Generic Names for Streams

Young kids quite quickly pick up some of the basic aspects of things like graph theory, set theory, and even abstract algebra in the right contexts. I've seen multiple mathematicians speculate that teaching such topics more and at much younger ages could raise both kids interests in math and their long term prospects in pure math. The issue is that for 99% of people these math subjects have no direct practical use (still great mental exercises in multiple ways though), and some efforts to teach such subjects in the past did so at the expense of more practical arithmetic and applied math that people need in today's world. While I'm all for kids exploring topics for sake of interests or to help improve abstract thinking, the basics still need to be covered.

But with the way math is taught in most schools now, the closest most get to pure math is a proof-centric geometry course (which some like much more than a cookbook algebra course), and those that trying to go more heavily into math in university hit a wall with an abstract algebra course that weeds out a large number of people from math programs.