Curiosity and wanting to know is a valid enough reason by itself...

To understand how bitcoin works, you'll need to know some cryptography though. Applied cryptography from Bruce Schneier is a pretty good book to get started on cryptography, and for reference too. Knowledge about integer algebra and having a computer science degree would help. Once you have that, reading Satoshi's paper is completely straightforward. It's short, concise and to the point, he doesn't beat around the bush.