I haven't taken a math class in a while, unless computer logic counts, where we used formulae and proofs just like in math class.
I'm not sure free learning is a good idea. It interferes with the established power structure where only the social and economic elites can succeed without a lot of effort. Also, free learning is dangerous because terrorists can finally learn what to do with the glowing rocks they acquired but have no idea how to use to kill people en masse.