHEST problem TO SOLVE (till '94)!!

*Last edited by ZHero (2008-07-30 23:09:15)*

If two or more thoughts intersect, there has to be a point!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Some people think that Fermat's proof had a flaw in it (there are certainly some flaws that could have come up, as people who tried proving it have shown).

After he proposed this theorem, he later proved that no integers a, b and c exist such that a^4 + b^4 = c^4. If he believed in his theorem, then there would be no need to do that, so people think he made a mistake and then discovered it later.

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

You don't have a chance at understanding the proof. I can say this because I don't have a chance at understanding the proof, at least not yet. You need to understand some rather complex machinery before you can even start to read it. And once you do, it's 200 pages long and from what I hear, a rather complicated argument.

I am interested to know if the theorem was valid even before it was proved?

Unless you think there were integers that fit the theorem before Wile's proof and disappeared as soon as he came up with it, yes it was valid.

Is there any corollary to the theorem?

Not quite. Rather, Fermat's Last Theorem is a corollary to a rather huge theorem. That rather huge theorem is what Wiles proved, known as the Modularity theorem. Specifically, Wiles proved that all elliptic curves were modular, and if there was a solution to FLT, then it would be an elliptic curve that wasn't modular.

FLT is simply a single example of the theorem he proved.

Which other problems make use of Fermat's Last theorem??

None that I'm aware of.

Some people think that Fermat's proof had a flaw in it (there are certainly some flaws that could have come up, as people who tried proving it have shown).

I think he was just making it all up...

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

JaneFairfax wrote:

Is this the most difficult proof ever?

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Identity wrote:

JaneFairfax wrote:Is this the most difficult proof ever?

No. That would probably be, "Classify all finite simple groups." That spanned thousands of papers and hundreds of mathematicians. Another good one is "Prove that any group of odd order is solvable." That one was 255 pages.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

Ricky wrote:

Identity wrote:JaneFairfax wrote:Is this the most difficult proof ever?

No. That would probably be, "Classify all finite simple groups." That spanned thousands of papers and hundreds of mathematicians. Another good one is "Prove that any group of odd order is solvable." That one was 255 pages.

Perhaps it's not the longest proof, but has any other theorem taken longer to prove from the time it was first proposed? My hunch is that there has been, but I don't know off the top of my head.

Wrap it in bacon

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

What about the 4-colour proof?

The one that says it only ever takes 4 colours to fill in a map of regions such that no two regions sharing a border (points don't count) have the same colour.

Does anyone know how long that one is, and if it compares to some of the others here?

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

If you want length, look at the classical greek problems like trisecting an angle with a compass and straight edge. That was only answered 1500+ years later. But then again you might say that doesn't count...

It's the longest (definitive) problem that was every constantly worked on.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

Thx Jane that was very useful. Thats gonna occupy me for an year or so. I m goin to try and understand it if i can.

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

mathsyperson wrote:

What about the 4-colour proof?

The one that says it only ever takes 4 colours to fill in a map of regions such that no two regions sharing a border (points don't count) have the same colour.Does anyone know how long that one is, and if it compares to some of the others here?

What I meant is in terms of conceptual and mathematical difficulty. The 4-colour theorem (I think) is a computer proof, and covers lots of cases. This may make it long, but it may not make it difficult.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

careless25 wrote:

Thx Jane that was very useful. Thats gonna occupy me for an year or so. I m goin to try and understand it if i can.

You should listen to my warning. Go to college, get an undergraduate degree in mathematics, then a few years in graduate school. Then you can start trying.

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

Ricky wrote:

You should listen to my warning. Go to college, get an undergraduate degree in mathematics, then a few years in graduate school. Then you can start trying.

Sry i didnt take your warning seriouly the first time but after reading the first 2 pages i think i shall.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Identity wrote:

mathsyperson wrote:What about the 4-colour proof?

The one that says it only ever takes 4 colours to fill in a map of regions such that no two regions sharing a border (points don't count) have the same colour.Does anyone know how long that one is, and if it compares to some of the others here?

What I meant is in terms of conceptual and mathematical difficulty. The 4-colour theorem (I think) is a computer proof, and covers lots of cases. This may make it long, but it may not make it difficult.

Ah, so you did. Ricky distracted me by mentioning the length of his example, but that one's probably long *and* difficult.

Why did the vector cross the road?

It wanted to be normal.

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 339
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Ricky wrote:

Identity wrote:JaneFairfax wrote:Is this the most difficult proof ever?

No. That would probably be, "Classify all finite simple groups." That spanned thousands of papers and hundreds of mathematicians. Another good one is "Prove that any group of odd order is solvable." That one was 255 pages.

I believe we have a new contender for the record:

Baffling ABC maths proof now has impenetrable 300-page ‘summary’.

A summary of a massive mathematical proof that has baffled mathematicians for the past five years may help a few more people get to get grips with the key ideas. How long is the explainer? A mere 300 pages.

And that is only the summary: the original work – Shinichi Mochizuki’s proof of the ABC conjecture published in 2012, using a radical new theory developed over two decades – contained over 500 pages.

*Last edited by Alg Num Theory (2017-11-25 09:43:54)*

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