system
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human
ELI5: How did we determine the order of operations in mathematics?

I'm very bad at math so I know little about it, but I was wondering, how did we discover the rules for the order by which we perform operations in algebra? Surely it was not some arbritrary decision to make multiplication and division come before addition and subtraction?
gpt
Everyone else is wrong. Math isn't arbitrary, there are reasons for everything. Let me give a simple example. Lets find out how much money you have. You have a dollar and 3 five dollar bills. A math equation would be

    1 + 3 x 5 = 

If you think about it like money, you know you have $16 and not $20. There is no reason to add the $1 to the number of bills you have. But why? The answer is just to ask, "What is multiplication?" Multiplication is just short had for repetitive addition. If we expand the equation we get

    1 + 5 + 5 + 5 = 

Now if we add everything together it's easy to see the correct answer. It's easier to see that adding the one to either the 3 or the 5 completely messes up the short hand.

Well what about exponents? Again exponents are just short hand for multiplication. 2^3

    2^3 = 8
    2 x 2 x 2 = 8
    2 + 2 + 2 + 2 = 8

Because exponents are short hand for multiplication, they must be addressed first or you mess up the original meaning. Multiplication and division come next as they are both the same. Dividing by 2 is the same as multiplying by .5. Then addition and subtraction as they are the same. 5 - 2 is the same as 5 + -2.