I liked John Derbyshire’s “Unknown Quantity: A Real and Imaginary History of Algebra”, but I still didn’t really grok why fifth order (and higher) polynomials don’t have general solutions. The answer has to do with group theory, which I don’t think is taught in high-school. For a while I had it in mind to eventually learn some group theory, but didn’t act on it. Last night I decided to try googling for an introduction, and one of the first results was, of all things, a tripod page. I know, who uses them. Seems pretty good though.