PEMDAS/BODMAS is a rigid left-to-right rule for solving math problems.
PEMDAS is a convention, not a natural law. In some countries and contexts, different conventions exist. The ambiguity of expressions like 8÷2(2+2) reveals that implicit multiplication and division left-to-right can produce different answers depending on convention.
What changed?
In the summer of 2019, a Twitter post asked: what is 8 ÷ 2(2+2)? The post attracted tens of millions of views and a fiercely confident argument between two camps. One side calculated 1. The other calculated 16. Both groups cited PEMDAS. Both groups were certain the other was simply wrong.
Neither camp was entirely right, because the expression is genuinely ambiguous, and the ambiguity reveals something most people were never taught: PEMDAS is a convention, not a mathematical truth.
The order of operations exists because we need one. Without an agreed convention, the expression 3 + 4 × 2 could equal 14 (left to right) or 11 (multiplication first). Mathematicians and educators adopted the rule that multiplication and division take priority over addition and subtraction, and that within equal-priority operations, you proceed left to right. This is not something that was derived from axioms. It was decided, and different communities decided slightly differently.
The controversy around 8 ÷ 2(2+2) hinges on what "implicit multiplication" means: the absence of an explicit × sign between the 2 and the parenthesis. Many mathematicians and most professional journals treat implicit multiplication as having higher priority than explicit division, so they read 2(2+2) as a single unit to be evaluated before the division. Under that convention, the answer is 1. Under the strict PEMDAS reading, treating the implicit multiplication the same as any other multiplication and proceeding left to right, the answer is 16.
The disagreement is not hypothetical. Casio calculators have historically returned 1 for that type of expression. Texas Instruments calculators return 16. Both are implementing consistent conventions; the conventions simply differ.
BODMAS, the British equivalent mnemonic, lists Division before Multiplication, which, taken literally, suggests the reverse priority, though both mnemonics intend the operations to be treated as equal priority and done left to right. The two acronyms have generated decades of confusion about whether the order within a group matters at all.
The actual principle is simpler than any mnemonic: write expressions that are unambiguous. In any context where the meaning matters, scientific publication, engineering, programming, explicit parentheses eliminate the debate. PEMDAS is a useful classroom tool for learning to evaluate simple expressions. It is not a law of nature, and the universe will not enforce it consistently.