So I posited this question a long while back, but didn't

>Why is it that the Order of Operations is what it is?
Because it's convenient.

>And How would the entirity of Mathematics be different if the order was different?
Not at all.

Order of operations is a notational convenience, not a piece of mathematics as such. It is an agreement on how we write certain mathematical things on paper, nothing more. If we were to switch to different conventions here, the way we put ink on paper to describe math would change, like writing it in a foreign language; but the underlying math would not change one bit.

>Is there a logical reason why the order is, the way it is? What is the logic behind the way it is now?
The logic is that this particular notation leads to the simplest and shortest writing for the mathematical things we want to write down often.

>So what would things look like if the order was agreed upon to be like... PDMSAE ?
We would write a bunch more parentheses when doing math, making everything harder to read and easier to misunderstand.

>doesn't that make it completely "made up"? And just artifical?
The *notation* is made up and artificial. The *concepts* we describe using this notation is natural, and would not change if we were to change notations.

>>9129502
You should take Algebra to understand this

http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

The Order of Operations Is an Intrinsic Property of our Universe.

It is as Logical and Fundamental as the Speed of Light.

I don't think you guys get it... I understand Algebra, I'm asking as to WHY certain properties like 2^0 whose value is human crafted are inserted into the natural order of math, and why they work. and if we should apply our own "inventions" like that to Mathematics

>>9129502
The order of operations was purely invented by humans who created the syntax of math. Math would not be different if the order was different, we'd just be writing the symbols differently but it would all mean the same thing still

The conventions of math are indeed artificial and made up. We could switch around all the symbols and everything would still be the same. It's like a language. There is one language of math with some variations in obscure topics for instance Newton vs. Leibniz notation for calculus

You can write the sentence "The brown dog sucked a cock and ate some dick" in English and in French and it will look completely different but it means the same thing. The meaning of math is what matters