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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?"
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
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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.
Surely "undefined" is the right answer?
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
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