Numberphile and the Cult of Collegiality

Mathologer recently posted a long video addressing the “proof” by Numberphile of the “astounding result” that 1 + 2 + 3 + … = -1/12. As well as carefully explaining the underlying mathematical truth, Mathologer tore into Numberphile for their video. Mathologer’s video has been very popular (17K thumbs up), and very unpopular (1K thumbs down).

Many who objected to Mathologer’s video were Numberphile fans or semi-literate physicists who were incapable of contemplating the idea that Numberphile could have gotten it wrong. Many others, however, while begrudgingly accepting there were issues with the Numberphile video, strongly objected to the tone of Mathologer’s critique. And it’s true, Mathologer’s video might have been improved without the snarky jokes from that annoying cameraman. (Although, awarding Numberfile a score of -1/12 for their video is pretty funny.) But whining about Mathologer’s tone was mostly a cheap distraction from the main point. Fundamentally, the objections were to Mathologer’s engaging in strong and public criticism, to his lack of collegiality, and these objections were ridiculous. Mathologer had every right to hammer Numberphile hard.

Numberphile’s video is mathematical crap and it continues to do great damage. The video has been viewed over six million times, with the vast majority of viewers having absolutely no clue that they’ve been sold mathematical snake oil. Numberphile made a bad mistake in posting that video, and they’re making a much worse mistake in not admitting it, apologising for it and taking it down.

The underlying issue, a misguided concern for collegiality, extends far beyond one stupid video. There is so much godawful crap around and there are plenty of people who know it, but not nearly enough people willing to say it.

Which brings us to Australian mathematics education.

There is no shortage of people happy to acknowledge privately their frustration with or contempt for the Australian Curriculum, NAPLAN, VCE, AMSI, AAMT, MAV, teacher training, textbooks, and on and on. Rarely are these people willing to formally or publicly express any such opinions, even if they have a natural platform for doing so. Why?

Many feel that any objection is pointless, that there is no hope that they will be listened to. That may well be true, though it may also be self-fulfilling prophecy. If all those who were pissed off spoke up it would be pretty noisy and pretty difficult to ignore.

More than a few teachers have indicated to us that they are fearful of speaking out. They do not trust the VCAA, for example, to not be vindictive. To us, this seems far-fetched. The VCAA has always struck us as petty and inept and devoid of empathy and plain dumb, but not vengeful. The fear, however, is clearly genuine. Such fear is an argument, though not a clinching argument, for remaining silent.

It is also clear, however, that many teachers and academics believe that complaining, either formally or publicly, is simply not nice, not collegial. This is ridiculous. Collegiality is valuable, and it is obviously rude, pointless and damaging to nitpick over every minor disagreement. But collegiality should be a principle, not a fetish.

At a time when educational authorities and prominent “experts” are arrogantly and systemically screwing things up there is a professional obligation for those with a voice to use it. There is an obligation for professional organisations to encourage dissenting voices, and of course it is reprehensible for such organisations to attempt to diminish or outright censor such voices. (Yes, MAV, we’re talking about you, and not only you.)

If there is ever a time to be quietly respectful of educational authority, it is not now.

8 Replies to “Numberphile and the Cult of Collegiality”

  1. Speaking only for myself, but under the cover of anonymity, in some ways like one of the keyboard “warrior” trolls who somehow managed to take down one of my favourite columns in The Age online… I digress…

    I do not fear VCAA. In fact, I would love to be hated by VCAA and love even more for this to mean I could no longer teach a unit 3+4 sequence.

    I do not fear my colleagues. Some of them, I suspect, stay out of my way to avoid confrontation, but I would not class this as fear.

    No, what I fear is history repeating itself. Being labelled by management as a trouble maker, unpromotable and (it seems like management talks between schools) not much wanted in other schools, so, jokes on them, I stay and teach VCE Mathematics.

    I have watched “colleagues” suck up to VCAA, MAV and even the union officials, some of whom seemingly have no grasp of the concept of a percentage increase when it comes to making their wild claims about the pay rises they have “won” (that is another story for another time) and I have watched the “cool group” achieve the promotions, all the time suspecting (but only once being able to prove) that those of us who do not tow the party line will be undermined professionally and sometimes quite badly.

    At the end of the day, I need a full time job and teaching seems to be where I have found myself for the moment. If I knew that management would not judge based on the opinions of others, maybe I would speak out a lot more and a lot more widely.

  2. This is an artifact of our times, too many can’t tell the difference between people and ideas. Unlike people, ideas have no rights. They deserve no charity whatsoever, and upon being born be presumed guilty, to be beaten thoroughly and persistently until they show the slightest sign of weakness, at which point they are to be immediately and summarily executed.

  3. 3 Blue and 1 Brown had an excellent video on Analytic Continuation of the Riemann Zeta Function that gives a visual explanation of where that -1/12 comes from. They admit that the sum of the infinite number of positive integers do not “add” up to -1/12″ but they do see a relation there. See

    1. Thanks, John, but this is missing the point. Everyone who understands the stuff acknowledges that there is a “relation” via analytic continuation. But relation ≠ equality.

      It’s not a matter of 3B1B or anyone “admitting” that there is a relation there, like it’s some grudging confession. It’s a matter of Numberphile “admitting” that there is no equality there in any standard use of the word, and then taking down their poisonous video.

  4. I thought the Mathologer video was great. Explained a lot. And I don’t even think it was more aggressive than it needed to be. Thought it was very gentle and calm.

    Also, FWIW, if you allow some of the silly games that Numberphile allows (manipulations of divergent series), you can drive those series to even different values than shown. So, it really was a silly Numberphile video. One of their worst.

    And the Mathologer thing was beautiful in teaching the properties of series…lot of good training, even outside of the correcting ‘phile.

      1. The Marty content was pretty small percent and what was there was pretty gentle (for you). Heck…the -1/12 score was like comic relief. Honest…it wasn’t that harsh.

        I thought it was a great video. Seriously. I learned some stuff about series. Mathologer rox!

        P.s. I actually think Numberphile is very good (in general) and think Mathologer also thinks that. This is not about dissing their overall oevre. Just that one video.

        1. Yes, it was an excellent video. And yes, my bits were small and (for me) not too strong. Still, it was a mistake.

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