Recently, there was a viral post about solving the equation below:
Many mathematicians and social media powerhouses have weighed in on what the answer should be. But, why has this equation led to a lot of debate? This is not the first time that an equation or math problem has become an internet sensation and I suspect it won’t be the last (see “10 viral math equations that stumped the internet”). Depending on the order of operations you apply to this equation you will end up with an answer of 16 or 1.
Every time a new viral equation storms the internet, I casually scroll through all the responses. What draws my attention the most is the way people interact with these types of posts. Many seem to jump at the opportunity to flex their math muscles while others reach for their calculators. The perception seems to be that this basic math question should have solely one answer and however disagrees is wrong. The answer to this viral equation, as Steven Strogatz explains in his recent article, depends on what conventions you are using.
What jumps at me is that, when presented with solving an equation, it’s is rare to discuss how we write mathematics and why we interpret it in a particular way. Mathematical grammar matters and conveying the “right” statement of a problem relies on using the symbols that have become our language. As told in this 2013 article “What Is the Answer to That Stupid Math Problem on Facebook?” by Tara Haelle, ‘Consider how often people debate grammar. Math has syntax just as language does—with the same potential for ambiguities. And just as word-based riddles exploit the ambiguities of language, so do these math problems’. As Hanna Fry mentions, ‘This is like a maths version of the sentence “He fed her cat food”. Does it mean the man gave some food to a cat? Or – slightly darker- fed some cat food to a woman. It’s impossible to tell from the information we’ve been given’. We have allowed the perception that math is unambiguous to reign. But different from a language, being right or wrong in math, tends to be associated with how smart a person is. This mindset ultimately is what leads to these heated debates and causes a divide. As expressed in this essay by Kenneth Chang, “It implies that the point of mathematics is to trip up other people with stupid rules.”
Don’t get me wrong, mathematicians spend a lot of time trying to be as unambiguous and precise as possible. However, math can be written in ways that make the reader interpret its meaning in unintended ways. Last year, I taught a course that was aimed at future elementary school teachers. This class was a great way to see how we can build our interpretation of math when most of the tools we use are suddenly are unavailable. Students struggled with playing with assumptions, definitions, and ultimately engaging with mathematics in a playful way. We explored the number systems that were used in different cultures, build proofs using physical objects, and played with what makes and breaks definitions. Yet, the idea that there is only one way to interpret a problem stayed throughout the course. The more time I’ve spent teaching (and learning) mathematics the more dangerous this perception feels. It hides away the fact mathematics was built, written, and interpreted by humans, and sometimes this leads to fun internet debates.
Mathematics has a rich history of how we’ve built the conventions that we use every day. In his blog “What is 00, and who decides, and why does it matter? Definitions in mathematics”, Art Duval shares why definitions (I would also extend this notion to conventions) are useful and highlights how we can still have choices to make even for precise definitions. For example, Terry Moore’s short TED video, “Why is ‘x’ the symbol for an unknown?”, illustrates that even some conventions have origin stories outside of mathematics. But often, students learn acronyms like PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction) without knowing the history of these conventions. We may not have the time to unpack the history of all the conventions that we use but we can highlight how they help us communicate math. Next time a viral equation floods the internet, don’t fret! This can be the perfect opportunity to share a bit of the history of our conventions and the importance of how we write (and interpret) mathematics.
