My mom’s a mathematician, she got annoyed when I said that the order of operations is just arbitrary rules made up by people a couple thousand years ago

I'm not surprised. Here's the proof of the order of operations rules. Also, the equals sign wasn't invented until the 16th century, so only 500 years old at most (the earliest references to order of operations are over 400 years ago).

[–] AdrianTheFrog@lemmy.world 1 points 7 months ago (1 children)

That proof for the order of operations sure seems to rely a lot on our current order of operations...

[–] SmartmanApps@programming.dev 1 points 7 months ago

That proof for the order of operations sure seems to rely a lot on our current order of operations

Doesn't use order of operations at all. It only uses the definitions of the operators. i.e. 3x4=3+3+3+3 by definition. i.e. nothing to do with order of operations.

If I have 1 2l bottle of milk, and 4 3l bottles of milk, how many litres of milk do I have? It can be solved by simply adding them up - again, nothing to do with order of operations here, just simple addition. Now, write it out as a mathematical expression which uses multiplication, and tell me which order of operations gets you the right answer. Voila! Welcome to how we worked out what the order of operations rules had to be.