That's because mathematical notation is context-bound and telegraphic. Gerry Sussman has gone so far as to call it "Impressionistic". Beyond basic arithmetic and elementary algebra, it is much more concise than it is precise -- it is often inconsistent (the "power" in cos^2 x doesn't mean the same thing as it does in cos^-1 x, for instance), and there's a lot of hand-waviness (and sometimes some outright lies) in order to make the notation concise. It's a useful jargon for the initiated, but it is hardly self-explanatory even if you know what the individual symbols are supposed to mean.

A code-like representation may have the disadvantage of being more verbose, but it has the advantage of being unambiguous. It gives up conciseness in favour of precision. And no, it is not impossible to represent mathematical concepts in a code-like manner -- it just forces you to actually say all of what you mean rather than using an ambiguous and incomplete shorthand.