First it was black and blue or white and gold. Then it was Yanny or Laurel. Now it’s 16 or 1.

It’s about time the Internet found something new to take sides on, and this time, the debate is over what the correct answer to a seemingly simple mathematical equation is:

This equation has taken social media by storm, with different users desperately trying to defend why the answer is 16 and not 1 or vice versa. The arguments differ, but they are all based on the same fundamental principle: PEMDAS.

“Please Excuse My Dear Aunt Sally” – the one phrase that every student is guaranteed to leave fourth grade math class knowing, albeit not fully understanding its implications. This silly mnemonic is used by math teachers nationwide to help kids remember PEMDAS, the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction.

However, even after elementary school, PEMDAS is relevant. High school math classes still require us to evaluate what’s inside the parentheses before we look at what’s outside. Everyday life activities such bookkeeping and calculating tip and discounts also demand that we follow this set order of operations. But if we all know the rules of PEMDAS, why do we still have vexing math equations like the one above?

The Internet wholeheartedly agrees that we first simplify the equation from 8 / 2 (2+2) to 8 / 2 (4). It’s the next step that causes a disparity: do we divide first and get 4 * 4 = 16 or do we multiply first and get 8 / 8 = 1? PEMDAS says multiplication and division hold equal importance, so like most cases we should work from left to right and get 16. However, users have been quick to point out that there are still parentheses around the 4, which we need to evaluate first according to PEMDAS, leading us to 1 as another possible answer. 

But why is there room for interpretation? We’re always told by our teachers that math is objective and that there’s only one correct answer. After all, it’s not like our color vision and hearing can change the way we perceive numbers and operation signs. 

In the end, it’s because PEMDAS is simply a convention that society has chosen to accept. We decided to hold parentheses and exponents precedent over multiplication and addition. We decided that 2 + 5 x 3 is never 21 but in fact 17. We decided to teach our fourth grade students PEMDAS instead of something like SADMEP. Because we were the ones to create the rules, there will always be differing perspectives on how to interpret them. Despite its concrete numbers and symbols, math is still a language, and in certain cases, it too can be subjective.

This means that there is technically no correct answer to this viral equation. Or there are countless correct answers – it all depends on how you look at it. 

However, one must remember that in the real mathematics world, equations are rarely set up to be ambiguous. Mathematicians add clarifications (oftentimes in the form of extra parentheses and brackets) to ensure that there is no room for interpretation. This social media math question, on the other hand, was intentionally made unclear to cause debate and discussion. But the controversy isn’t necessarily a bad thing; after all, a viral math tweet once in awhile exposes the fun and allure that mathematicians experience every day to the general public. 

Ultimately, “2” will always be 2. “+” will always mean addition. But 8 / 2 (2+2) can be 16, or it can be 1.

Sources

Laconte, S. (2019, August 1). Everyone’s Arguing Over This Very Simple Math Equation — Here’s Why It’s Going Viral. Retrieved from https://www.buzzfeed.com/stephenlaconte/viral-math-equation-controversial-pemdas

Strogatz S. (2019, August 2). The Math Equation That Tried to Stump the Internet. Retrieved from https://www.nytimes.com/2019/08/02/science/math-equation-pedmas-bemdas-bedmas.html