He's basically saying you have to be an idiot to think that you put that whole term in the denominator when there's no fraction bar.

Even if he's right, this is hardly a fair judgment. I have *always* been taught that you can assume there are "understood parentheses" around any two juxtaposed symbols for quantities, and that they are to be multiplied. I do not know myself ever to have missed any math exercise by following this rule. I and the many others who make this assumption are hardly "idiots" regardless of whether it turns out this assumption reflects general mathematical practice or not.

Nobody with half a brain would ever present an equation this ambiguously with the attempt to assess your mathematical capabilities. Your teacher, your book, your boss won't write the equation this way, they will write it out as a multi-level expression with a fraction bar and the terms in their correct places. The problem comes from the fact that this is being entered as a single line, which confuses most people when division is involved. The only way you would ever be tested on this is that stupid STAR standardized testing at the end of whatever grade they introduce orders of operations in, and then you don't even know how you did, the school just knows 96% of kids (example) failed it, so they teach harder the next year. It is purposefully deceptive, and no one interested in your education would purposely deceive you.

Any MATHEMATICIAN will defend the fundamental principles of math to the death.

But we're not talking about fundamental principles of math. We're talking about mere notational conventions.

Notational conventions are directly related to order of operations, which is a fundamental principle of math. A math problem should never have a disputable answer. It can have many answers, infinite answers, but those answers are either right, or wrong. They either fulfill the constraints of the expression following the fundamental principles of math, or they don't. There is no ambiguity. This isn't about whether or not the MLA method is the correct way to site your sources. The rules of math are not open for debate. So yes, this is a discussion about the fundamental principles of math.