By the way, there are schools where you actually do math. I was lucky to get into one of these on the second try, after 7 series of exams and interviews. The math lessons (apart from algebra and geometry, which we had to learn too, of course), were set up pretty simple: you were given a single sheet of paper with some axioms and definitions about the topic at hand and a list of lemmas and theorems that you had to prove. When you thought you could prove on of them, you called on of the teachers (there were about 5 per class), sat down with them, and tried to defend your proof. No homework, nothing else but this sheet.

I didn't pursue a career in mathematics, like a lot of my classmates, but these lessons gave me more anything else I did in all years spend on 'education'.