For more stuff like this, check out Love and Math (http://www.amazon.com/gp/product/0465050743/ref=as_li_ss_tl?... , disclaimer: affiliate link). It's a great book I'm just in the middle of that talks a little about doing maths and the mindset and heart behind it. Some of the OP's observations are echoed in the book and it's nice to have the OP and the author of Love and Math give words to my own obsession to problems I've tackled and failed to solve.