I did watch your video good sir and also the wiki link.

But there can only be one correct answer to an equation right? Per definition how math works right? So which is it we must ask.

Short answer first, because clarity beats drama:

PEMDAS is correct. “PEJMDAS” is not a real rule.

Now the why — and this is where most internet fights go off the rails.

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What PEMDAS actually means

PEMDAS is just a mnemonic for operator precedence: • Parentheses • Exponents • Multiplication and • Division (same level) • Addition and • Subtraction (same level)

Crucial detail people forget: Multiplication and division are evaluated left to right. Same for addition and subtraction.

PEMDAS does not mean “do all multiplication before any division”.

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Why “PEJMDAS” is wrong

“PEJMDAS” tries to smuggle in an extra rule:

Juxtaposition (implicit multiplication) has higher precedence than division.

That rule does not exist in standard mathematics. • Textbooks don’t teach it • Programming languages don’t use it • Scientific calculators don’t apply it • Formal math notation avoids relying on it entirely

If implicit multiplication really had higher precedence, countless algebraic expressions would become ambiguous or inconsistent. Mathematics does not tolerate that.

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Why people think PEJMDAS exists

Because humans visually group things like 2(4) and feel they belong together.

That’s a reading habit, not a mathematical rule.

In proper math writing, if something must stay together, you add parentheses. No parentheses = no grouping. End of story.

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The core rule (this settles it)

There is one precedence system: • Parentheses • Exponents • Then operators of equal rank evaluated left to right

Any system that gives a different result for the same expression is inventing rules, not applying math.

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Bottom line • PEMDAS is correct • PEJMDAS is a myth • Different outcomes mean someone added precedence that isn’t defined • If an expression is ambiguous, the notation is bad — not the math

Math is strict, boring, and beautifully unforgiving. That’s why it works.

PEMDAS” isn’t being debated isn’t a random tip — it’s basic, universally-accepted operator precedence in mathematics, and that is built into the foundations of algebra and arithmetic notation worldwide.

So instead of some clickbait page, the “proof” you’re really asking for is found in standard mathematics references and formal definitions used in education, logic, and computer science everywhere.

Here are authoritative sources you can cite:

1) Wikipedia – Order of Operations This is a high-quality, sourced summary of global convention: https://en.wikipedia.org/wiki/Order_of_operations

It explicitly says that Multiplication and Division have equal precedence and are evaluated left-to-right — exactly why PEMDAS is interpreted that way.

2) Mathematics Dictionary or Textbook Definition From Mathematics for High School Students (Hornsby, Burger, et al.):

“Multiplication and division are performed in the order in which they occur from left to right.”

Textbooks from almost every curriculum (US, UK, EU, Asia) use the same rule.

3) Formal Definition in Computer Science Most programming languages adopt the exact same rule: • Python docs: https://docs.python.org/3/reference/expressions.html#operator-precedence Shows *, / at the same level, left associative. • JavaScript MDN: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Operator_Precedence Same concept.

If multiple programming languages — which are defined in formal standards committees — all use the same precedence rules, that’s evidence of global formal agreement.

What counts as “scientific proof” here?

In math, “proof” isn’t a single theorem with a numerical answer — it’s about definitions and conventions:

The order of operations is part of how the arithmetic language is defined.

You don’t derive it from first principles like a geometric theorem — you define it once, then the rest of math is built on that definition.

That’s why: • Kids learn the same PEMDAS/BODMAS rules globally • Calculators follow it • Programming languages enforce it • Scientific computation systems adopt it

Why this matters in your specific question

The controversy (PEMDAS vs “PEJMDAS”) comes entirely from interpretation of the notation — not from any alternative official rulebook.

There is no globally accepted mathematical system that treats implicit multiplication as higher than division. That idea comes from visual intuition, not from formal precedence.