One thing that bugs me about this symbolic fetishism is that it really is cargo culting to an almost literal degree.
First of all, mathematicians don't really care that much about notation and notation isn't very fixed. There are some broad conventions, but fashions change all the time within a relatively short time span (relative to the history of mathematics). It wasn't that long ago that "_|" instead of "!" was used for the factorial, and you can find 20th century texts that use that notation.
Second of all, most mathematicians really really do not care about notation that much. Notation isn't what makes mathematics, because it's dictated by fashions, whims, and very often, even by jokes. It's completely incidental, to the point that we did mathematics for thousands of years with very little expressions that we would recognise today as "notation".
If you're writing computer code, I say it makes more sense to follow the fashions of code than to try to squeeze them into the fashions of mathematics. Too often I see programmers trying to emulate the style but not the substance of mathematical writing, in an attempt to invoke the favour of the ghosts of Euler and Gauss (who, by the way, would not recognise much of the notation that we use today).
I think good notation is pretty important in mathematics. See for example the difference it makes in calculus. Good notation can make complicated things tractable.
Sure, I'm not saying it's not important at all. It's very helpful to be able to have some shorthand instead of using Latin abbreviations for everything like they did in the fifteenth century.
It's just that people that are relative outsiders to the mathematical community give it way more importance than mathematicians do. This is particularly true of computer people, I think, because compilers and interpreters are very rigid about the syntax that they accept. Computer people pass these expectations into mathematics and assume that mathematical writing has some strict, rigid syntax that if not religiously followed nothing makes sense.
Terry Tao has something to say about these "compiler errors":
Notation is created to encode information - the intent here. A silly example: replacing self with a snowman unicode. There is no reason to do so - but now when you look at a buffer, you will be able to see all instances of self instantly. Its about parsing semantics, not making things pretty (despite the package names).
First of all, mathematicians don't really care that much about notation and notation isn't very fixed. There are some broad conventions, but fashions change all the time within a relatively short time span (relative to the history of mathematics). It wasn't that long ago that "_|" instead of "!" was used for the factorial, and you can find 20th century texts that use that notation.
Second of all, most mathematicians really really do not care about notation that much. Notation isn't what makes mathematics, because it's dictated by fashions, whims, and very often, even by jokes. It's completely incidental, to the point that we did mathematics for thousands of years with very little expressions that we would recognise today as "notation".
If you're writing computer code, I say it makes more sense to follow the fashions of code than to try to squeeze them into the fashions of mathematics. Too often I see programmers trying to emulate the style but not the substance of mathematical writing, in an attempt to invoke the favour of the ghosts of Euler and Gauss (who, by the way, would not recognise much of the notation that we use today).