Maths can be useful. It can also be elegant, even beautiful – a word you’ll often hear mathematicians say when they describe the discovery of a nugget of surprising insight.
That seemingly simple equation that ricocheted across the internet recently was neither useful nor elegant.
By now, you’ve likely seen it: 8 ÷ 2(2+2) = ?
“I HATE this,” Amie Wilkinson, a mathematician at the University of Chicago, commented on a Facebook post by a colleague about the equation, echoing the disdain felt by many mathematicians for the trending question.
Kenneth Ribet of the University of California, Berkeley described it as “irksome”.
“I didn’t care. I wasn’t interested,” said Greg Kuperberg of the University of California, Davis. “I stared at it a little bit and moved on.”
You might think that mathematicians would be happy about a rare instance when people are enthusiastically talking about maths.
That was the assumption of Rachel Pulido Oakley, a former writer on The Simpsons and an old college friend of Wilkinson’s. She texted Wilkinson – “Amie Amie Amie … urgent question!” – asking which of two common calculating procedures was the correct one to use.
“Secretly, it enraged me, but I didn’t actually take it out on Rachel fully,” Wilkinson said.
Instead, she texted back to Pulido Oakley: “LOL. That’s not math.”
For mathematicians, equations like this one – something that looks like what you learned in school, but which has been twisted with intentionally ambiguous notation – reinforce the trope that the core of maths consists of memorised recipes of calculation.
“It implies that the point of mathematics to trip up other people with stupid rules,” Wilkinson said.
The ruckus was like expounding the exceptions to “i before e except after c” and wondering why a Shakespearean scholar is not sharing your excitement in discussing the English language.
Interpret the expression one way, you get 1.
Interpret it the other way, you get 16.
There’s no aha moment, just confusion and discord.
“No one in good spirits would ever want to inflict it on anyone else,” Ribet said.
In isolation, without context, mathematical expressions like this say nothing.
But equations really can solve problems when they describe a question you want to answer.
Consider this word problem: A restaurant employs eight waiters who split into two equal-sized shifts, each waiter earning $2 in wages and $2 in tips per hour. How much per hour does a shift of waiters earn in total?
Translating the words into an equation yields: (8/2)(2+2) = ?
In this context, the alternative interpretation of the expression makes no sense and so there is no ambiguity.
When the problem is set up properly and the equation is written down properly, it’s easily solved – $16 per hour – and there’s no controversy, although these servers are clearly exploited and undertipped.
-New York Times