system
Given the following post, respond as if you're commenting on Reddit:
human
What would happen in mathematicians decided to change the order of operations? Would math still work if everyone agreed, or is something about it intrinsic?
gpt
Mathematics doesn't depend on the order of operations. That concept is just something we need for the way we typically write down operations. If we were to change the order of operations, all that would be needed is for existing texts to be rewritten to add parentheses to formulas that were affected, but nothing would fundamentally change.

Note that there are other ways to write down mathematical operations where something like the order of operations isn't even a thing, because the notation is unambiguous. One such example is the "Polish notation". This notation places the operator in front of the operands. So instead of "1 + 2", one would write "+ 1 2".

Combining operations is easy too: "(1 + 2) * 3" becomes "* + 1 2 3".

To evaluate expressions in Polish notation, you always evaluate the innermost expression first and work your way outwards. There is no need to decide on whether multiplication or addition takes precedence or where to include parentheses. There is only one way to interpret this notation.