Those sound like what's needed. Thanks for making awesome concrete suggestions!
I wonder whether the Math category should be broken down a bit. There's calculation - which is sometimes easier to start with e.g. things like basic arithmetic operations, representing real quantities with mathematical numbers and shapes), then there's algebra/geometry and the things which follow, and probability starts with a new set of axioms and applies to a different sort of problem, so it may deserve a separate skill hierarchy. I might also separate out "proving" as a standalone skill, though with not very many levels. (You learn to prove advanced math by learning the math, but initially you still have to learn how to follow and then how to generate a proof). Or maybe as part of a" logic" skill hierarchy?
I worry that the system will get way too complicated if we're splitting things up at that level. But maybe with many worker bees, it will thrive, like Wikipedia or MathWorld. In my leveling references (various games I've played), you could get to level 4 in Math, but put a note that said "strong on probability theory, average on the rest".
I think we need to determine if we want a Level system as found in various games, or a Badge system, that quantifies/commemorates particular tasks (your breakdown reminds me more of Badges, not Levels).
Maybe bot...
I just got this random idea that people who want to become better at life could benefit from a common scale of "leveling". No, I don't mean vague Lesswrongey things like "changing your mind". I mean a set of concrete criteria like "you qualify for level 2 if you can do 5 pull-ups, have solved 30 Project Euler problems, and did 10 cold approaches". Obviously there would be separate ladders for different character classes, but not too many. Also obviously, my example was a bit too high for level 2. So I guess I really want to ask some meta questions here:
1) Do you think agreeing on a common leveling scale would be a good thing for a substantial subset of LW users? Would you feel good about leveling up and telling other people about it on LW?
2) Is there some good way to determine leveling criteria that are neither too high nor too low? Maybe make an intermediate scale of "experience points"?