I like what you wrote and here is my perspective as a mathematician. A lot of the notation is due to legacy and common practice. For instance, we write y=f(x)

I like what you wrote and here is my perspective as a mathematician. A lot of the notation is due to legacy and common practice. For instance, we write y=f(x) and think of x as the independent variable. If I switch it around and write x=f(y) that would confuse a lot of people (especially students and non experts). In one sense it doesn’t matter what letters I use but in terms of how things are normally communicated it does. If I break with tradition this causes a cognitive burden on the reader and that detracts from the purpose which is to communicate ideas. Also, the people who come up with a new idea tend to be the ones who decide on the notation. After using it for a while one acquires an intuition about the notation. When I see lim I think an infinite process is being described. That could be the limit from calculus or the direct limit in algebra. The result of how things have developed is that we end up with some things that are nonsensical if taken literally but do make sense as they are used. For instance it is nonsensical to say that x=1 is the solution to x+4=5. What is really meant is that both equations have the same solution set and it’s easy to see from the first equation that this solution set is {1}. Shakespearean language is weird to modern speakers of English even though it is correct English. In a similar way I think mathematical notation/usage is like a spoken language. One gets a feel for it after learning it and using it for a while. There are unwritten rules that people abide by to facilitate communicating ideas. I imagine a similar thing is true for programming languages.