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 both? Generic human levels for the things most of us agree are important for everyone to work on, plus badges for the specializations, like algebraic geometry or the computational astrophysics of stellar dust? Maybe "numeracy" for the generic human version of math, cf. John Allen Paulos' "Innumeracy" book.
Right now I'm most interested in "generic human levels", but several people here in the comments have independently expressed interest in the idea of "badges" for specialists. Perhaps you could make something out of it? :-)
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"?