What’s lazy about learning PEMDAS?

Nothing. Only people who don't know what they're talking about say that.

Yes, it is. The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b. Alternative definitions are also based on a multiplication.

That's why divisions are called an auxilliary operation.

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.

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.

And that’s why people don’t write equations like that

Says someone who clearly hasn't looked in any Maths textbooks

If you wrote 6 + 4 / 2 in a paper you’d get reviewers complaining that it’s ambiguous

Only if their Maths was very poor. #MathsIsNeverAmbiguous

Working mathematicians never came up with PEMDAS

Yes they did.

which disambiguates it without parenthesis

It was never ambiguous to begin with.

Noone else does it that way

Says someone who has never looked in a non-U.S. Maths textbooks - BIDMAS, BODMAS, BEDMAS, all textbooks have one variation or another.

You might be smart

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

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 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.

For me it’s the arguments when there is a parentheses but no operator (otherwise known as implied multiplication)

No, it's known as Factorised Terms/Products, solved via The Distributive Law, a(b+c)=(ab+ac). "implied multiplication" is a made up rule by people who have forgotten the actual rules, and often they get it wrong (because, having wrongly called it "multiplication", they then wrongly give it the precedence of multiplication, not brackets).

Where I live, this would be considered juxtaposition

Not just where you live, everywhere, in Maths textbooks. Adults forgetting the rules (and unqualified U.S. teachers not teaching what's in the textbooks) is another matter altogether.

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.

Hey, this is Presh Talwalkar

Person who has forgotten about The Distributive Law and lied about 1917.

Discussion of a brief history of this viral math problem

Including lying about 1917

Ultimately followed by brief discussion on the order of operations

But forgets about Terms and The Distributive Law.

And that’s the answer

Now watch his other ones, where he screws it up royally. Dude has no idea how to handle brackets. Should be avoided at all costs.

So order of operations is hard?

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

The issue normally with these “trick” questions

There's no "trick" - it's a straight-out test of Maths knowledge.

the ambiguous nature of that division sign

Nothing ambiguous about it. The Term of the left divided by the Term on the right.

A common mistake is to think division is prioritised above multiplication

It's not a mistake. You can do them in any order you want.

when it actually has the same priority

Which means you can do them in any order

Right to left:

6 * (4 / (2 * (3 / 9)))

Nope! 6 × 4 ÷ 2 × 3 ÷ 9 =4 right to left is 6 ÷ 9 x 3 ÷ 2 × 4 =4. You disobeyed the rule of Left Associativity, and your answer is wrong

Multiplication first: (6 * 4) / (2 * 3) / 9

Also nope. Multiplication first is 6 x 4 x 3 ÷ 2 ÷ 9 =4

Left first: (24 / 6) / 9

Still nope. 6 × 4 x 3 ÷ 2 ÷ 9 =4

Right side first: 24 / (6 / 9)

Still nope. 6 × 4 x 3 ÷ 9 ÷ 2 =4

And finally division first: 6 * (4 / 2) * (3 / 9)

And finally still nope. 6 ÷ 9 ÷ 2 x 4 x 3 =4

Hint: note that I never once added any brackets. You did, hence your multiple wrong answers.

It’s ambiguous which one of these is correct

No it isn't. Only 4 is correct, as I have just shown repeatedly.

Hence the best method we have for “correct” is left to right

It's because students don't make mistakes with signs if you don't change the order. I just showed you can still get the correct answer with different orders, but you have to make sure you obey Left Associativity at every step.

I stand corrected

No, you weren't. Most of their answers were wrong. You were right. See my reply. 4 is the only correct answer, and if you don't get 4 then you did something wrong, as they did repeatedly (kept adding brackets and thus changing the Associativity).

until the ambiguity is removed

There isn't any ambiguity.

all those answers are correct

No, only 1 answer is correct, and all the others are wrong.

Until the author gives me clarity then that sentence has multiple meanings. With math

Maths isn't English and doesn't have multiple meanings. It has rules. Obey the rules and you always get the right answer.

it doesn’t click for people that the equation is incomplete.

It isn't incomplete.

100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution

It's not a rule, it's a convention, and it exists so as to avoid making mistakes with signs, mistakes you made in almost every example you gave where you disobeyed left to right.

It’s so we don’t have to spam brackets everywhere

No it isn't. The order of operations rules were around for several centuries before we even started using Brackets in Maths.

((((((9+2)-1)+6)-4)+7)-3)+5

It was literally never written like that

we only need parentheses when we want to deviate from the norm

That has always been the case

The solution accepted anywhere but in the US school system range from “Bloody use parenthesis, then” over “Why is there more than one division in this formula why didn’t you re-arrange everything to be less confusing” to “50 Hertz, in base units, are 50s-1”.

No, the solution is learn the rules of Maths. You can find them in Maths textbooks, even in U.S. Maths textbooks.

so no actual mathematician, or other people using maths in earnest, use that kind of notation.

Yes we do, and it's what we teach students to do.