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news re ABC conjecture

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  • Steven Harvey
    http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911   Comments, anyone?   Steven Harvey
    Message 1 of 8 , Sep 11, 2012
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      http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911
       
      Comments, anyone?
       
      Steven Harvey

      harvey563@...

      [Non-text portions of this message have been removed]
    • Phil Carmody
      ... Well, the maths is so far above my head I cannot comment on it at all. However, I must say that I m worried that he seems to be working in a vacuum - about
      Message 2 of 8 , Sep 12, 2012
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        --- On Tue, 9/11/12, Steven Harvey <harvey563@...> wrote:
        > http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911
        >  
        > Comments, anyone?

        Well, the maths is so far above my head I cannot comment on it at all. However, I must say that I'm worried that he seems to be working in a vacuum - about 60% of the references in his paper were to his own prior work, and many of the others were to standard background texts not pertinent to the main thrust of his paper. If people are going to give this the thumbs up, they're going to have to do a lot of groundwork on his prior stuff too. I'll just wait until the Taos, Mazurs, and Elkies are satisfied. I'm prepared to wait several years.

        Having said that, a couple of those have made some fairly positive comments about the paper being worth looking into already so we're not looking at Gene Ray inventing a Time Tesseract.

        Phil
      • Maximilian Hasler
        ... Hum, In this case, in which r=2, sqp(abc)^r/c is nearly always greater than 1, and always greater than zero. Nearly always does not mean anything, and
        Message 3 of 8 , Sep 12, 2012
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          > --- On Tue, 9/11/12, Steven Harvey <harvey563@...> wrote:
          > > http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911
          > >
          > > Comments, anyone?

          Hum,

          "In this case, in which r=2, sqp(abc)^r/c is nearly always greater
          than 1, and always greater than zero. "

          "Nearly always" does not mean anything, and "always greater than zero"
          is trivial, for a,b,c positive.

          Maximilian
        • Jack Brennen
          ... Actually the ABC conjecture states that for any r 1, sqp(abc)^r/c 1, except for some finite number of exceptions. There s your nearly always ,
          Message 4 of 8 , Sep 12, 2012
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            On 9/12/2012 11:03 AM, Maximilian Hasler wrote:
            >> --- On Tue, 9/11/12, Steven Harvey <harvey563@...> wrote:
            >>> http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911
            >>>
            >>> Comments, anyone?
            >
            > Hum,
            >
            > "In this case, in which r=2, sqp(abc)^r/c is nearly always greater
            > than 1, and always greater than zero. "
            >
            > "Nearly always" does not mean anything, and "always greater than zero"
            > is trivial, for a,b,c positive.
            >
            > Maximilian
            >

            Actually the ABC conjecture states that for any r > 1,
            sqp(abc)^r/c > 1, except for some finite number of exceptions.

            There's your "nearly always", reworded to mean something.
          • James Merickel
            Phil Carmody has suggested that there are standard texts that are not pertinent in reference.   Phil, would you be so kind as to name these (to facilitate
            Message 5 of 8 , Sep 12, 2012
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              Phil Carmody has suggested that there are standard texts that are not pertinent in reference.
               
              Phil, would you be so kind as to name these (to facilitate answering the question I have--and others may--of 'rhetoric' in a 'mathematical world')?  I don't know the leveling you place on this statement. Nor is the 'a couple of these' phrase clear.  You may save us some time if this is a form of play.  You may push somebody serious onto the ledge with the other already serious people to this question of validation.  Thank you, if you would.  And no offense intended in singling you out (to anyone).  I merely wish to know what these books are (whether, now, I understand your expression entirely, partly, or not at all; and whether I can quickly understand it or only slowly, if I ever do).
               
              Yours Truly, James G. Merickel

              --- On Wed, 9/12/12, Phil Carmody <thefatphil@...> wrote:


              From: Phil Carmody <thefatphil@...>
              Subject: Re: [PrimeNumbers] news re ABC conjecture
              To: "primenumbers@yahoogroups.com" <primenumbers@yahoogroups.com>
              Date: Wednesday, September 12, 2012, 9:43 AM



               



              --- On Tue, 9/11/12, Steven Harvey <harvey563@...> wrote:
              > http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911
              >  
              > Comments, anyone?

              Well, the maths is so far above my head I cannot comment on it at all. However, I must say that I'm worried that he seems to be working in a vacuum - about 60% of the references in his paper were to his own prior work, and many of the others were to standard background texts not pertinent to the main thrust of his paper. If people are going to give this the thumbs up, they're going to have to do a lot of groundwork on his prior stuff too. I'll just wait until the Taos, Mazurs, and Elkies are satisfied. I'm prepared to wait several years.

              Having said that, a couple of those have made some fairly positive comments about the paper being worth looking into already so we're not looking at Gene Ray inventing a Time Tesseract.

              Phil







              [Non-text portions of this message have been removed]
            • Jack Brennen
              ... Here s one from the bibliography: [DmMn] H. Dym and H. P. McKean, Fourier Series and Integrals, Academic Press (1972). There are others.
              Message 6 of 8 , Sep 12, 2012
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                On 9/12/2012 5:35 PM, James Merickel wrote:
                > Phil Carmody has suggested that there are standard texts that are not pertinent in reference.
                >
                > Phil, would you be so kind as to name these (to facilitate answering the question I have--and others may--of 'rhetoric' in a 'mathematical world')? I don't know the leveling you place on
                > this statement. Nor is the 'a couple of these' phrase clear. You may save us some time if this is a form of play. You may push somebody serious onto the ledge with the other already
                > serious people to this question of validation. Thank you, if you would. And no offense intended in singling you out (to anyone). I merely wish to know what these books are (whether, now,
                > I understand your expression entirely, partly, or not at all; and whether I can quickly understand it or only slowly, if I ever do).
                >
                > Yours Truly, James G. Merickel

                Here's one from the bibliography:

                [DmMn] H. Dym and H. P. McKean, Fourier Series and Integrals, Academic Press (1972).

                There are others.
              • djbroadhurst
                ... The claimed inequality of bounded discrepancy classes in Theorem A of Paper IV is mind-boggling general; much wider than ABC. It may take a long time for
                Message 7 of 8 , Sep 13, 2012
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                  --- In primenumbers@yahoogroups.com,
                  Steven Harvey <harvey563@...> wrote:

                  > http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378?WT.ec_id=NEWS-20120911

                  The claimed inequality of "bounded discrepancy classes"
                  in Theorem A of Paper IV is mind-boggling general;
                  much wider than ABC. It may take a long time for a few
                  knowledgeable souls to work through these 4 dense papers.

                  I am deeply impressed by how hard the maths community
                  is prepared to work on corporate validation of significant
                  claims. Here is a recent example:

                  http://www.iitg.ernet.in/a.saikia/workshop.htm

                  David
                • Phil Carmody
                  ... Perhaps pertinent was too weak a word. an essential or direct precursor would have been better. For example, Jack pulled out the Fourier Transform one.
                  Message 8 of 8 , Sep 13, 2012
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                    --- On Thu, 9/13/12, James Merickel <moralforce120@...> wrote:
                    > Phil Carmody has suggested that there
                    > are standard texts that are not pertinent in reference.

                    Perhaps "pertinent" was too weak a word. "an essential or direct precursor" would have been better. For example, Jack pulled out the Fourier Transform one. IIRC, other ones which had a publishing date before the author's first paper caught my eye (Wiles?). There of course may be some relevance, some use, of such papers, but they're more for scene setting than anything else.

                    Phil
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