The reason the whole internet and even the New York Times is a-buzz with this seemingly simple math expression is rooted in a catastrophe called PEMDAS or more precisely a part of that mess called the left-to-right rule. Students worldwide are subjected to this ridiculous “anti-mathematical” activity and in my humble opinion it is the primary reason students start to hate math as early as 6th grade.
The confusion about this expression comes from whether to apply this left-to-right rule or not:
everyone agrees that parentheses go first:
If we use the left-to-right rule we divide first and get 4 x 4=16, but if we go with the multiplication first and do not use the left-to-right rule (tempting because of the way it is written close to the parentheses) we get 8/8=1.
Here’s an excerpt about this from my upcoming book “Why Everyone Hates Math”:
“The left-to-right rule is the main reason parents are often humiliatingly forced to give up on helping their child in math around 6th grade. Obviously, most adults have forgotten all about this since 7th grade (the rule disappears in 8th grade), so they are actually incapable of doing their child’s 6th grade homework!
…
After making up a confusing, if not incorrect, acronym (PEMDAS) for something 3rd, 4th, and 5th graders thought they understood (and probably did until PEMDAS happened and exponents suddenly magically appeared), 6th grade school-math with the left-to-right rule now refuses to follow the one piece of actual solid advice contained in PEMDAS, parentheses.
The left-to-right rule is necessary because PEMDAS does not tell us whether to multiply or divide first , even though it sure looks like it does! This should be resolved by using parentheses as is always later the case in mathematics. There is no good reason not to. And yet, for some unknown reason, and despite the prominence afforded the concept of parentheses in PEMDAS, 6/7th grade school-math does not use parentheses to clear this up. Instead the left-to-right rule creates a clumsy, anti-mathematical mess and confusion that often lasts a life-time.
Finally, in 7/8th grade as a grand finale, school-math abruptly and silently abandons the left-to-right rule with absolutely no further explanation, as if it never happened. It becomes a fleeting memory, remaining stuck somewhere in the students’ math sub-conscience like a scalpel a doctor forgot in a patient after an operation. Search deeply enough and you too will probably vaguely remember something about reading math left-to-right? What happened to that?”
What happened was that the left-to-right rule was not math in the first place, and so it had to be abandoned in 8th grade because it contradicts actual mathematical notation.
Even mathematicians (and now the whole internet) I have spoken with don’t recall this absurd made-up school-math rule, and are puzzled by 6th grade homework.
This really is a great way to start things off and get on the right foot with the students and their natural interest in math.”
The real kicker is that this expression everyone is discussing is even not the worst of it. There are actually expression that defy PEMDAS completely!
Depending on what exponent you do first you get two different answers. PEMDAS and the left-to-right rule both utterly fail here, and do not tell you what you should do first! This is an actual mistake in school-math not just an ambiguous confusion like the expression above everyone is discussing!
The poor kids!
Here is the link to the (almost) full chapter from “Why Everyone Hates Math”: