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...for no other reason than "this is how people have been doing it for a long time".I disagree. Math notation has evolved to be as it is because it is useful for the purpose of doing math. If there were some way of doing it better, people would be evolving to be doing so.
In some ways they are ... people are using computer algebra packages more for a lot of the grunt work, and are using proof assistants to verify some things, but there's a lot of math that's still done by sketching why something is true and letting the reader work through it. Math notation isn't about executing algorithms, it's about communicating what the result is, and why it works.
"Doing Math" is not "Writing Programs", so math notation is different.
