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Yet another failed attempt?

  1. Feb 23, 2006 #1
    Apparently someone thinks they might have proved the Riemann Hypothesis. What do you think?

    http://www.aronpalmer.com/riemann_proof.htm
     
  2. jcsd
  3. Feb 24, 2006 #2

    mathman

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    I think the proof should be submitted to a reputable math journal and refereed. If it is correct, the author will become very famous.
     
  4. Feb 24, 2006 #3
    The author would be a millionaire AND gain instantaneous immortality.
     
  5. Feb 24, 2006 #4

    quasar987

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    And the women, ô, the women!
     
  6. Feb 25, 2006 #5
    I must say how polite everyone is here, I had expected to be slammed. Would love to get it refereed but finding it quite difficult, I might as well send a stock tip to the journals as this for the interest I get. All of which is totally understandable, I am sure I wouldn't behave much differently, but if anyone has any ideas on how to proceed they would be very welcome. Even any feedback on whether its clearly rubbish so that at least I can stop making a fool of myself.
    Thanks,
    Aron.
     
  7. Feb 25, 2006 #6

    HallsofIvy

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    I don't understand. Send it to a journal and it WILL be refereed. That's what journals do. Of course, they are not in the business of fixing mistakes for you- you might well get back a message saying "No, thank you we're not interested"- which means "No, this is not a valid proof".
     
  8. Feb 25, 2006 #7

    matt grime

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    Actually, a rejection from a journal does not mean that the proof is incorrect, and acceptance in a journal does not mean the proof is correct either. The referee process is to ensure that the result is not obviously false, satisfies the criteria of the journal's acceptance policy and that it is original work as far as it is reasonably possible to tell.

    Some referees do take it as part of their job to make sure the proof is actually correct, and they will certainly make sure it is not obviously false. This is why the conditions for getting a Clay prize are not merely that the result is published in a high-profile journal, but that it stands 18 months of scrutiny after publication without any (serious, ie fatal) errors in the proof being found.

    A quick scan of the result makes me instantly sceptical.

    I see no explanation of what the 'real positive continuous decreasing function' that is used is to determine something about the zeta function actually is.

    One simple line, after the theory, which states: let f=????? then we see that.... would make all the difference, plus a proof that the f so used actually satisfies the criteria given would be required.
     
    Last edited: Feb 25, 2006
  9. Feb 25, 2006 #8

    mathwonk

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    matt is right. refereeing is a difficult, time consuming, anonymous, and essentially thankless job. I received a lengthy and difficult paper some time back that I had no time to review, but a few months later I received it back again with a personal apeal from the editor, since no one else could be found to review it either.

    I accepted but said it woiuld take a long time. 7 months later or mroe I received a followup appeal from the editor, but i was still checking laboriously, every detail in the terse arguments, and every reference of the sort " this proved in my [300 page] paper", with no specific page citation.

    It was very impressive, but the logic was not clear. When I finished after one year, and laid it all out clearly, there was a big gap in the argument. He had simply assumed some other author, whose work he used, had proved an if and only if statement where in fact that author only proved an "only if" statement.


    I sent it back with a favorable review but pointing out the gap. A couple weeks later the author sent back a revised version with a "completed" version of the other authiors work.

    I did not have time to c=verify this so just let it go.


    There is no guarantee from em that the mpaper is correct, and indeed I am very rare in even checking as far as I do the correctness of authors's works.

    Matt is giving you valuable free advice here. If you cannot get your work refereed it is probably because it is not clearly enough written to make it possible to review without great effort, and that effort is not justified in the case of a theorem whose proof from anyone is so difficult that it is likely to be wrong.
     
  10. Feb 26, 2006 #9
  11. Feb 26, 2006 #10
    Good luck!
     
  12. Feb 26, 2006 #11
    Thanks, realise odds are against me.
    Does anyone have any ideas who I should approach in order to get this published. I am new to all of this.
     
  13. Feb 26, 2006 #12

    matt grime

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    So when I said you merely ought to state: let f=something, why have you not said what f is equal to in any clear or concise way. I scanned taht page.I didn't see the word zeta at any point. Perhaps I was just being too quick.
     
  14. Feb 26, 2006 #13

    quasar987

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    :p

    -----------
     
  15. Feb 26, 2006 #14
  16. Feb 26, 2006 #15
    And I have added more detail regarding
    quasar987's comments.
     
  17. Feb 26, 2006 #16

    matt grime

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    You did not say you'd altered the original page, merely gave a new link.

    Well, the obvious counter example is: let f(t)=0, this satisfies all the criteria you place on f (at least the only ones you give), and by your 'proof' you're saying that the laplace transform of the zero function (which is the zero function) is never zero (in the right half plane).
     
  18. Feb 26, 2006 #17
    0 is excluded because the integral of f(t) from 0 to Infinity is 0 and part of the proof requires this to be non zero. I originally had a comment pointing this out but I removed it because I thought it didn't help, obviously I was wrong.
     
  19. Feb 27, 2006 #18

    matt grime

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    You cannot require something to be a condition in the proof if it is not met or deduced from the hypotheses. What else do you add in to the proof that is not in the hypotheses (which are not clearly stated; I guessed that the first three things you wrote were all that was required).
     
  20. Feb 27, 2006 #19
    This is just me talking here, but if you gave it a duller title, something other than "PROOF OF RIEMANN HYPOTHESIS", it might not provoke instant skepticism.
     
  21. Feb 27, 2006 #20
    f(t)=0 is the only continuous function I excluded and didn't mention.
    I expexcted instant skepticism, and so far have found everything on this board very constructive, but would realy like to find a referee/publisher. So far (7 days),no one has pointed out an obvious mistake (in fact no-one has said anything at all) and this is the only board its been posted on (not by me, blame devious :-) ).
    Hopefullly my next post will be more extreme (one way or the other).
    Thanks,
    Aron
     
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