For the fourth time in a row, the Summer of Math Exposition competition asked people to create an explainer—video, blog, game, etc.—about mathematics or something related. Grant Sanderson¹, who ran it the past three years, decided to take a break because it is a lot of work. The community wanted to do one anyway, and so we did. “We”, in particular, because I ended up as one of the main organizers.

At the start, the main idea was to curate a simple YouTube playlist. To indicate that it is an interstitial event, we gave it the number π as it sits between the third SoME from 2023 and Grant Sanderson might hopefully return to host it in 2025 with iteration number four. After some talks with James Schloss, the organizers of the first three iterations, we were able to use the “official” SoME website and the event this year is by and large indistinguishable from the others—except for the 3Blue1Brown winner video and the associated prize money.

You can find the website with the results of this and the previous years here: https://some.3b1b.co

More importantly, at least for this post, is that the creators got a lot of feedback and I want to go through the comments I received. So, if you haven’t watched my video for SoMEπ yet, here it is:

My overall performance

First and foremost, my video landed at place 27 out of 142 video entries.

This is very close to the “honorable mentions” section which would be the top 25 entries, but for video and non-video combined. Notably, it’s much higher than last year’s 105th place or the previous one which was around place 80. Obviously, the fact that we had only a fraction of submission has played a role. But these three data points indicate that I’m somewhat improving. Let’s look at my actual score next.

Entries were graded on a continuous scale from 1 to 9² and we got a histogram with votes sorted into 0.5-wide bins. Here’s mine:

It is the bell-shape you would expect and averages out to a score of 6.5. But with only 31 votes, it is of course quite jagged. To interpret this histogram properly, you need to know that the task for the judges was not to simply rate the entry. They were prompted with:

How valuable is this entry to the space of online math exposition, compared to the typical math video you’ve seen?

Over the slider was a coarser categorization from notably worse over not as good, about the same and better than most to outstanding. And here lies the crux, of course. If you only watch the likes of 3Blue1Brown, Stand-Up Maths and Mathologer, you would have to grade most SoME entries on the lower end. In other words, do you place the big dogs of online maths exposition in the centre of this scale or on the right? The way the prompt and the categorization are formulated, both would be justified.

Granted, with enough votes coming in, it shouldn’t matter too much how exactly each individual judge determines their score for an entry if we want to rank the submissions. As long as each judge is consistent. But this could explain why many histograms that creators shared in the SoME Discord Server³ had two distinct peaks.

So… am I satisfied with this score?

Compared to the average maths YouTube video⁴, I am certain that mine are better than most. So, getting an average score of 6.5 is… fine. But I think it could have been higher. Moreover, If I do be so bold to compare myself to the big names in maths YouTube: My explanations aren’t any worse? My videos do have quite a few production issues, though:

• The sound isn’t too bad, but could be improved. (More on that later.)
• I’m not really comfortable enough when doing the voice-overs. Especially compared to when I’m standing in a lecture hall. In particular, I always try to emphasize certain words and create a certain rhythm in my speech. And while it does sound somewhat right when I speak, the actual recording is always super flat and monotone. It gets better with each video, of course, but not as much as I’d like.
• My videos aren’t edited that well. In particular, I often have an empty screen where I just talk for half a minute. And while I think that this is fine from a didactical perspective, it makes the video less appealing.

And my animations alone aren’t enough, no matter how good they are.⁵ So, while I do genuinely think that I am better than the average maths YouTuber, I understand why my channel isn’t successful. But that’s okay. After doing this for two years now, I’m content with where I’m at. Speaking of which…

The video itself did fine. It has 1800 views as of writing this. Much more than my channel average, but much less than my other two SoME entries. Without a 3Blue1Brown winner video to push people, we had a drastic drop in creators and probably in judges, too. Consequently, the YouTube Algorithm likely didn’t see enough cross-watching during the peer-review process.

The channel also saw a boost in subscriber numbers and I now have over 3000. I’m considering launching a Patreon once I hit 10000 to gauge interest. But I have little to no idea if and when I should approach YouTube more professionally. But that’s a topic for another time…

The feedback

Despite the almost 1000 words above, I mostly want to talk about the comments I got during peer-review. In addition to the prompt for the grading, judges where asked to consider motivation, clarity, novelty and memorability when making their decisions. With that in mind, let’s look at few short comments first:

Grade 7.8:
Very well done, impressive animations and exposition.

Grade 7.1:
Great Video

Grade 7.1:
Very interesting. Covers a lot of ground without feeling overwhelming.

Grade 8.2:
Simple explanation of a rather complex topic. Well done.

So, that’s nice! Especially the last two. I’m mostly doing rather broad overviews of certain topics and that’s the best reaction I could wish for. Next…

Grade 8.6:
Hi !
I absolutely love your video, the animations are beautiful, your pace is really good, each scene is well balanced with the right amount of formulas, text and visualizations. Just to nitpick, I would say that the topic of the video is very well known from a lot of undergrad students, so revisiting it is not that original. However, I think you managed to make the best video on this topic by far !
Another thing is that you could probably improve your audio quality, but it is already very decent. Maybe also add a little bit of music, and you’ll have the perfect videos !
Thanks for your work and for submitting this wonderful presentation.

It’s never an easy decision of which topics to cover. If I did YouTube more seriously, I would probably try to mix well-treaded topics with more niche ones. But even if something was done to death, I hope/try to add something new and worthwhile. In the context of SoME, the video I made before this—about five different ways mathematicians talk about cutting things, explained with food—would have been better, I guess. But with videos taking so long to produce, strategizing on the topic is a bit tricky.

The audio quality of this video is in deed noticeably worse than usual! I’m certain I did turn the same dials the same way as always in DaVinci Resolve, but somehow the sound is… grainy? Crackling? I don’t know…

And the part about the music: In my first video, the music was way too loud. In subsequent videos, I turned down the volume more and more; and for the last two, I left the music out completely. Not sure what I or my viewer want here. Will probably experiment a bit more in the future.

Grade 5.0:
I really enjoyed seeing your individual based simulations matching up quite well with the logistic growth and Lotka Volterra predictions. For me, that was the most interesting part of the video. It would have been nice if more was made about the link between your simulation and the differential equations which approximate the behaviour of the simulations. When they matched up well it felt a little like plausible magic to me.

I also think that this submission would benefit from being more homogeneous in the level of prerequisite knowledge that is assumed. You start by explaining differentiation from first principles, but later on you don’t explain more advanced topics in the same detail, such as infinite series, orbits and velocities in phase space etc. I personally think it would be better to just assume that your audience knows about derivatives, and to point those that dont know to a source which explains derivatives as a prerequisite to this video. This lets the audience know from the beginning the rough level of knowledge they will need to understand the video.

I always struggle with handling prerequsits for my videos. In general, I do want most people to be able to understand most of the things I talk about in any given video. And personally, I do quite enjoy the arc from arbitrary functions over linear and exponential functions to a system of ODEs. But I can see how a two-parter on the topic might have been a good idea. But I will always try to avoid adding “We assume the viewer is familiar with X, Y and Z” to a video.

And I agree with the first part: Focussing more on the simulations would have been much more fun. But they are super hacky and I’m far from good enough as a programmer to do a video on something like that.

Grade 8.4:
Overall, a very good and well-executed introduction for advanced high school to lower university students. If there is one area where this video is not as strong, it is that the topic is not that novel.

One errata: at around 2:00 the equation is shown with f(h) rather than f(x). Also, the English I am familiar with uses the soft ‘g’ in ‘logistic’.

As a physicist, I was a little disappointed that you didn’t take the opportunity around 18:00 when you stated there is an invariant quantity, to relate this to other fields which use differential equations such as mechanics.

Again, noting that the topic is not super novel. But I think the simulations brought something new to the table, so I’m fine with the topic itself being “old”.

And the last paragraph, about examples from physics: Talking about one or two examples outside of the application in ecology would have been nice. But I wanted to keep the video as close to 20 minutes as possible.

All in all, I’m quite happy with the remarks! They aren’t “useful” in the sense that they didn’t reveal anything I’m not thinking about anyway. But it’s nice to get feedback that’s a bit more focussed than a YouTube comment.

---