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Does anyone know of any cases of students being adversely affected by cranks or trolls in online math forums (e.g. sci.math)? Are they even a minor problem?

Dan

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    $\begingroup$ I don't know of any particular examples, but I also don't see how this is a problem that is particular to mathematics. There are Cantor cranks, and flat Earthers, and young Earthers, and racists, and all manner of other cranks and trolls on the interwebs. It seems to me that one of the jobs of the secondary instructor is to help students spot those kind of cranks, and work out the flaws in their arguments. ;) $\endgroup$ – Xander Henderson Dec 4 '17 at 20:05
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    $\begingroup$ Do you have relevant examples that motivated this question? $\endgroup$ – Benjamin Dickman Dec 4 '17 at 21:32
  • $\begingroup$ Honestly, I think the perpetuation of things like "infinity is just a concept" is a bigger issue. Unless you count that as cranky too. $\endgroup$ – Hurkyl Dec 4 '17 at 22:19
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    $\begingroup$ Do you mean things like $\displaystyle \sum_{j=1}^{\infty}j=\frac{-1}{12}$? $\endgroup$ – user negative one over twelve Dec 5 '17 at 22:27
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    $\begingroup$ What kind of answers are you looking for and why? $\endgroup$ – Nate Bade Dec 5 '17 at 22:43
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I had a couple but one in particular sticks out: years ago I was teaching a summer program for middle school students, one of the other instructors suggested I show my students the youtube video "Imagining the 10th Dimension." So I watched the first 5 minutes and it looked like a nice flatland-like explanation of higher dimensional space, so I let my TA show it while I was out of town. It turns out after about 6 minutes of flatland it runs off into a really misguided attempt justify the conformal anomaly (sometimes understood as 10 spacial dimensions) in string theory in terms of "all the possible version of actions in the universe."

It's a great example of bad mathematics/physics (although the author doesn't really understand the difference). It slips from well established mathematics to incorrect and incoherent speculation without batting an eye, and the narrator has an easy authority that says "just trust me." My poor TA luckily figured out something was seriously wrong and told the students that they shouldn't take it seriously. We took it as a teaching opportunity and had an hour long lesson about evaluating claims, thinking for yourself, and the difference between speculation and proof.

I had a conversation about it with the person who suggested me the video, but he didn't really seem to understand the problem...

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  • $\begingroup$ This is an eye-opening example, and I'm glad you shared it. However, I think it doesn't really answer the original question (Are students adversely affected?), and it's worth emphasizing what you said towards the end: you turned this situation into an occasion for a class discussion about precisely this kind of phenomenon. So, I think an answer to the original question is, "Yeah, probably". And as far as what we can do about it... we cab simply let students know this is possible in reality and to talk about it with them. $\endgroup$ – Brendan W. Sullivan Dec 6 '17 at 23:08
  • $\begingroup$ I think I would go farther and say that while they clearly could be, they sort of don't seem to be. As Dan pointed out in the comments under his question the lack of response here probably indicates that it's not that big of a problem. But it could also be that the students who would be effected arn't talking to their instructors. $\endgroup$ – Nate Bade Dec 7 '17 at 16:29

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