Students are taught that "math" is doing arithmetic by hand, simplifying and factoring expressions, memorization, plugging-and-chugging formulas, and in general

Students are taught that "math" is doing arithmetic by hand, simplifying and factoring expressions, memorization, plugging-and-chugging formulas, and in general performing rote computations with pencil and paper. These things are simply not pleasant for a lot of people. Nothing anti-authoritarian about it, they're just unpleasant and repetitive tasks that any good hacker would be aching to automate. I had great science teachers who taught me about fundamental soundness, reasoning from first principles, developing/testing/revising quantative models, and describing the state and behavior of the universe (i.e. what calculus was created for in the first place). That was fun. But nobody was doing that thinking "so this is math" because it wasn't called that, it was called physics or chemistry. When you are in an a middle or high school classroom called "Math" with a book called "Math" you are doing rote algebraic manipulation, full stop. So that is what math is to you. No wonder people hate it. Fundamental soundness, proof, etc. has very little to do with numeracy in the sense of mental arithmetic, estimation skills. Those are useful too, but different things. I still can't multiply two-digit numbers in my head but that never posed a problem in calculus, computer science, chemistry, physics, or anything else.