Before digging into the various books others have suggested, you would do well to read "Where Mathematics Comes From" by George Lakoff and Rafael Nunez: http://

Before digging into the various books others have suggested, you would do well to read "Where Mathematics Comes From" by George Lakoff and Rafael Nunez: http://www.amazon.com/Where-Mathematics-Comes-Embodied-Brings/dp/0465037712/ref=pd_bbs_sr_1/103-1216395-3355860?ie=UTF8&s=books&qid=1202144892&sr=1-1 http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... That book explains the origins and understanding of the basic items of mathematical analysis: infinity, sets, classes, limits, the epsilon-delta of calculus and alternatives, infinitesimals, etc. The explanation is from the viewpoint of psychological understanding. It details how we build up a scaffolding of tools (starting with basic counting) sufficient to slay the dragons of modern physics and mathematics.