January 18th, 2009, 03:01 PM  #1 
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Riemann Hypothesis
Hi, I've just joined in the hope that someone here will have enough time and patience to help a nonmathematician gain a better understand Riemann's hypothesis. I don't want to understand the mathematics as such, the Zeta function will always be incomprehensible hieroglyphics to me, but I do want to understand the principles at work. I want to understand what R's nontrivial zeroes actually are, their relationship to the primes, why they are sometimes likened to tuning forks, and a bit about the consequences of R's hypothesis being demonstrably true or false. I'm not being lazy. I've read the obvious books and trawled the Internet. But too much of it is over my head and what little remains does not address my questions. I have a fairly good understanding of the behaviour of the primes but little or no mathematics. I could tentatively start be asking how the imaginary numbers fed into the Zeta function are chosen and why, and what distinguishes the numbers which transform into nontrivial zeroes from the rest. No doubt this question is perfectly idiotic, but I did say some patience would be required. Thanks for any help. Whoever 
January 26th, 2009, 03:14 AM  #2 
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Re: Riemann Hypothesis
Hmm. Obviously this was not a good question. I'll try another which is closely related. A while ago I managed to prove that there is an infinite quantity of twin primes. Dr. Booker at Bristol Uni. agreed to have a look and congratulated me on constructing a correct heuristic proof, but then went on to say that the proof is not rigorous. I am still trying to find out why it is not rigorous. Indeed, I don't even understand how a proof can be correct and unrigorous. I would have expected it to be both or neither. My question is, then, why is my proof not rigorous. The proof depends on showing that the behaviour of the products of the primes is such that for any two consecutive primes there is a twin prime between p squared and p1 squared. It is easy to show this for small primes, and easy to show that the quantity of TPs in this range increases with p. Yet I am told that such a proof cannot work because the interaction of prime products eventually becomes too complex to predict. I think this is nonsense, and that their behaviour is entirely predictable forever, in principle at least. What am I not understanding? Can someone explain to me how a proof can be correct but not rigorous. Whoever 
January 26th, 2009, 06:06 AM  #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  Re: Riemann Hypothesis Quote:
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But without seeing your proof, it's hard to say. You don't actually say anything about your method, only that it's "easy".  
January 28th, 2009, 06:14 AM  #4  
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Re: Riemann Hypothesis Quote:
If I had an algorithm which generated only even numbers, could I not prove, by an analysis of the mechanics of this algorithm, that it can never produce an even number? Would this not count as a proof? Quote:
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Thanks for your help. Much appreciated. Whoever  
January 28th, 2009, 07:54 AM  #5  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Riemann Hypothesis Quote:
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Thanks for your help. Much appreciated. Whoever[/quote:r8en1efh] The problem with the wave analogy, is that waves follow a relatively fixed path. As far as we know, there's no function to generate all the primes, no less all the twin primes they aren't very predictable. Getting back to your question, did he say it's a "good heuristic" or a "correct but nonrigorous proof"? A good heuristic just means it can make us reasonably certain the conjecture is true, but is not a proof. A "correct" proof that isn't rigorous is a proof that isn't quite right, but could easily be made rigorous, and would almost certainly be correct.  
January 28th, 2009, 08:04 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  Re: Riemann Hypothesis
You asked "how a proof can be correct and unrigorous". I said that heuristics aren't the same as proofs, because the professor you quoted said you had a "correct heuristic proof". He didn't say that you had a proof (a heuristic proof is not a proof, just like a skew field is not a field), and you haven't shown one. Quote:
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Also, your description of the proof sounds like it proves something stronger than the existence of infinitely many twin primes, and I'm concerned that what it 'proves' is in fact false. Wouldn't that show that Omega(n) is bounded on average as n > infty?  
January 28th, 2009, 08:24 AM  #7  
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  Re: Riemann Hypothesis Quote:
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Code: . / \     
January 29th, 2009, 03:56 AM  #8  
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Re: Riemann Hypothesis Quote:
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I suppose I'm trying to understand the distinction between a mathematical proof and a mechanical proof, if I can put it that way. Quote:
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This is all very interesting. Thanks Whoever  
January 29th, 2009, 04:35 AM  #9  
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Re: Riemann Hypothesis Quote:
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I'm slightly reluctant to say much more about my proof since either it is flawed and I'm a fool, which is the most likely outcome, or it isn't and I don't want to give it away just yet. Before I post it I'd like to be sure I understand it properly myself. I suppose that's annoying. Quote:
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I have wondered if I''ve proved something more, and have a suspicion it has a bearing on Riemann's hypothesis, if only I could understand it. But I daren't go there in a discussion with mathematicians. I'll post a better summary of the proof when I've time. Thanks Whoever  
January 29th, 2009, 04:40 AM  #10  
Member Joined: Jan 2009 Posts: 36 Thanks: 0  Re: Riemann Hypothesis Quote:
Oh Hell. I meant to say that it could not produce an odd number. No wonder this question was incomprehensible.  

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