Slashdot Mirror
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?"
What is the name of God? (cliff's notes for the lazy)
This question has already been debated quite extensively in the newsgroup sci.math.
It's quite an interesting read!
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 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
watch this
For those interested, the function is:
[ (1 + sqrt(5))^n - (1 - sqrt(5))^n ]/[sqrt(5)*2^n]
Free Java games for your phone: Tontie, Sokoban
Um... you seem to forget the Arabs. In the Middle Ages, the Arabic culture flourished and was the intellectual center of the world, particularly in fields like mathematics and astronomy. It's my understanding that the Arabs were largely responsible for maintaining the knowledge that the ancient Greeks, and others, had developed.
Why do you think we use "Arabic numbers"?
Why do you think most stars have Arabic names?
It's unfortunate that advanced Middle Eastern culture has largely disappeared in the last millenium, and surely Europe, the New World and Far East lead the world in scientific and cultural development now, but there was a lot happening in the Middle Ages.
And let's not forget Europe. Even before the Renaissance, Europe, while certainly not advancing like it did starting in the 15th century, was hardly stagnant. Most of Western society's major secular institutions: hospitals, universities, etc, were founded in the Middle Ages.
And of course, we all know that the Chinese had many advanced developments centuries before the rest of the world (gunpowder, paper, etc).
You are in a maze of twisty little passages, all alike.
You're forgetting the Arabs. If you want something truly novel, try trigonometry. The entire concept, sine*, cosine, tangent, etc., was invented during the Middle Ages (by Arabs like Abu al-Wafa and Abu Nasr Mansur).
* The Hindus knew about sine, but they didn't understand it very well and certainly didn't extend the notion to the other sides of the triangle.
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.
I have seen the future, and it is inconvenient.
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?)
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)
thank God the internet isn't a human right.
The entire concept, sine*, cosine, tangent, etc., was invented during the Middle Ages (by Arabs like Abu al-Wafa and Abu Nasr Mansur). ... who then sent their work back in time to roughly 1900BC, in order that the Babylonians could inscribe a table of secants into Plimpton 322.
Tarsnap: Online backups for the truly paranoid
1) The library wasn't burned by an angry mob, it was burned accidently, by Caeser's army, when some of their missiles (launched from boats) went astray.
Very interesting. I hadn't heard that before but a quick web search led me to this page where the authors agree with you. I had only heard the mob-burning-library-after-killing-Hypatia story.
2) Most written documentation on the "great library" suggests it wasn't a library like LoC, but more like a collection of erotic art and poems.
This statement I find no evidence for in my web search. Most everything I find (such as this) seems to suggest it was the center of learning in the ancient world as I originally posted. It's possible that the scholarly works were in the minority in the library. However it should be noted that this link does describe Alexandrian literature as erotic.
It would have been nice if you had posted some links but I thank you for the clarifications in any case.
GMD
watch this
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?
If you were a true Trekkie, you would know that and would have copies of the original, uncut episodes...
(* The port of Alaxendria, one of the busiest port-cities, had a law that required ships that came to port to loan all their written scrolls etc. to the library, where it was faithfully copied and archived. That's what made the library (one of) the greatest of its time. *)
If they were so great, how come they did not have an off-site back-up policy in place?
Table-ized A.I.
(* 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.
Table-ized A.I.
(* 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.
Table-ized A.I.