An idea that I will never implement is to create a mathematics wiki site structured as a "lattice", meaning that all links within a given explanation can only point "down", for suitable definitions of down. It's frustrating to try to learn anything from Wikipedia because it'll freely jump up to post-graduate math on any topic without warning. Despite it being suboptimal from a pure math perspective, I figured "down" would likely end up being "a topic covered earlier in the standard mathematics curriculum"; any other attempt to be clever I came up with always backfired for the "able to learn math from this resource" goal.
The second paragraph of the Wikipedia page on integers, about as simple a "math" page as I can imagine, as I write this, brings in "subset" and "countably infinite", and the third paragraph just goes off the rails if you're trying to use this to learn about the integers: "The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers."
I know enough of the relevant maths to actually perfectly understand that. I also remember enough about when I didn't understand the relevant maths to remember what it felt like to read stuff like that. My point here is not that it's a "bad page", just that it is very hard to learn anything that way.
This is exactly it. You want a directed tree for learning, whereas wikipedia is an undirected graph. Mathematics suffers the most since its tree is unusually deep, not wide.
The second paragraph of the Wikipedia page on integers, about as simple a "math" page as I can imagine, as I write this, brings in "subset" and "countably infinite", and the third paragraph just goes off the rails if you're trying to use this to learn about the integers: "The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers."
I know enough of the relevant maths to actually perfectly understand that. I also remember enough about when I didn't understand the relevant maths to remember what it felt like to read stuff like that. My point here is not that it's a "bad page", just that it is very hard to learn anything that way.