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Man, you're spot on. I've felt that the way math is taught now is akin to spending 10 years on 'if', 'for', 'while', and 'switch' statements (and being able to evaluate them perfectly without a compiler).

Beautiful point. It's along the lines of "How can you learn programming without the details of how to turn a series of tokens into an AST?"

I am so stealing this analogy!

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