For an excellent treatment of how doing mathematics is a subtle and dynamic interplay of the "Greek" and "Babylonian" approaches I recommend Imre Lakatos' "Proo

For an excellent treatment of how doing mathematics is a subtle and dynamic interplay of the "Greek" and "Babylonian" approaches I recommend Imre Lakatos' "Proofs and Refutations" (http://books.google.ca/books?id=EjQqJT4Z-VoC&lpg=PP1&dq=proofs%20and%20refutations&pg=PP1#v=onepage&q=&f=false http://books.google.ca/books?id=EjQqJT4Z-VoC&lpg=PP1&#38...). It's presented as a Socratic dialog and is simply fantastic.