÷ could be a minus sign

No it couldn't.

https://en.wikipedia.org/wiki/Division_sign?wprov=sfla1

Did you check the reference? It says % can be used as a minus sign, not the obelus. Welcome to what happens when you're next-door neighbour Joe Blow can edit Wikipedia.

So order of operations is hard?

Not for students it isn't. Adults who've forgotten the rules on the other hand...

There’s no “whatever-the-fuck-your-country-calls-it”

Yes there is. BEDMAS, BODMAS, and BIDMAS

the US is the only country using it

No they're not.

at some point they’re dropping it

No, at no point do the order of operations rules ever get dropped

using multiplication by juxtaposition (2x + 4x2)

They're called Terms/Products.

You understand that gen x starts around 1965, right?

10 years earlier than that actually. Johnny Rotten, Billy Idol, etc. The U.S. came late to the party and started using their own definition.

This kind of problem falls under “communicating badly and acting smug when misunderstood”.

No it doesn't. It falls under adults forgetting the rules of Maths.

Use parenthesis and the problem goes away

There is no problem, other than adults who have forgotten the rules.

You might be smart

Smart-arse more like. A serial troll who doesn't actually know what they're talking about.

6 + 4 / 2 is 8 instead of 5?

The fundamental property of Maths that you have to solve binary operators before unary operators or you end up with wrong answers.

Maths is not about memorisation

It is for ROTE learners.

You are not supposed to remember that the area of a triangle is a * h / 2

Yes you are. A lot of students get the wrong answer when they forget the half.

you’re supposed to understand why it’s the case

Constructivist learners can do so, ROTE learners it doesn't matter. As long as they all know how to do Maths it doesn't matter if they understand it or not.

You’re supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it’s stuck in

No they're not.

If you’ve understood that once, there is no reason to remember anything because you can derive the formula at a moment’s notice.

And if you haven't understood it then there is a reason to remember it.

you can derive the formula at a moment’s notice

Students aren't expected to be able to do that.

All maths can be understood and derived like that

It can be by Constructivist learners, not ROTE learners.

The names of the colours, their ordering, the names of the planets and how they’re ordered, they’re arbitrary

No they're not. Colours are in spectrum order, the planets are in order from the sun.

Maths doesn’t, instead it dies when you apply memorisation

A very substantial chunk of the population does just fine with having memorised Maths.

I like the version where these problems are made purposefully ambiguous

None of them are ambiguous. They all have only 1 correct answer, just like this one only has 1 correct answer. They all test if people remember the order of operations rules. Those who got it wrong, don't.

did addition before subtraction instead of left to right

No, what you actually did was put it inside brackets, thus changing the number of terms. Doing addition first gives the exact same answer as doing subtraction first...

subtraction first 10-1+1=9+1=10

addition first 10+1-1=11-1=10

You did 10-(1+1), hence the wrong answer. It doesn't matter which order you do it, though often students make mistakes with signs when they change the order, which is why we teach to do left to right.

You do the exponent first, then multiplication.

-3² = -1 * 3²

There's no multiplication, just subtraction (from an unwritten 0). -3² = 0-3²

there is no space to indicate the - represents a subtraction operator

Spaces don't mean anything in Maths, and I don't know why people keep adding them in! A minus sign is a minus sign, whether there are spaces next to it or not.

the immediate prefix - actually represents: (-1)x

No, it actually doesn't. It represents 0-x. Every operation on the number line starts from 0.

this actually represents (-1)(x²)

No, it actually represents 0-x²

such that PEMDAS is upheld

Which what you wrote doesn't. M refers literally to Multiplication signs. S refers literally to subtraction signs. -x² is E then S in PEMDAS.

I don’t make these rules

You did make those up actually (or you've repeated someone else who made them up).

but this is how it works

No it isn't. A minus sign is the S in PEMDAS, not M.

Double check in wolfram alpha if you doubt it

Look in a Maths textbook. Wolfram is known to be wrong in several areas. University professors warn their students against using it without adding brackets everywhere.

My point (made poorly) was there is “expand and simplify” and also “factor and simplify”. Two different things.

And my point is there's no such thing as "factor and simplify", since they are opposite operations to each other.