I once promised someone here I'd write a post called "(pure) mathematics for rationalists," and I tried, but it was way too big a subject and I couldn't figure out a good way to get started or exactly what I should be writing about. If someone would like to request a substantially narrower version of this post, I would be grateful. Some possible ideas, phrased in the form of questions:

• What is pure math, anyway? I sort of know what physics and biology and chemistry are, but I don't have a concrete visual picture in my head of what a person does when they tell me they're a mathematician.
• What would I get out of studying pure math, e.g. in terms of possible rationality skills?
• How do I get started learning pure math if I haven't done much math before? (I don't know if I have anything intelligent to say about this, though.)
• To what extent is it justifiable to study pure math relative to something more useful, e.g. programming?