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In math, the more experienced you are, the more comfortable you get with using shortcut notations and omitting obvious details. Students like to use verbose, explicit notation, and feel lost when they encounter shortcuts -- thinking they're missing important details.
This reminds me of a pattern I see a lot in grad students in ML -- those least comfortable with abstracting away boilerplate are usually those least familiar with what the boilerplate represents.
I mean, can I really trust a library to compute my gradients? I don't know what's going on behind the scenes... 
In anthropology, we call it procedure as magical thinking. Without a solid understanding of what you are doing and why, you replicate and imbue every step with deep meaning, and are scared of changing anything lest it break for reasons you don’t comprehend.
I agree, except when the abstractions are leaky. Bad notations and bad boilerplate abstractions can make the picture less clear.
that's not true. in programming you tend to use way more black box approach, that is not exactly being sure what's going on behind the scenes and being ok with that. doesn't really work with math that way.
The opposite is true for me. 
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