The same reason we write sentences the way we do. Arbitrary tradition seeking to remove ambiguity while also conveying information with as little effort as possible.
"Put the cookies in the box on the counter" can mean, "put the cookies into the box which is currently on the counter", or it can mean, "put the cookies which are currently in the box on to the counter". So we rely on context clues to give us the correct interpretation. Because maths can exist in a bit of a context less void, the correct way to write an equation removes any ambiguity, but failing that, we rely on the most accepted context, which in this case is the order of operations.
Whyistheplatypus t1_iyc854z wrote
Reply to ELI5 why we first multiply, then add by TheManNamedPeterPan
The same reason we write sentences the way we do. Arbitrary tradition seeking to remove ambiguity while also conveying information with as little effort as possible.
"Put the cookies in the box on the counter" can mean, "put the cookies into the box which is currently on the counter", or it can mean, "put the cookies which are currently in the box on to the counter". So we rely on context clues to give us the correct interpretation. Because maths can exist in a bit of a context less void, the correct way to write an equation removes any ambiguity, but failing that, we rely on the most accepted context, which in this case is the order of operations.