Mathematics is based on strict rules and it needs to be defined by them, otherwise the whole field falls down around itself.
I fully agree with you. A language without pre-defined rules is chaotic.
But that doesn't mean we shouldn't try to improve on the rules, making them simpler, easier and more straight-forward to understand for a wider range of people, thus including more people in the club of those who understand it and can use it. There's no reason to make it harder than it has to be
'Order of appearance' is subjective and whilst it makes sense with 10 + 10 * 0 it gets entirely confusing with more complicated equations.
Could you give me an example-equation?
An equation that would be more difficult to write if using only a left-to-right order of precedence for the operators (you're still allowed the use of brackets)
I was just thinking that since western standard is to read from left to right, it would make more sense to students (and non-mathematicians in general) if math followed that same standard (reduce and simplify... I believe that's a golden rule of math
)
Is there ever a time where an educated mathematician would need to write 10 + 10 * 0 rather than 0 * 10 + 10 ?
As a fun experiment; try opening your windows calculator.
Enter 10 + 10 * 0 in both standard view and scientific view... you get 2 different results based on which view you're in. That's not good.
Now enter 0 * 10 + 10 in both standard view and scientific view... you get the same result in both views. That's much better. More consistent, more rigid, more stable = less confusion, less prone to errors, closer to the goal of a universal language.
KISS: when using a left-to-right order of precedence your calculator doesn't need to be clever to give the correct answer = everybody wins