My impression is that school doesn't really teach any advanced math, for some people it's really essential, for some it may seem advanced, but a maths professor usually calls it trivial. Of course that makes it more important to know. It's not just about giving them what they need to do a certain job, as Rhyfelwyr says, but also about making them able citizens which are ready to do a lot of things that go beyond a factory job. A large part of schooling is also about teaching critical thinking, at least it was on our school.
I don't really think understanding Shakespeare reveals the upper echelon elite superkids, in many cases the upper echelon elite superkids from space are revealed because they're doing really bad since they're bored.
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