SmartmanApps

That’s not even an equation, just basic arithmetic

Basic Algebra actually. Students aren't taught the Distributive Law until they start on Algebra

the 5 next to the parentheses indicates multiplication

No, it indicates Distribution, a(b+c)=(ab+ac), 5(8-5)=(5x8+5x5).

It should be limited - like Orders - to only Multiplication and Addition

Because you don't want people to know when to do Division and Subtraction? 😂

Because division is the same operation as multiplication

No it isn't, but they are both binary operators.

they have the same “weight” in the order of operations (meaning, you do them left-to-right)

And where are they going to do Division and Subtraction in the left to right if you've left them out? 🙄

O - oxponent?

To the Order of. 2² is 2 to the order of 2

so 5 literally cannot be a function if that’s the case

No, but it can be and is a coefficient of the Term 5(8-5)

Depends on the language

No it doesn't

5 isn’t a valid function name, is obviously the right answer.

5 is a coefficient of the Term 5(8-5) is the correct answer

insist mathematics has exactly one perfect unambiguous syntax,

It sure does! 😂

2*(1+3) is somehow different from 2(1+3)

Yep, one is Multiplication - 2x3 - the other is The Distributive Law - (2x1+2x3) - both easily found in Maths textbooks

Syntax error

Nope! The Distributive Law

If kids where taught how to solve them properly we wouldn’t need to dumb down equasions

They are taught how to solve them properly. It's only adults who've forgotten the rules of Maths who get them wrong

an implied multiplication

There's no such thing. It's a Term/Product.

is the normal thing you learn in (I think?) somewhere between 5th to 7th grade

Yes, you learn that it's a Term/Product in Year 7

You only add an operator if it’s something else

You never add an operator, or you end up with wrong answers.

I thought math was relatively universal

It is

The US education system may be different

They have the same rules, but they don't require Maths teachers to have a Maths qualification (in Australia you have to have a Masters), and they have been sliding in world rankings for more than a decade.