This is perhaps more a comment on Wikipedia's coverage of mathematics. They have some general guidelines in their manual of style, but it's really hard to write math articles in a way such that something like the Rees algebra without defining 1000 thinks beforehand.
To understand the definition of the Rees algebra, you would need to define, mostly in order: sets, groups, abelian groups, rings, ideals of rings, algebras over rings, direct sums of rings, adjoining things to rings, etc.
This is just to understand the definition; to understand its significance in algebraic geometry (which I have no idea of), there are a thousand more definitions.
The issue with trying to understand a concept in math is there is a massive directed acyclic graph of prerequisites leading to these concepts, and one needs to traverse this graph in the right order. Unfortunately, knowing the right order is almost tantamount to understanding the concept itself.
I'm not sure in what sense there isn't a recipe for arms in our DNA. To me, it seems the DNA does encode that stuff, but in a highly compressed format that is then "unzipped" through the laws of physics and biology into a living and breathing being with arms.
I mean, the information has to be in there somewhere, right?
Right, it seems reasonable to run away when people wearing masks and holding guns, with no police ID in sight, are chasing you. In the moment, how can you be sure these people are really federal law enforcement?
I think the viewpoint articulated in this post fits quite well with the one expressed in the often-shared "Programming as Theory-building" article (I think it was shared here just a few days ago).
Scientists, mathematicians, and software engineers are all really doing similar things: they want to understand something, be it a physical system, an abstract mathematical object, or a computer program. Then, they use some sort of language to describe that understanding, be it casual speech, formal mathematical rigor, scientific jargon -- or even code.
In fact, thinking about it, the code specifying a program is just a human-readable description (or "theory", perhaps) of the behavior of that program, precise and rigorous enough that a computer can convert the understanding embodied in that code into that actual behavior. But, crucially, it's human readable: the reason we don't program in machine code is to maximize our and other people's understanding of what exactly the program (or system) does.
From this perspective, when we write code, articles, etc., we should be highly focused on whether our intended audience would even understand what we are writing (at least, in the way that we, the writer, seem to). Thinking about cognitive load seems to be good, because it recognizes this ultimate objective. On the other hand, principles like DRY -- at least when divorced from their original context -- don't seem to implicitly recognize this goal, which is why they can seem unsatisfactory (to me at least). Why shouldn't I repeat myself? Sometimes it is better to repeat myself!? When should I repeat myself??
If you want to see an example of a fabulous mathematician expressing the same ideas in his field (with much better understanding and clarity than I could ever hope to achieve), I highly recommend Bill Thurston's article "On proof and progress in mathematics" <https://arxiv.org/abs/math/9404236>.
To understand the definition of the Rees algebra, you would need to define, mostly in order: sets, groups, abelian groups, rings, ideals of rings, algebras over rings, direct sums of rings, adjoining things to rings, etc.
This is just to understand the definition; to understand its significance in algebraic geometry (which I have no idea of), there are a thousand more definitions.
The issue with trying to understand a concept in math is there is a massive directed acyclic graph of prerequisites leading to these concepts, and one needs to traverse this graph in the right order. Unfortunately, knowing the right order is almost tantamount to understanding the concept itself.