All order of operation rules are made up, but some of them are more useful than others. Rules that jive with associative and communtative laws are preferred.
None of them are made-up. They are all a natural consequence of the way things have been defined. e.g. 2x3 is shorthand for 2+2+2, so if you don’t do multiplication before addition then you get the wrong answer, hence the order of operations rules.
All order of operation rules are made up, but some of them are more useful than others. Rules that jive with associative and communtative laws are preferred.
Or come over to RPN and stop worrying about it.
None of them are made-up. They are all a natural consequence of the way things have been defined. e.g. 2x3 is shorthand for 2+2+2, so if you don’t do multiplication before addition then you get the wrong answer, hence the order of operations rules.