abc conjecture proved? (1 Viewer)

[tywebb]

Do these 4 documents constitute a proof of the ABC conjecture?

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory II.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory III.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory IV.pdf

If so this will also constitute a new proof of Fermat's Last Theorem:

http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378

 

[seanieg89]

Do these 4 documents constitute a proof of the ABC conjecture?

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory II.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory III.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory IV.pdf

If so this will also constitute a new proof of Fermat's Last Theorem:

http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378

This is an incredible achievement, especially if the proof is verified!

 

[deswa1]

Ok I can't follow anything those papers are saying but I googled abc conjecture and that would be heaps cool/impressive if he got a proof for it.

I still don't get though how people can get 500 page proofs- its actually amazing. I was proud of myself when I proved the AM-GM inequality in a 4U paper and that took just over a page lol.

 

[barbernator]

The one thing i got out of these documents is that S.Mochizuki can lift. so dont ask him if he even lifts, because he obviously can.

"[CanLift] S. Mochizuki, The Absolute Anabelian Geometry of Canonical Curves, Kazuya
Kato’s fiftieth birthday, Doc. Math. 2003, Extra Vol., pp. 609-640."

 

[RealiseNothing]

Ok I can't follow anything those papers are saying but I googled abc conjecture and that would be heaps cool/impressive if he got a proof for it.

I still don't get though how people can get 500 page proofs- its actually amazing. I was proud of myself when I proved the AM-GM inequality in a 4U paper and that took just over a page lol.

You can prove the AM-GM inequality in a couple of lines using circle geometry.

 

[barbernator]

You can prove the AM-GM inequality in a couple of lines using circle geometry.

for n integers?

 

[deswa1]

You can prove the AM-GM inequality in a couple of lines using circle geometry.

Really? Can you show me- this would actually be fascinating.

Nah unfortunately though I had to do the question that way- it had a hence bit etc. (though I don't know of any other way to do it)

 

[RealiseNothing]

for n integers?

You just prove:

 

[bleakarcher]

Really? Can you show me- this would actually be fascinating.

Nah unfortunately though I had to do the question that way- it had a hence bit etc. (though I don't know of any other way to do it)

Isn't this in Q8 of a hsc paper before 2000?

 

[deswa1]

Isn't this in Q8 of a hsc paper before 2000?

Yeah 1998 from memory. It was also in Syd Grammar 2003 (different proof) and one other paper which is the one I'm referring to (forgot which one though)

 

[seanieg89]

You just prove:

That is not the general AM-GM. And there is a good reason why mathematicians don't like to use geometry to prove things like AM-GM, it turns out geometry is much harder to axiomatise.

 

[barbernator]

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2000exams/hsc00_maths/98MATH4U.PDF last question

 

[RealiseNothing]

Really? Can you show me- this would actually be fascinating.

Nah unfortunately though I had to do the question that way- it had a hence bit etc. (though I don't know of any other way to do it)

 

[RealiseNothing]

That is not the general AM-GM. And there is a good reason why mathematicians don't like to use geometry to prove things like AM-GM, it turns out geometry is much harder to axiomatise.

I find it to be a cool little proof for that case though.

 

[deswa1]

That's fairly neat actually- I like it

What I was referring to is the general AM-GM. Can that be done with circle geo? You can prove the case for n=2 in two lines starting with (root a-rootb)^2 is greater than or equal to zero

 

[seanieg89]

That's fairly neat actually- I like it

What I was referring to is the general AM-GM. Can that be done with circle geo? You can prove the case for n=2 in two lines starting with (root a-rootb)^2 is greater than or equal to zero

Well the n=2 case is enough to kickstart an induction, but I don't know if you would call that a circle geometry proof then.

 

[Sy123]

But cant we just do this for AM-GM (my knowledge of this inequality is a 2 min google search and I found that it is an inequality)



Is this not axiomatic enough?

(Im missing something I think)

 

[deswa1]

But cant we just do this for AM-GM (my knowledge of this is a 2 min google search and I found that it is an inequality)



Is this not axiomatic enough?

(Im missing something I think)

Yeah this is the standard proof for n=2 (I think I posted that a few posts up). Its harder to prove it more generally.

 

[bleakarcher]

But cant we just do this for AM-GM (my knowledge of this inequality is a 2 min google search and I found that it is an inequality)



Is this not axiomatic enough?

(Im missing something I think)

We are talking about the general form of the inequality.

Edit: Damnit deswa

 

[Sy123]

Yeah this is the standard proof for n=2 (I think I posted that a few posts up). Its harder to prove it more generally.

We are talking about the general form of the inequality.

Oh, sorry guys..