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.
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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.
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I mean, can I really trust a library to compute my gradients? I don't know what's going on behind the scenes...
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My tutoring students love to just pull a number out of thin air as the result and they're gobsmacked when I ask them to prove how they got there haha
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“The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.” — Edsger Dijkstra “A programming language is low level when its programs require attention to the irrelevant.” — Alan Perlishttps://twitter.com/kncukier/status/965667050193551361 …
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They are, because the missing things aren't obvious to them.
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That might be true. But sometimes we have to spell out the details ourselves explicitly because true understanding comes about when we can work out all the details ourselves. I think you confound explicit notation and explicitly working things out.
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So, who are you communicating with? Rule of technical communication: write for your audience not yourself.
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The maths papers I see usually are very precise. It's the ML folks who seem to be shortcutting the corners. Sometimes this helps for understanding. Very often it does not.
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You can be totally precise yet completely impregnable to someone who isn't an expert
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