Order of operations - Wikipedia, the free encyclopedia
Scroll down to "Gaps in the Standard."
What this section states (or implies) is that if you try to interpret 6÷2(1+2) strictly by the HUMAN-MADE order of operations, it is ambiguous. The system is not perfect. There are gaps where additional parens are needed to remove ambiguity. But as long as ambiguity exists, it can go multiple ways.
Of course the problem is, most people don't believe that it's ambiguous; they think there must be a correct answer and that their interpretation of PEDMAS is absolutely correct. And in both directions, it's a correct interpretation. That is the definition of ambiguous. That's the reason people are split 50/50 no matter where this question is posed.
It doesn't matter how many PhDs you have and in what field. I'm sure there are super-intellects on both camps. The right answer is: don't expect a consensus until you add parentheses to the original problem to make it unambiguous. The problem was designed to exploit the gap in the order of operations