Do you know your constructivists from your formalists. Your realists from your platonists? I certainly didn't but I'd seen these terms pop up whenever I skirted around the edges of the philosophy of mathematics.

This book provides an excellent overview of all the above positions and more, dissecting each using a couple of nice questions: "What is the position's take on infinity: actual or potential?" And "what is the ontology and epistemology of mathematical objects?".

Me, I think I'm a formalist with constructivist leanings with occasional lapses into realism when thinking about infinity. ( )