Alexandre Borovik wrote a really wonderful "http://www.maths.manchester.ac.uk/~avb/pdf/WhatIsIt.pdf" [Broken] on this topic, as a comment and aid in the problem of developing the next generation of creative mathematicians in the UK, his adopted country. He takes a hard cold look at the realities, as indicated by this passage: This sure resonates with me; in the course of writing my abortive Ph D thesis I generated and proved several good theorems, and oh! it was hard! Not just difficult, but wracking. As the man says, junkies. If you lke his style, you can read Alexandre Borovik's blog at http://www.maths.manchester.ac.uk/~avb/micromathematics/ [Broken].