Usually the stuff I'm implementing is complicated enough that reading the code without reading the paper won't have much meaning. And if you're reading the paper, it's good to have as close to a 1-1 representation to help give confidence that I implemented it right.
I've had non-zero times where I took his pseudocode, pasted it into my IDE and did a search and replace of begin/end to braces and "<-" to "=" and it "just worked" on the first try. I always found that amazing that he could write this stuff without ever trying it (outside of his head).
* r,g,b,a
* h,s,l
* x,y,z
If you want people to understand, you skip the mathematical notation and use pseudocode, or at least you start with an explaination and once people know what they are looking at you go into the math notation.
I understand that mathematical notation can be very practical for describing a certain class of problems concisely, but especially if you teach or explain things, consider that being concise is meaningless if people don't understand what you describe.
Sometimes my feeling is that this is on purpose. People not understanding what you are doing (but you come across soo smart), is a feature to many. Even better: The layperson cannot tell whether you are talking utter gibberish or using the most precise language on earth.
I, however, think you can recognize real smart people by the phenomenon that every room they are in seems to become smarter in total, because they lift people up in their wake of understanding things so deeply, they can just break them down into their very simple, managable parts and translate obscure domain-specific languages into something people can grasp.
I too can go into deep domain specific lanuages, be it in philosophy, electrical regulation, film theory, programming lingo, music theory, control theory etc. But what is the point of doing that without making the person opposite understand what you're waffling on about? Because either you will seem like a knowledgeable person that has a total lack of self-perception or like a brick that doesn't care what message reaches the person opposite as long as rhey can hear themselves talk.
That being said: Domain-specific language can be okay if it is used between people within that domain. But I have met many physicists or mathematicians who also think math notation sucks, so maybe there could be something better.
I still haven't quite forgiven the writers of UMAP for writing a theorem that uses pi^n/2 / Gamma(n/2+1) instead of the more reasonable "volume of the unit sphere". It makes it so confusing that they fail to spot the theorem doesn't work for low dimensional objects embedded in high dimensional spaces, which is their exact use-case. Luckily their informal conclusion does work, mostly.
The more pure the mathematics the shorter the scope of most variables. Typically a variable is defined just before it's used, with a scope no longer than the proof or derivation it's in.
Also some of the choices in this article are just plain silly. Such as using P as both variable and index, and then use it for the covariance matrix when the precision matrix is the exact inverse.