mechaniker

I mean, that's mostly a nonsense sentiment, but I really enjoyed the allegory so I will not hold it against you. The widest ranging theorem in mathematics was created by a bunch of greek cultists who believed that the natural numbers were at the heart of existence. The most important mathematical textbook, one that was taught almost exclusively for over a millenia in the west, was steeped in the traditions of said cult. That tradition is still there and has, for the most part, always been there (although, as an extremely applied mathematician, I find it's practioners to be alien).

Plus, tell me: how do you learn proofs? They aren't statements in a textbook that you just learn and recite like poetry. You have to learn to see them, to understand how all those moving parts fit together. When done right, teaching proofs is an exercise in illumination. I find it is more enjoyable all around when performed as a creative, exploratory exercise: give the students the axioms, set them lose on a conjecture.

Of course, for that you need a) Teachers who can serve as guides in the mathematical worlds and b) Students who aren't culturally predisposed to dislike mathematics.

I'm not even convinced that schools teach math as a tool. Too few students are aware of the raw power that learning how to think mathematically and use mathematical knowledge as a problem-solving tool gives them. It provides new insight into fields as diverse as visual art and as applicable as physics. The latter of which only became the potent subject it is today after being mathematized.

Forget about about students, there are career programmers out there who only began their careers after a google search on whether they needed math to be a good programmer assured them otherwise. It's so ridiculous to me that I can't help but feel that some shadowy worldwide illuminati-esque force is intentionally sabotaging mathematical education to keep the populace unaware of how much more capable they could be when fully trained in mathematics. (Why would they do this? I don't know, but I think it has something to do with the pyramids.)

Jokes aside, I do wonder what the flaws in the mathematical education system are. Anecdotally, I've found that the truly skilled mathematics students rarely go into teaching careers, which is understandable. One of my favorite mathematics books, How to Solve It by George Polya, outlines a style of teaching that requires the teacher to be as much a confident performer as well as a skilled mathematician. It's worth saying that Polya was Hungarian, growing up at a time that mathematics teachers were expected to have serious postgraduate qualifications. Whilst it would be nice to go back to such rigorous standards, I can't imagine the resulting lack in qualified teachers such a policy would produce...