Not really.
Math, at it's basis, doesn't have an order of operation, as I've illustrated in my previous comment by breaking the left-to-right rule, doing addition before multiplication and ignoring brackets until the very end.
It only exists as a method of teaching students because it works. It's simple and easy to remember.
The rest is me explaining how basic properties work:
Instead, mathematicians have long derived the basic properties that are supposed to be taught to students later on and is pretty much the first thing you learn in mathematical analysis in uni.
Those are:
- commutative: a+b=b+a | same for mult
- associative: (a+b)+c=a+(b+c) | same for mult
- distributive: a×(b+c)=a×b+a×c
- identity: a+0=a | a×1=a
- inversion: a+(-a)=0 | a×(1/a)=1
This is what math is. Every equation is solved using those properties. Every theorem can be broken down into those actions. (Technically speaking, you can break it down even more - into addition only)
This is why in GEMA, BODMAS, etc, you have multiplication and division before addition and subtraction. Because (a×b)+c=a×(b+c) isn't a property that exists. Try it. The sides won't always be equal.
And those properties are also the reason why you don't have to abide by an order of operations. Commutative and associative properties directly contradict them without making the solutions incorrect.