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June 15th, 2014, 02:13 AM  #1 
Newbie Joined: Jun 2014 From: Croatia Posts: 8 Thanks: 0  Goldbach's conjecture  proof ???
Hi everyone, If you follow the link at the bottom of this post, you'll find yet another (proposed) proof of Goldbach's conjecture. The proof's been written by my uncle and I just translated it into English since his English is basic at best. Not being a mathematician myself, the translated text probably contains some terminology that is slightly off but hopefully the content will make up for that. The formatting of the manuscript leaves a lot to be desired too but I hope that it won't matter much. One final thing, since the author doesn't speak English, he will not answer your questions regularly but you might expect to hear from him from time to time (provided, of course, that the text sparks your interest). http://www.ibhr.info/downloads/Goldbach_conjecture.pdf 
June 16th, 2014, 07:29 PM  #2 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 
What language is the original paper in, and may I see it?

June 16th, 2014, 09:48 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
June 17th, 2014, 10:53 AM  #4 
Newbie Joined: Jun 2014 From: Croatia Posts: 8 Thanks: 0 
It's in Croatian, and yes, you can see the original text if you wish.

June 17th, 2014, 10:59 AM  #5  
Newbie Joined: Jun 2014 From: Croatia Posts: 8 Thanks: 0  Quote:  
June 17th, 2014, 11:34 AM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
June 17th, 2014, 12:11 PM  #7 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 
Since it's not the original paper, #1 and #5 don't seem to apply.

June 17th, 2014, 02:01 PM  #8 
Newbie Joined: Jun 2014 From: Croatia Posts: 8 Thanks: 0 
The paper does list some examples relating to natural number decompositions. These examples alone can't prove Goldbach's conjecture but the equations derived from them were used in the proof. While the proof uses very simple math, it can be heavy going at times (and the translation doesn't help either) so I'll try to outline its main points in a day or two, when I find the time. 
June 18th, 2014, 06:21 AM  #9 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26 
It's worrying that the terms are illdefined early on: S is defined as a) number of pairs of odd composites within 2K b) number of different odd composites which form pairs within 2K Which is two different numbers. Not sure if this affects the maths but it makes it hard to read as you can't be sure which definition applies. 
June 18th, 2014, 06:40 AM  #10 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26 
Also, while some of the argument is a bit confused, I think there is a more serious problem here: Q is defined as a number that you can multiply PP by to reach S S = Q x PP If PP = 0 then there is no solution for Q (or Q is infinite). This means that the equation manipulations that follow are flawed when PP = 0. In particular this step (I've added the missing brackets) is illegitimate: 5) (NP x Q) – (NP x Q) = NP – PR Which is cancelled down to NP  PR = 0 This seems to lead on to the rather odd theory that a counterexample to Goldbach must have a symmetrical array where each prime is symmetrically matched against a composite which is of course impossible. I think it is the illegitimate bit above that leads to this flawed approach. Last edited by Hedge; June 18th, 2014 at 06:46 AM. 

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