pure mathematics is...
"Pure mathematics is, in its way,
the poetry of logical ideas."
I love this quote. Anybody that can make it past the basics in mathematics and get to the really interesting stuff, has the opportunity to see it in this poetic kind of way.
I would liken it to looking very closely at a painting. When you are really close to it, and all you see is a couple of brush strokes, and your eyes are sort of crossed because your nose is up against the painting, then it usually isn't a brilliant piece of art. But as you draw back, and bring more and more of the picture into view, you suddenly begin to see this brilliant painting. (And for many, you begin to see the artist through the painting.)