> The structure of formal proofs is taught in geometry. That's pretty much the only course where students are expected to prove theorems about the subject via p

> The structure of formal proofs is taught in geometry. That's pretty much the only course where students are expected to prove theorems about the subject via proofs. In most of the other courses students are taught the formulas and techniques, axioms and theorems, but then apply them, rather than attempt to develop or prove them themselves. They're also, typically, not shown a proof of the theorems they learn, they're just told to accept them. Wow! I can't even imagine how that works. When I went to school (and that's in Europe, not Asia), the notions of theorem and proof were taught in the fifth year of school (out of 12 pre-college years -- 8 in elementary, 4 in high school). That was, indeed, as part of geometry. Starting from high school, however, pretty much no formula is given without prior demonstration. Subjects where they can't do that (like mechanics -- that's taught in Physics prior to pre-calculus and calculus) are a royal fuckup. You aren't usually expected to be able to reproduce the proofs for those formulae, but a) you're strongly encouraged to study them, because they help you with the exercises and b) it's usually implied that, if you can't remember the formula, but you can prove it, it's OK. For example, if you can't finish a problem in a test because you don't know the formula, but you obviously try to find it, the professor will sometimes give you full credit, depending on circumstances and following a short talk. I didn't even like math back then, save for geometry, but I reckon this was the most important thing I learned there. Unless you're dumber than a toaster, you're typically able to apply what you learned to everyday phenomenae after ten years of school; the bonus you get is also being able to reason rigorously and correctly, which is an important takeaway no matter what path you choose to follow.