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road to perfection

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  • cino hilliard
    Hi, I thought of a catchy phrase today and would like to hear views on it. There are many roads to Rome but there is only one road to perfection -
    Message 1 of 9 , Jun 4, 2008
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      Hi,
      I thought of a catchy phrase today and would like to hear views on it.

      "There are many roads to Rome but there is only one road to perfection - mathematics."

      Maybe just "There is only one road to perfection - mathematics." would suffice.

      My thinking is this is an axiomatic truism with few instances of disagreement. Certainly, notcalling the number 1 prime ruffles my feathers and moreover not calling "1" compositeand inventing a name of convenience calling 1 "unity" bothers me too. I guess becauseI am ignorant of some of the deep esoterics being invented.

      Spatial diminsions > 3 bothers me. Also, Wiles' proof of Fermat's Last Theorem completely disgruntles me. He proved another conjecture which implied the FLT. How can we say thisis perfect when maybe 100 people in the world understand it?

      I wished Fermat had said there are no integers a,b,c,n>2 such that a^n+b^n=c^n can beproved to be true or false for all n using elementary methods.

      Having said these things, the phrase is still quite strong. Surely, more ideas are out there.
      Enjoy,
      Cino

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    • Peter Otzen
      ... perfection - mathematics. ... would suffice. ... I would have thought that Physics was the road to perfection - and the scenery along the way. So many of
      Message 2 of 9 , Jun 4, 2008
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        --- In mathforfun@yahoogroups.com, cino hilliard <hillcino368@...>
        wrote:
        >
        >
        > Hi,
        > I thought of a catchy phrase today and would like to hear views on it.
        >
        > "There are many roads to Rome but there is only one road to
        perfection - mathematics."
        >
        > Maybe just "There is only one road to perfection - mathematics."
        would suffice.
        >

        I would have thought that Physics was the road to perfection - and the
        scenery along the way.

        So many of the "weird" mathematical theorms and derivations seem to be
        developed to cover up shortcomings in the mathematical ideas we have
        defined to model the physical world - then the wild imaginings that
        have followed from those qualifications/cover-ups.

        Peter
      • cino hilliard
        Hi,--- In mathforfun@yahoogroups.com , cino hilliard wrote: Hi, I thought of a catchy phrase today and
        Message 3 of 9 , Jun 6, 2008
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          Hi,--- In mathforfun@yahoogroups.com<mailto:mathforfun@yahoogroups.com>, cino hilliard <hillcino368@...>wrote:>>> Hi,> I thought of a catchy phrase today and would like to hear views on it.>> "There are many roads to Rome but there is only one road toperfection - mathematics.">> Maybe just "There is only one road to perfection - mathematics."would suffice.>>I would have thought that Physics was the road to perfection - and the>>scenery along the way.>So many of the "weird" mathematical theorms and derivations seem to be>developed to cover up shortcomings in the mathematical ideas we have>defined to model the physical world - then the wild imaginings that>have followed from those qualifications/cover-ups.Indeed, Every time I read on cosmology in Scienticic American or books or internetor see it on the discovery channel or Science Channel, there is a new theory out there. How do these guys know? Even Hawking has back tracked. Brian Green's String theoryis becoming unraveled too.

          Once in a while though, something is found that is so simple and elegant that it has to be true.
          Just recently I posted on another forum my formula for the sum of the primes < n ~ n^2/log(n)-1).
          The created a stir that the Bach-Shallit estimate for the first n primes has been out there 12 years.
          This estimator Bach-Shallit is n^2*log(n)/2. So you have to use n = Pi(x) to estimate the sum of primes < n with this formula. Also = P(x) ~ x/log(x) can be used with a little more error. You can use Li(x) which is also quite good and then there is Riemann-Gram's estimate which is accurate for the first half of the digits.

          It is quite simple how I (heuristically) derived ths formula n^2/(log(n)-1). I posted this in wikipedia.

          http://en.wikipedia.org/wiki/Prime_number

          This is probably not quite the elegance mentioned above, but it is roughly 414 times more efficient for large n than the formula many authors think is the Gospel. Apparantly, Bach and Shallit proved n^2*log(n)/2 is asymptotic to the sum of the first n primes.

          http://en.wikipedia.org/wiki/Prime_number

          "There is only one road to perfection - keep trying."

          Have fun,
          Cino

          [Non-text portions of this message have been removed]
        • ramsey2879
          ... would suffice. ... disagreement. Certainly, notcalling the number 1 prime ruffles my feathers and moreover not calling 1 compositeand inventing a name of
          Message 4 of 9 , Jun 7, 2008
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            --- In mathforfun@yahoogroups.com, cino hilliard <hillcino368@...>
            wrote:
            >
            > Maybe just "There is only one road to perfection - mathematics."
            would suffice.
            >
            > My thinking is this is an axiomatic truism with few instances of
            disagreement. Certainly, notcalling the number 1 prime ruffles my
            feathers and moreover not calling "1" compositeand inventing a name
            of convenience calling 1 "unity" bothers me too. I guess becauseI am
            ignorant of some of the deep esoterics being invented.
            >
            You seem to say that perfection is the absence of disagreement, and
            that there is only one road to perfection, but I for one disagree!
            As for "1" not being a prime, the number "1" reason is to avoid the
            necessity of changing "Any composite number can be expressed as the
            product of primes in one and only one way" to --any composite number
            can be expressed as the product of primes that are greater than 1, in
            one and only one way--. The theorem is much easier for one to say
            when "1" is not prime. I for one prefer that one not be deemed
            prime. The less one has to say "1" or "one" the better.
          • cino hilliard
            Yes, Your argument is the classical one. I just think we should be able define 1 in contextof the problem being worked on. Sometimes it could be prime other
            Message 5 of 9 , Jun 7, 2008
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              Yes, Your argument is the classical one. I just think we should be able define 1 in contextof the problem being worked on. Sometimes it could be prime other times composite and othertimes what it has been decreed to today. There are only a handful theorems 1 prime violates.

              Definition! That is the order of our time. Certainly I would not want to go one on one with Carl Sagon, if he were still here, who deemed 1 as prime. There were others too. The statement defining a prime:

              A prime number is a number that is divisible by itself and one only. This is true for 1. To take 1 out of the set of primes, we have to stipulate number > 1. So we have to say 1or "one" every time we express the definition of a prime number.
              Just think of it. The oddity of the first prime number being even would be relaxed. I guess we could take 2 out of the set of primes for certain theorems out there.

              It is a moot point but it still ruffles my feather.

              Enjoy,
              Cino


              To: mathforfun@yahoogroups.comFrom: ramsey2879@...: Sat, 7 Jun 2008 21:20:45 +0000Subject: [MATH for FUN] Re: road to perfection




              --- In mathforfun@yahoogroups.com, cino hilliard <hillcino368@...> wrote:>> Maybe just "There is only one road to perfection - mathematics." would suffice.> > My thinking is this is an axiomatic truism with few instances of disagreement. Certainly, notcalling the number 1 prime ruffles my feathers and moreover not calling "1" compositeand inventing a name of convenience calling 1 "unity" bothers me too. I guess becauseI am ignorant of some of the deep esoterics being invented.> You seem to say that perfection is the absence of disagreement, and that there is only one road to perfection, but I for one disagree! As for "1" not being a prime, the number "1" reason is to avoid the necessity of changing "Any composite number can be expressed as the product of primes in one and only one way" to --any composite number can be expressed as the product of primes that are greater than 1, in one and only one way--. The theorem is much easier for one to say when "1" is not prime. I for one prefer that one not be deemed prime. The less one has to say "1" or "one" the better.







              [Non-text portions of this message have been removed]
            • MorphemeAddict@wmconnect.com
              In a message dated 6/8/2008 00:47:06 AM Central Daylight Time, ... The second prime number being the only even prime would be even more odd. stevo
              Message 6 of 9 , Jun 7, 2008
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                In a message dated 6/8/2008 00:47:06 AM Central Daylight Time,
                hillcino368@... writes:


                > Just think of it. The oddity of the first prime number being even would be
                > relaxed.

                The second prime number being the only even prime would be even more odd.

                stevo </HTML>


                [Non-text portions of this message have been removed]
              • cino hilliard
                Is there an echo in here? Ok even more odd is a schos less reverberating. 2 must be an Irish prime done wrong. Cino To: mathforfun@yahoogroups.comFrom:
                Message 7 of 9 , Jun 8, 2008
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                  Is there an echo in here?

                  Ok "even more odd" is a schos less reverberating.

                  2 must be an Irish prime done wrong.

                  Cino

                  To: mathforfun@yahoogroups.comFrom: MorphemeAddict@...: Sun, 8 Jun 2008 02:32:46 -0400Subject: Re: [MATH for FUN] Re: road to perfection




                  In a message dated 6/8/2008 00:47:06 AM Central Daylight Time, hillcino368@... writes:> Just think of it. The oddity of the first prime number being even would be > relaxed.The second prime number being the only even prime would be even more odd.stevo </HTML>[Non-text portions of this message have been removed]







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                • Cino Hilliard
                  Hi, ... Ok. The Irish prime doesn t get mad, he just gets even ... 0400Subject: Re: [MATH for FUN] Re: road to perfection ... hillcino368@... writes: Just
                  Message 8 of 9 , Jun 9, 2008
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                    Hi,

                    --- In mathforfun@yahoogroups.com, cino hilliard <hillcino368@...>
                    wrote:
                    >
                    >
                    > Is there an echo in here?
                    >
                    > Ok "even more odd" is a schos less reverberating.
                    >
                    > 2 must be an Irish prime done wrong.

                    Ok. "The Irish prime doesn't get mad, he just gets even"

                    >

                    >
                    > To: mathforfun@...: MorphemeAddict@...: Sun, 8 Jun 2008 02:32:46 -
                    0400Subject: Re: [MATH for FUN] Re: road to perfection
                    >
                    >
                    >
                    >
                    > In a message dated 6/8/2008 00:47:06 AM Central Daylight Time,
                    hillcino368@... writes:> Just think of it. The oddity of the first
                    prime number being even would be > relaxed.The second prime number
                    being the only even prime would be even more odd.stevo </HTML>[Non-
                    text portions of this message have been removed]
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    > [Non-text portions of this message have been removed]
                    >
                  • MorphemeAddict@wmconnect.com
                    In a message dated 6/9/2008 12:16:40 PM Central Daylight Time, ... I m glad you cleared that up. I had given it up for gibberish. stevo [Non-text
                    Message 9 of 9 , Jun 10, 2008
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                      In a message dated 6/9/2008 12:16:40 PM Central Daylight Time,
                      hillcino368@... writes:


                      > > Is there an echo in here?
                      > >
                      > > Ok "even more odd" is a schos less reverberating.
                      > >
                      > > 2 must be an Irish prime done wrong.
                      >
                      > Ok. "The Irish prime doesn't get mad, he just gets even"
                      >

                      I'm glad you cleared that up. I had given it up for gibberish.

                      stevo </HTML>


                      [Non-text portions of this message have been removed]
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