I see what you're saying, but I would say there's a strong "doing" component in math.
It's still really important to work through problems mechanically (often with only partial understanding) if only to become familiar with patterns. Whether this exploration is done via a CAS or by hand, acquiring this mechanical familiarity is important if one is to go deep. Math is often not merely read but done.
Take something like automatic differentiation (AD) for instance. It's just the chain-rule in principle right?
One could try to study the principles of AD in textbooks/journal pubs and then try to implement it in code. Chances are one is unlikely get it right the first few times because anyone who's ever tried to implement anything from numerical computation papers knows that published papers regularly omit important implementation details (unless they also publish code). There's so much heuristic/unintuitive behavior [1] in the world of numerical computation that first principles alone is rarely enough to get you a decent implementation in code.
On the other hand, if one mechanically works through AD derivations for a bunch of functions and observing the patterns that emerge (without necessarily grasping all the principles at first), one begins to notice things, like difficulties posed by corner cases like non-smooth/discontinuous functions, non-n'th differentiable functions, etc. A CAS could be used for this exploration (manually doesn't necessarily literally by hand) but it's so important to actually try stuff out and really grasp how mathematical objects work in practice. Once this contextual understanding is acquired, going back to AD journal pubs and reading about the principles is likely going to make way more sense because one has seen the behavior "in the field".
I do think the pure mechanical repetition is often underrated as a autodidactic mechanism. (again I don't mean literally by hand, but rather "doing" instead of just "reading and thinking").
[1] non numerical comp folks are often surprised to hear this because they think everything's super deterministic -- it's not. Tiny random perturbations in matrix can change things wildly. Take naive Gaussian elimination -- the ordering of the rows of equivalent linear systems can vastly affect solution efficiency and numerical stability, but one can't appreciate that unless one understand how GE works mechanically and has worked through examples.
It's still really important to work through problems mechanically (often with only partial understanding) if only to become familiar with patterns. Whether this exploration is done via a CAS or by hand, acquiring this mechanical familiarity is important if one is to go deep. Math is often not merely read but done.
Take something like automatic differentiation (AD) for instance. It's just the chain-rule in principle right?
One could try to study the principles of AD in textbooks/journal pubs and then try to implement it in code. Chances are one is unlikely get it right the first few times because anyone who's ever tried to implement anything from numerical computation papers knows that published papers regularly omit important implementation details (unless they also publish code). There's so much heuristic/unintuitive behavior [1] in the world of numerical computation that first principles alone is rarely enough to get you a decent implementation in code.
On the other hand, if one mechanically works through AD derivations for a bunch of functions and observing the patterns that emerge (without necessarily grasping all the principles at first), one begins to notice things, like difficulties posed by corner cases like non-smooth/discontinuous functions, non-n'th differentiable functions, etc. A CAS could be used for this exploration (manually doesn't necessarily literally by hand) but it's so important to actually try stuff out and really grasp how mathematical objects work in practice. Once this contextual understanding is acquired, going back to AD journal pubs and reading about the principles is likely going to make way more sense because one has seen the behavior "in the field".
I do think the pure mechanical repetition is often underrated as a autodidactic mechanism. (again I don't mean literally by hand, but rather "doing" instead of just "reading and thinking").
[1] non numerical comp folks are often surprised to hear this because they think everything's super deterministic -- it's not. Tiny random perturbations in matrix can change things wildly. Take naive Gaussian elimination -- the ordering of the rows of equivalent linear systems can vastly affect solution efficiency and numerical stability, but one can't appreciate that unless one understand how GE works mechanically and has worked through examples.