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Science

What is the Oldest Unsolved Math Problem? 73

Posted by Cliff from the mysteries-of-the-unknown-starring-peter-graves dept.
evilquaker asks: "After finding a reference to the (still open) odd perfect number problem, which is claimed to date back to Euclid, I wondered: what are the oldest unsolved math problems? The folklore answer is that the odd perfect number problem is the only one posed by the Greeks which is still open. However, it seems there is some doubt as to whether Euclid actually wondered about odd perfect numbers. Further, there's a claim that the twin primes conjecture dates back to the Greeks. So what's the oldest documented still-open math problem? Perhaps something about Fibonacci numbers?"
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What is the Oldest Unsolved Math Problem? More

What is the Oldest Unsolved Math Problem?

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    • Whoever modded you "Troll" is probably right. Oh well, I'll bite anyway.

      If we're talking about the Jewish/Christian God (as your link seems to imply), it's a well-known fact that his name is spelled "Yohdh He' Waw He'", commonly transliterated into English as "Yahweh" or "Jehovah". This is not exactly a hidden secret.

      I'm not aware of any Jewish beliefs about a 216-letter name, or even anything close to the mystical powers described in the link you gave. Methinks this is either an obscure cabbalistic fiction or the sheer invention of the screenplay writer.

      Oh, and to debunk the "numerology of the Torah" stuff once and for all: although the overall message of the Hebrew Scriptures has stayed intact (the Dead Sea Scrolls, among others, verify the accuracy of the Masoretic text), the actual spelling of various words, the number of letters used, and in some cases even the exact choice of words all vary from manuscript to manuscript.

      This stuff is not scientific in any sense of the word, and certainly not up to the rigors of mathematical proof.

      Okay, I'll stop there... I don't want to go too far off-topic...

    • Someone mentions God and gets modded as a troll?

      Presumably the moderator in question didn't follow the link, or do we really have such extreme fundamentalists on /. as to be offended by a movie like Pi [filmmonthly.com]?

  • sci.math (Score:5, Informative)

    by SpatchMonkey ( 300000 ) on Thursday July 04, 2002 @08:56PM (#3824504) Journal
    This question has already been debated quite extensively in the newsgroup sci.math [google.com].

    It's quite an interesting read!

  • Hard to say since Library of Alexendria burned (Score:5, Informative)

    by GuyMannDude ( 574364 ) on Thursday July 04, 2002 @08:57PM (#3824513) Journal

    I know you are asking for the oldest documented math problem, but do remember that the Great Library of Alexandria was burned down by an angry mob. That library housed most of the world's knowledge up until that point. So documentation of any super-old problem was probably destroyed in the fire.

    By the way, a search on google for "oldest unsolved math problem" comes up with this page [newphys.se] which states

    PROOF OF THE INFINITUDE OF PERFECT NUMBERS (IPN). The IPN is either the second oldest, or the oldest unsolved problem of mathematics (debatable with the No Odd Perfect Number Problem), and this proof will easily evince anyone why it is one of the two oldest unsolved math problems.

    So I guess the IPN is a contender.

    GMD

  • Documented? (Score:1, Flamebait)

    by fm6 ( 162816 )
    So what's the oldest documented still-open math problem?
    What?! You're only interested in verifiable information????!!!! Fascist!
  • 1/0 is defined as undefined, I think that just means no one has ever figured out the right answer.
    • Well, whatever the answer is, it ain't a number. If 1/0 was a number, then 0 would be equal to 1, and all hell would break loose. If you like you can say that the answer is "infinity", since "infinity" isn't a number either.
      • If you like you can say that the answer is "infinity", since "infinity" isn't a number either.

        Just saying infinity doesn't tell the whole story, because the function f(x)=1/x diverges in different directions as x approaches 0. From the left, the limit is negative infinity, and from the right it is positive infinity.
        • 1/0 = +/-infiniti?

          • 1/0=1/0

            You can solve problems like 1/0 but you need to have context, numbers on there own are meaning less.

            so
            given 1 loaf is equivelent to 2 fishes

            1 pie / (2 fishes - 1 loaf)

            in just numbers becomes
            1/0

            but it's really
            1 pie / (2 fishes - 1 loaf)

    • Re:1/0 (Score:1, Informative)

      by Anonymous Coward
      Surely "undefined" is the right answer?
    • 1/0 is defined as undefined, I think that just means no one has ever figured out the right answer.

      No, this means that the quantity 1/0 is literally not defined. Within the field of rational numbers (and also within the reals and complex numbers), there is no number x such that 0 * x = 1, i.e. 0 has no multiplicative inverse. For any number x, 1/x represents the multiplicative inverse of x. Since 0 has no multiplicative inverse, 1/0 is undefined.

      • though on the complex sphere [the complex plain with an extra point, infinity, defined 1/0 is equal to infinity and is a reasonably sensible 'number'.

        Maths is all about context.
        • Well, if you do that, you no longer have a field. For instance, I assume 1+inf=inf. In which case (1+inf)-inf = inf-inf = 0 != 1 and you've lost the associative law. Which is certainly a nice property for 'numbers' to have.
    • (* 1/0 is defined as undefined, I think that just means no one has ever figured out the right answer. *)

      What do you mean? I can use Visual Basic's trusty console panel to figure it out.

      Okay, let's see. The result is........Damned BSOD! Rats! I'll hafta get back to you on this.
  • Contrary to common belief, Fermat's theorem is not solved or proven.
    Captain Picard refers to it in "The Royale", so that must be 2362 or something.

    The overzealous mathematician that did try to prove it a couple of years ago, almost created a time-space paradox and disaster, which was only just averted.

    Luckily for the Church of Trek
    "And Scotty beamed them to the Klingon ship, where they would be not tribble at all"
    "All power to the Engines"
    • You don't understand. All Trek episodes are vetted for Prime Directive violations before being sent back in time for our viewing pleasure. They couldn't reveal that Fermat's theorem was going to be solved in our near future, without disrupting the timeline. So "The Royale" had to be censored, of course.

      If you were a true Trekkie, you would know that and would have copies of the original, uncut episodes...

    • (* The overzealous mathematician that did try to prove it a couple of years ago, almost created a time-space paradox and disaster, which was only just averted. *)

      Oh, you mean Enron? It was not averted.

      Beware of accountants using Calculus.

  • I seem to remember that all of the math books we have from the "Greeks" (actually, people from the east costs of the Mediterranean who happended to use some greek dialect for commercial and cultural exchanges) were meant to show results, not problems: most of them are some sorts of summae where somebody expose everything that is known about some subject, with more or less comments and precisations. Some of them actually include what probably were original results of the authors, but always as facts, not problems.

    So, if we look back to greek times we can't have documented problems, but only problems that could have been asked with their knowdlege, expecially if it's similar to some problem they actually solved. If we accept this kind of problems, I believe that the existance of infinite perfect numbers could be a good candidate, as the Greek knew about them, and actually worried about the existence of infinite numbers of other kinds (prime, etc.).

    If, on the other side, you want actual written documentation about the problem, I'm afraid that either we find some fragment of a letter written by some greek or arabian mathematician (quite unlikely) or we have to focus on renaissance.

    Anyway, I'm not sure that problems with fibonacci numbers actually date to Fibonacci's era, as i seem to remember that they were only a small part of his work, and that they were extensively studied only later (by some 1800 French matematician?)

    • I seem to remember that all of the math books we have from the "Greeks" were meant to show results, not problems: most of them are some sorts of summae where somebody expose everything that is known about some subject, with more or less comments and precisations.

      Even so, it seems strange that they wouldn't indicate what definitely isn't known about a subject, to differentiate it from what is known but not said (because something will always be left out). Perhaps that's a modern development, though...

      • I think it is a modern developement: in ancient times people actually believed that one could write everything about a subject without leaving anything, probably also because in most disciplines people knew much less than we do today (and as a matter of fact many people succeded in gaining an almost complete knowdlege of disparate disciplines, without our need to specialize).

        Another possible reason is that we consider books to be a way to communicate ideas between contemporary people, so that knowdlege can be shared and used; in ancient times I believe that books were meant more for posterity than for their contemporaries, as most people who studied some subject tended to live in the same place (Alexandria, in a certain period), so they probably foud easier to share their knowdlege between themselves orally.

  • I don't know... but the answer is 42!
  • ... some of them *can't* be solved, like `express the roots of a quintic by radicals.'
  • 0 ^ 0 = 1

    Why can't we apply this to solve our financial dire strait?
  • I don't know but the answer is 42.

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