You are opposing “learning math deeply” to rote memorization of brittle special cases, but the threshold of being able to work with standard tools (for e.g. understanding technical content of physics/statistics courses) is only rigorous level. Moving further requires additional practice/motivation, when you are already capable of using the tools, and that is not separately discussed in the post.
One (wo)man’s brittle special case is another’s generalization. There are many different levels of abstraction. One can be at the rigorous level on some dimensions and at the post-rigorous level on others. In the other direction, many things that once required post-rigorous thinking are now sufficiently codified so that they now require only rigorous thinking. There’s not a well-defined body of “standard tools.”
Thanks Vladimir!
Why does my post give the impression of talking about the rigorous level?
You are opposing “learning math deeply” to rote memorization of brittle special cases, but the threshold of being able to work with standard tools (for e.g. understanding technical content of physics/statistics courses) is only rigorous level. Moving further requires additional practice/motivation, when you are already capable of using the tools, and that is not separately discussed in the post.
One (wo)man’s brittle special case is another’s generalization. There are many different levels of abstraction. One can be at the rigorous level on some dimensions and at the post-rigorous level on others. In the other direction, many things that once required post-rigorous thinking are now sufficiently codified so that they now require only rigorous thinking. There’s not a well-defined body of “standard tools.”