Comment by jancsika
Mathematicians explain things the way I imagine musicians would if the ancient Greeks had insisted on making all musical instruments in a range audible only to dogs.
I'd be like, "How do I actually hear the difference between a major and minor sixth?" And the musician would be like, "Just play them into the cryptophone and note the difference in the way your dog raises its eyebrows."
The very few remaining musicians in this hellscape would be the ones who are unwittingly transposing everything to the human range in their sleep, then spending the day teaching from the Second Edition of the Principles of Harmonic Dog Whistling for all us schmucks.
Luckily we don't live in that musical universe. But mathwise, something like that seems to be the case.
Look, I think it's pretty hard for most of us to read long math arguments in plain text, so I wrote in the simplest language I could, leaving the simple details for the reader to fill in.
I will add that in the vast majority of mathematical literature, both in pedagogy and in research, the active participation of the reader is assumed: the reader is expected to verify the argument for themselves, and that often includes filling in the details of some simple arguments. That's exactly why math literature uses the plural first-person "we," because it's supposed to be as if the writer and reader are developing the argument together.
In contrast, listening to music can be purely passive (but doesn't need to be).