Q.E.D.

I did a lot of material really early (including the original content of this post; it’s not that I never did it, but it was almost a decade ago). Then because of the way my institution’s math major works, I don’t need that many more upper-level classes. So I haven’t had intros to all the major fields yet. Plus a detour through the comp sci major (overlaps yayyy).

sometimes texts are hard because the translation was terrible and now it’s illegible

sometimes texts are hard because the writer is overcompensating for their own or their field’s perceived inadequacy

sometimes texts are hard because the writer’s not sure what’s important and what isn’t, and can’t guide the reader through the morass

sometimes texts are hard because the author was afraid that you’d miss a step, and so wrote absolutely everything out in excruciating detail, and so the whole thing is just incredibly tedious to read now and the struggle is staying awake and conscious enough for whenever things become important

sometimes though

sometimes texts are hard because the thing they’re trying to talk about is hard

because the world, ultimately, is complicated and hard to understand

i’m not trying to defend academic (or in my particular case, mathematical) obscurantism here.

rather, what i’m trying to get at is that writing good texts, that people find compelling enough to read and clear enough that they don’t struggle more than they need to? that requires that you be good at writing. writing! literally just writing.

and, yknow, if you’re a math person like me, there’s a fair chance that you went into this whole business at least partially to get away from that. i mean, at least for me, i was a person that somehow didn’t understand that texts had a tone until I was in senior year high school, which i mention just because it suggests the conceptual problems i was having w/ text.

my impression of all of humanities back then was that it was a bunch of jerks who were incapable of explaining what it is that they meant, and essentially coasted along on their lack of need for communication with anyone who didn’t, at some basic level, already understand them. (i’ve gotten better since then but that’s not what this post is about)

so, yeah, i get not wanting to think of mathematics as writing.

but that is what it is. you need to pay attention to pacing, you need to provide adequate motivations, you need to give your reader just enough that they can follow, but not so much that they forget what they’re doing, you need to provide partial culminations to sustain them towards your goal, and breathers between sections that are hard to follow.

which is writing. which is stuff that you can’t really systematize perfectly. stuff you just have to practice for a while to get better at. (stuff i’m not very good at, but hopefully I’m getting better)

but this is one thing we understand better than writers, i think. the necessity of exercises. (or at least, last time i tried to look into “how to become a better writer” the idea that you should do exercises was uh. more novel than i’d expected)

i say all this here because literally no one will tell you this in your entire mathematics education otherwise. and then it’ll take you forever to notice that “hey, grothendieck writes super well, actually, isn’t that weird” and similarly for many of the other Greats, and by the time you’ve systematized all that and figured out the pattern, it’ll have taken way too much time that you could have been practicing by… idk. writing fanfic or something.