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What is the Oldest Unsolved Math Problem?
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?"
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 dunno... Slashdot readers watching a movie about a paranoid schizophrenic computer nerd who thinks he has the solution to everything and that everyone is out to get him. Might hit too close to home.