If you need "practical applications" for some part of math to have value to you, then large parts of math will not be for you. That's fine, but that's also something you should accept and internalize: math is already its own application, we dig through it in order to better understand it, and that understanding will (with rather advanced higher education) be applicable to other fields, which in turn may have practical uses.
Those practical uses are someone else's problem to solve (even if they rely on math to solve them), and they can write their own web pages on how functions as vectors help solve specific problems in a way that's more insightful than using "traditional" calculus, and get those upvoted on HN.
But this link has a "you must be this math to ride" gate, it's not for everyone, and that's fine. It's a world wide web, there's room for all levels of information. You need to already appreciate the problems that you encountered in non-trivial calculus to appreciate this interpretation of what a function even is and how to exploit the new power that gives you.
I don't see any such "math gate" on this link. Also, this math does have practical applications, but they're not mentioned until very late in the article.
My suggestion is that briefly mentioning them up front might be nice. I didn't mean to start a big argument about it.
Yet some parts of math are 'preferred' over others, in that most 'serious' mathematicians would rather read 100 pages about functional analysis than 100 pages of meandering definitions from some rando trying to solve the Collatz conjecture.
Some people would like to have a filter for what to spend their time on, better than "your elders before you have deemed these ideas deeply important". One such filter is "Can these ideas tell us nontrivial things about other areas of math?" That is, "Do they have applications?"
Short of the strawman of immediate economic value, I don't think it's wrong to view a subject with light skepticism if it seemingly ventures off into its own ivory tower without relating back to anything else. A few well-designed examples can defuse this skepticism.
Those practical uses are someone else's problem to solve (even if they rely on math to solve them), and they can write their own web pages on how functions as vectors help solve specific problems in a way that's more insightful than using "traditional" calculus, and get those upvoted on HN.
But this link has a "you must be this math to ride" gate, it's not for everyone, and that's fine. It's a world wide web, there's room for all levels of information. You need to already appreciate the problems that you encountered in non-trivial calculus to appreciate this interpretation of what a function even is and how to exploit the new power that gives you.