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August 7, 2021

Why Aren’t You Making Math(s) Videos?

Posted by Simon Willerton

Over at 3Blue1Brown Grant Sanderson is asking the provocative question “Why aren’t you making math videos?”


Certainly for many of us there are reasons which include things such as lack of time or energy. However, if you have time, energy and desire but lack the encouragement, then perhaps this is for you.

To encourage more people to make videos explaining maths, last month Grant launched a competition: The Summer of Math Exposition. The idea is simply to make a expositional maths video and submit it. The deadline is 22nd August so you’d better get your skates on if you want to do it.

In the video at the link above, Grant gives some good hints and tips on how to get started. The first and foremost of these is the very sensible “Just start!”, certainly that’s what Eugenia and I did with the Catsters – there was no careful planning beforehand. As the story goes, we broke into Tom Bridgeland’s office one evening, ‘borrowed’ his webcam and just started making videos.

Anyway you have two weeks, which doesn’t give too much opportunity for procrastination!

Posted at August 7, 2021 4:43 PM UTC

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Re: Why Aren’t You Making Math(s) Videos?

Because I’ve been battling exhaustion, quasi-depression and the UK higher education system’s conflation of customer service with demands to filter according to a perceived external standard?

(Also trying to finish collaborations where I owe my colleagues, and look after my graduate students.)

Posted by: Yemon Choi on August 7, 2021 5:17 PM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

These are things I can identify with, Yemon. I didn’t intend this as a guilt trip! I’ve added a paragraph which is intended to address this somewhat.

Posted by: Simon Willerton on August 7, 2021 5:54 PM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

In response to both Yemon’s answer and Simon’s reply: well, quite. And anyone who doubts Simon’s sincerity should know that he had the, um, “luck” of being appointed head of teaching about five minutes before covid hit.

Although I don’t like the original clickbaity question that Simon’s quoting (cf. “what’s stopping you from having a body like this?”), I’ll take it seriously anyway and answer it.

Like many people, I had my first experience of making maths videos only quite recently, as part of online teaching necessitated by covid. I’ve only taught one course online, and made probably about 40 videos for it. Beforehand, someone gave me the excellent advice to stick rigidly to a one-take-only rule, which I did. (Except for that time I explained my heart out for 20 minutes only to discover that my microphone was off.)

As the semester went on, I got more relaxed about making videos, and I hope I improved a bit too. But one thing that was instantly and absolutely clear to me was how much of a beginner I am. By way of contrast, I’ve been writing maths for decades and am pretty comfortable sharing my writing with the world. Indeed, I did release the notes for this course. But I have no desire to share the videos. It’s not that I think I did them terribly, and I wouldn’t be embarrassed if, through some unlikely turn of events, they were leaked from my university’s login-protected platform. I just don’t think I did them well enough to want to release them to the world at large myself.

And generally, I don’t think that video is a medium I’m skilled enough in to want to make and share videos right now. So that’s my personal answer to the question.

I can see that the original Catsters spirit was full of fun: just do it, enjoy it, upload it, don’t worry. Perfectionism is the enemy. If I did have the desire to make maths videos, I might try to imitate that spirit myself.

Posted by: Tom Leinster on August 7, 2021 8:40 PM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

My experience video-lecturing for graduate statistical physics was similar, I think. The recordings probably wouldn’t be a complete disaster, but would they be worth sharing? Eh.

So, for the 3Blue1Brown event, I decided to go a different route, namely, into a local wildlife refuge.

Posted by: Blake Stacey on August 22, 2021 5:40 AM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

I’ve been giving talks online and some have been videotaped. Does that count?

Posted by: John Baez on August 10, 2021 12:37 AM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

I had a go at explaining linear algebra, and quantum physics, via “path counting”.

This is the approach used in graphical linear algebra. If you go back and look at the Feynman lectures, volume III, the rules he presents for combining amplitudes are the same as the rules for counting paths. So this just looks like a great way for people to appreciate something about linear algebra and how it applies to quantum physics directly.

One big idea here is to “categorify” amplitudes. These are inner products in a Hilbert space, so it makes sense that these would categorify as Hom’s. The path counting idea is a tiny bit of success along these lines. But amplitudes can be negative, and it seems no-one knows what negative numbers are counting, especially in quantum physics. It’s a mystery.

In the video above, I get to the point of explaining the Born rule, which has a nice interpretation in terms of paths. You just rewind everything back to the start! So amplitudes count paths from point a to point b, and the corresponding probability counts loops from point a through point b. I wonder if there is some interesting homotopy theory interpretation of this.

Posted by: Simon Burton on August 23, 2021 8:27 PM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

I’d love to see this explained in more detail – have you got any useful links you could share?

Posted by: Chris B on December 5, 2021 10:28 PM | Permalink | Reply to this

Re: Why Aren’t You Making Math(s) Videos?

I have been meaning to create more maths videos. I used to love giving seminar talks at grad school and I feel like there should be more high level maths videos on the internet.

I have been playing around with the manim software, and while the results are gorgeous, the time it takes me to animate, narrate, and edit a talk are enormous. Grant’s talks are great fun, but I doubt you could make an entire lecture series this way (at least not on your own). The workload would be prohibitive. For example, (admittedly as a beginner) I coded and recorded a two hour lecture using manim and audacity and cinelerra… and I was still unhappy with the results after 6 months. This does not scale.

Furthermore, I don’t think that “video” is necessarily the best format for all content. At the higher level, so much mathematical communication is text based and having a video (that is purely graphical) representation of text is unsatisfying. There ought to be something better. Furthermore, when we imported lecture series to the internet by taping the lectures and putting the videos on youtube, we get a sub-optimal result there too. A lecture that might be enthralling in real life can become tiring and hard to follow on youtube. The choices you make for an in-person talk (content, pace, level of detail) are not optimised for digital consumption.

I could go on… but luckily I have already dumped my thinking on the matter at but have not pursued it further. I’d welcome any comments :)

Posted by: Aron Fischer on April 5, 2022 9:56 PM | Permalink | Reply to this

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