Page 2 of 4 FirstFirst 1234 LastLast
Results 16 to 30 of 46

Math Help - Riemann Hypothesis

  1. #16
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    (to the tune of "Sweet Betsy from Pike")

    Where Are The Zeros of zeta of s?
    G.F.B. Riemann has made a good guess:
    "They're all on the critical line", stated he,
    "And their density is one over two pi log T."

    This statement of Riemann's has been like a trigger,
    And many good men, with vim and with vigor,
    Have attempted to find, with mathematical rigor,
    What happens to zeta as mod t gets bigger.

    The efforts of Landau and Bohr and Cramer,
    Hardy and Littlewood and Titchmarsh are there.
    In spite of their effort and skill and finesse,
    In locating the zeros there's been no success.

    In 1914 G.H. Hardy did find,
    An infinite number that lie on the line.
    His theorem, however, won't rule out the case,
    That there might be a zero at some other place.

    Let P be the function of pi minus Li;
    The order of P is not known for x high.
    If square root of x times log x we could show,
    Then Riemann's conjecture would surely be so.

    Related to this is another enigma,
    Concerning the Lindelof function mu sigma,
    Which measures the growth in the critical strip;
    On the number of zeros it gives us a grip.

    But nobody knows how this function behaves.
    Convexity tells us it can have no waves.
    Lindelof said that the shape of its graph
    Is constant when sigma is more than one-half.

    Oh, where are the zeros of zeta of s?
    We must know exactly. It won't do to guess.
    In order to strengthen the prime number theorem,
    The integral's contour must never go near 'em.

    Tom M. Apostle
    Caltech, 1955
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by wingless View Post
    Tom M. Apostle
    Caltech, 1955
    Intersting to see that Apostle wrote this one.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Member
    Joined
    Mar 2008
    Posts
    182
    I did my final year project on trying to explain the Riemann Hypothesis - came across some really nice maths...

    I think any proposed proofs are given a 'scrutiny' time of 2 years before it'd be declared solved, and the prize awarded.

    It was my interest in number theory that led me to the problem, and I've always referred to it as a number theory problem because I hated complex analysis

    There's a huge number of number theory 'theorems' that begin with the assumption that Riemann's Hypothesis is true - so if it isn't, that's quite a number of conjectures that will have to be thrown out or adjusted...

    Ramanjuan worked on the Hypothesis with Hardy, but the only really remarkable thing in relation to it was the amount of stuff he REdiscovered, that had already been known in the west for some time.

    Hardy and Ramanjuan made inroads into Goldbach's weaker conjecture form assuming that the Riemann Hypothesis was true, although I never really got to look into how that worked.

    And interstingly if you prove the Riemann Hypothesis is impossible to prove - that means that it must be true Because if it's not true - there's a zero off the line - which would be provable

    It'll be interesting to see how this develops... Keep us updated!
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by Unenlightened View Post
    It'll be interesting to see how this develops... Keep us updated!
    Yes, it would be interesting.

    Maybe if TPH has more news from his tutor he will post it here. We'll have to wait and see.

    I read somewhere that if it is solved, then all cryptic codes like internet encryption could be easily decrypted, making online security(internet banking, online shopping, etc) a thing of the past. Is this really true?
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by janvdl View Post
    I read somewhere that if it is solved, then all cryptic codes like internet encryption could be easily decrypted, making online security(internet banking, online shopping, etc) a thing of the past. Is this really true?
    No.

    (I am not sure about this because this area of math never interested me). There happen to be faster primarility tests which involve the Hypothesis. The proof behind these tests working all the time use the truth of Hypothesis. Which means if the Hypothesis is true these primality tests would get faster. But that will not give us a way to factorize large numbers. That is not what the problem is about.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Member
    Joined
    Mar 2008
    Posts
    182
    No - the Riemann Hypothesis won't really help crack any codes. If you think about it - if it did help, people could just assume that it was true and work off that...

    Btw - I highly suspect this originated as an April Fools'...
    Follow Math Help Forum on Facebook and Google+

  7. #22
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Unenlightened View Post
    No - the Riemann Hypothesis won't really help crack any codes. If you think about it - if it did help, people could just assume that it was true and work off that...

    Btw - I highly suspect this originated as an April Fools'...
    i don't know about that. Mathematicians are not like everybody else who build foundations on shaky ground. something has to be proven to be true before they use it in anything else. and that is how it should be! It would be ok, I guess, to say, "If the Riemann Hypothesis were true, then it would mean this, but it's not, so we don't know!"
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Jhevon View Post
    i don't know about that. Mathematicians are not like everybody else who build foundations on shaky ground. something has to be proven to be true before they use it in anything else. and that is how it should be! It would be ok, I guess, to say, "If the Riemann Hypothesis were true, then it would mean this, but it's not, so we don't know!"
    But that is what he is saying. People are assuming it is true. And anyway these people who use it in algorithms are not really mathematicians. They do not care if stuff is proven or not. They just care for results. So if they can factor numbers more quickly and each time it works, they would just assume it always works.
    Follow Math Help Forum on Facebook and Google+

  9. #24
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by Unenlightened View Post
    No - the Riemann Hypothesis won't really help crack any codes. If you think about it - if it did help, people could just assume that it was true and work off that...

    Btw - I highly suspect this originated as an April Fools'...
    No, I read it on the website of some British newspaper(Mail & Guardian perhaps). It's an old article, I think it was written in 2005.
    Follow Math Help Forum on Facebook and Google+

  10. #25
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by janvdl View Post
    No, I read it on the website of some British newspaper(Mail & Guardian perhaps). It's an old article, I think it was written in 2005.
    It wasn't deBranges' proposed proof was it?
    That was quashed in 2006 or 2007 i think...
    Follow Math Help Forum on Facebook and Google+

  11. #26
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by Jhevon View Post
    i have to read up on how Riemann came up with the hypothesis...
    I can e-mail you a pdf of my final year project if you wish. There's an answer to that in there... whether it's 100% correct or not is another matter...
    Follow Math Help Forum on Facebook and Google+

  12. #27
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Unenlightened View Post
    I can e-mail you a pdf of my final year project if you wish. There's an answer to that in there... whether it's 100% correct or not is another matter...
    sure, you can send it to me
    Follow Math Help Forum on Facebook and Google+

  13. #28
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    651
    Thanks
    1
    Awards
    1
    It's said that Riemann's Hypothesis was a response to a paper by Gauss on the density of prime numbers and what it approached, Gauss' results became known as the Prime Number Theorem and Riemann's hypothesis related mainly to the error term and proving that it was in fact the best way to represent the error. He did some of the work through complex analysis.
    Follow Math Help Forum on Facebook and Google+

  14. #29
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by Jhevon View Post
    sure, you can send it to me
    You'll have to send me your e-mail address then, I can't send attachments from here...
    Follow Math Help Forum on Facebook and Google+

  15. #30
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    There was an episode of NUMB3RS a season or two back where a brilliant mathematician(played by Neal Patrick Harris) was secrectly working on solving the RH. Some 'nare-do-wells' decided they would kidnap his daughter until he showed them how to use it to decrpyt and break into sensitive areas and steal money. Of course, in the end, he hadn't actually solved it and the bad guys were apprehended.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 4 FirstFirst 1234 LastLast

Similar Math Help Forum Discussions

  1. Riemann-hypothesis
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 16th 2010, 09:47 PM
  2. Riemann's Hypothesis
    Posted in the Number Theory Forum
    Replies: 17
    Last Post: December 23rd 2009, 01:40 PM
  3. Riemann Hypothesis
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: January 29th 2009, 04:56 AM
  4. Hypothesis on Riemann Hypothesis
    Posted in the Advanced Math Topics Forum
    Replies: 4
    Last Post: March 12th 2006, 09:59 AM
  5. Riemann Hypothesis
    Posted in the Number Theory Forum
    Replies: 14
    Last Post: November 24th 2005, 04:52 AM

Search Tags


/mathhelpforum @mathhelpforum