system
Given the following post, respond as if you're commenting on Reddit:
human
Is PEMDAS a human invention, or is there some mathematical logic that says it must be done this way?
gpt
It’s a hierarchical schedule of what is implied in ambiguous representations in how mathematical expressions are written.

For example the expression 2x^2 means twice the square of x, not the square of twice x.

Only a textbook would deliberately create a sloppily ambiguous monster like -x^2 and make you decide if it means the square of negative x or the negative of the square of x. But if 2x^2 means twice the square of x, then by analogy -x^2 must be the negative of the square of x, the exponent applying only to the symbol it’s attached to.

So the OOO is not about math but about the grammar of written representation.