My science fair project is concerned with solving a general polynomial of arbitrary degree. Naturally, I've wanted it to be completely original, but I've found several citations regarding its already having been done:
Polynomial - Wikipedia, the free encyclopedia
Solving the Quintic (the section titled "solution based on series")
Abel's Impossibility Theorem@Everything2.com (mentioned at the very bottom of the article)
You can see that the wikipedia source is without citation for the part that mentions hypergeometric functions.
My questions is: really?! Part of my project is considering the implications of solving the problem, and they seem to be momentously profound. I'm talking prime number, Riemann hypothesis profound, so why have I been able to find only three sources and a research paper that I have to buy (click here to see what I'm talking about--it's the article that is mentioned in the 4th note of the above wikipedia article) on the subject? I'm currently studying linear algebra so I don't really know what an eigenvalue is, but I've looked up the motivation for the hypergeometric function and its application to finding zeros has at least held intuitively for me, and it may have some clear application. But apparently it's been shown to have a direct application! Gahh!!
I guess that there's actually two questions in there... I actually do want both to be answered =)