Often specific symbols have implicit meanings, like theta θ is pretty commonly used for some angle, r is often used to mean a radius. So you'll often see something like "r sin θ" with no explanation. At first it's meaningless, but once you know the conventions, it's crystal clear. It's considered so basic, that nobody would waste the space explaining it. Same is if you're reading something about code and something says "const float x = 0.1" or something. The author is probably not going to go into an explanation of what a const or a float is or what x means. You're expected to know.

So what I like about the book is that helps someone without knowledge of all these conventions to begin to understand them.

Sometimes the right kind of intuition is all it needs to make it click. Sometimes it's that tiny bit of knowledge one is missing to get the whole picture and suddenly everything makes sense.

(Btw I think we might have met ages ago at a conference or two in Cologne)

Whereas for math it does not seem to be the same. There is no documentation, and no-one ever seems to explain those basics online. Eg. this book is a pretty obscure pdf.

Can you elaborate on what you mean here?

In order to draw the curve I iterate through values of X for each pixel, plug those values into the right hand side, and what the right hand side of equation is equal to is my Y value for that point on the curve. So if they had just written that big fancy f(X) as Y it would have been much clearer and easier to understand for me initially.

Eg One might have f(x,y,z) = (...). If f is in some class of functions with some properties (homogeneous, linear, smooth, etc) we can operate on it abstractly. We could even derive properties of surfaces f(x,y,z) = C.

You mean the function? It could just as well be something like:

    f(x, y) = 5xy + 3x^2 + 4y^2

With respect to the use of Greek letters and such, I do lament that many writers of mathematics fail to define their terms. Instead assuming that the reader is fully conversant in the domain, when often a single paragraph at the start would add a great deal to the clarity of their work. However, that doesn't mean that the use of such variables is bad, they just need to be defined.

The benefit of the mathematical notation is that it permits conciseness and lends itself well to symbolic manipulation (that is, a large portion of what we do when we do algebra and calculus). The former is a tricky subject, conciseness at the cost of clarity can be a net negative. But the latter is crucial to a lot of work, the way that we write programs does not lend itself well to symbolic manipulation and would be counterproductive for mathematics.

In fact, I've often had to translate programs into a symbolic notation in order to try and decipher them because the long descriptive names, as useful as they are in isolation, ended up rendering the total procedure nearly impenetrable. Or at least unanalyzable. And the conversion to a symbolic notation permitted me to simplify the program substantially because I was able to apply ideas from algebra to the program (often boolean algebra, in particular, this is a very useful practice for condition heavy code with lots of predicates).

As to your original criticism, I'll wager that more people in this world will understand f(x) = 5x + 3x^2 than will understand rudimentary code, as it is taught a lot more than programming is. I don't mean anything negative when I say this, but the only people I know who complain about math syntax are programmers. By changing these conventions, you are asking all mathematicians, physicists, chemists, most engineers, economists, etc to change. I will wager that over 95% of them will not prefer your style.

Finally, the trouble with replacing f(x) with Y is that the former tells me I'm dealing with a function. The latter does not. In fact, for many mathematicians, y = 5x + 3x^2 is a constraint, not a function.