We didn’t discover it, order of operations is like grammar for math.
When you’re writing a sentence or an equation both the reader and the writer must agree on the correct structure, otherwise the meaning is lost.
The order of operations should be clear and easily followed. If it isn’t, the equation is poorly formatted.
It’s arbitrary, an artifact of writing mathemathical expressions as we do in everyday use (“infix notation”). The only thing that matters is that everybody uses the same order or stuff goes tits up.
As an example of a notation that doesn’t *have* the concept of “order of operations”, there is the Reverse Polish Notation / Postfix Notation:
1 2 + 4 *
means the same thing as (1+2)*4 and
1 2 4 * +
is the same as 1+2*4
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