After reading through a few other questions I was just asking myself: How was the Order of Operations defined, and why is it this specific order and not a different one?
Most of us know things like multiplication/division before addition/subtraction, parentheses first, etc - but what's the actual reason behind it? I'm probably biased by following those rules since childhood, so I can't really think of any other way.
2 + 2 x 2 = 6 and not 8
But if the order would be changed, let's say to "addition/subtraction before multiplication/division" would that order still work if we assume that mathematics would build up on it? Or is there some strange mathematical problem if we would be using a different order?
Of course, parentheses have a grouping function so they should always come first - I'm mainly talking about the exponents, multiplication/division, addition/subtraction (and maybe other operations left out).