My take on the “Math Test” problem

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I have no desire to further pollute YouTube with yet another video on the “3 = ?” so-called “controversy”, so I seem to feel better trolling my own blog about it.

If you have a mindless social media account, like Instagram, Facebook, or Twitter, you would have seen this “Math Test” being spread around over the past few years:

From Vi Hart’s video (https://youtu.be/Twik7wqdwZU)

I don’t wish to pick on Victoria Hart, as she was the second person I have noticed embarking on this trend to make something profound out of this poorly-worded, poorly-conceived “Math Test”. This was similarly done by Hank Green of Vlog Brothers fame.

The person formulating the question didn’t seem to care enough about forming their question properly enough to articulate what they really meant. I don’t think I would be making any controversial statement to say that 7 and 56 are not equal, not even for large values of 7 ☺. In fact, none of the numbers are equal. The vloggers have attempted to  ascribe genius to the author of the question and attempt to look past the abused equal signs, but there is no consensus, meaning you can make any nonsense up that you like. The author of this “test” has never come forward, so we will never know what they meant by these tortured equations.

It means that the ambiguity in the question is just left for everyone else to waste their time arguing over. Hart and Green appear to be playing a part similar to interpreters of ancient manuscripts whose authors have vanished over thousands of years without a trace of their existence. Both engage in a kind of exegesis of the work with nothing really to go on, since there is no time or place for this “test”. But they have to find something to say because this “test” has gone so viral, and they have to score engagement points with their viewers and with YouTube.

While Hart and Green make heroic efforts at making such dodgy questions seem profound and serious (in my opionon, Vi Hart wins top honors here), their profundity carries too many assumptions about the author (whom no one has met, remember), to take anything seriously. Too many what-if’s. The only thing that comes out of both videos is that they have been thinking about this way too much. Hank Green tries to turn it into a statement on the state of humanity; while Vi Hart tries to use it to comment on how logic is usad to carry forward various social and cultural biases made by imaginary scholarly people who sit in their armchairs and rationalize all day, whom it is implied we should all hate.

If there was no internet, and this was written on a piece of paper, no one would think twice about dismissing it. It relies on a certain number sense, yet, also relies on a certain functional illiteracy toward math symbols so that people reading this question engage with it. It shouldn’t take an Einstein to see there is something wrong by saying that “9 = 90“. But there is also a number pattern. It would have been better to use function notation. If f(x) represented an unknown formula, I would feel better if it were written this way:

f(9) = 90

This first equation says that if you plug 9 into the formula, you get 90. Other numbers are thus plugged in to get numerical results that hopefully bear some kind of relationship:

f(8) = 72
f(7) = 56
f(6) = 42

Finally, you jump to f(3), and if you know the pattern, you know the answer. Or do you?

f(3) = y

I am not promoting f(x) as “the correct interpretation,” and I can’t be bothered to propose a solution that hasn’t already been seen countless times in discussions over many parts of the Internet. There have been passionate arguments over what f(3) is (12? 18?), because more than one pattern has been proposed. Because the question is so sketchy, and the writer of the question is AWOL, and can’t be held to account, there really isn’t going to be any consensus possible.

The question is easy to dismiss, since the writer of the question has given us much to be dismissive of. The real question to ask here is: is it a productive use of our time to engage in math questions where we are forced to make assumptions based on information we don’t have (and will likely never have)? I think everyone knows the answer to that.