Hm, I've also decided (on the very contrary to my last guidelines) that I'd like to encourage the discussion of pure mathematics, since it's way cooler and far more beautiful than elementary problem-solving and high school math.

If you don't know what pure math is, then there's always wikipedia. In a succinct definition: pure math is rigorous, proof-based math that need not have any real-world applications, and is unlike anything in the high school curriculum.

How would you guys like it if I start a lecture series of posts on the topological derivation of calculus? There are really no prerequisites, and it's nothing like BC Calc (which isn't real math). How many people would participate in this? (I would leave some theorems for you to prove.)