If you have followed 3Blue1Brown, you might have heard of the previous three SoME (Summer of Math Exposition) contests. However, the associated workload was too much for Grant’s small team that they decided to take a hiatus. The community decided to do a SoME this year anyway, naming this SoMEπ, because it is between SoME3 and a possible future SoME4. There is no prize money or any dedicated video from Grant himself for this. More details here.

I decide to give shoutouts to my favourite videos / entries participating in this community-run contest. This blog post outlines my criteria to pick my favourites. They are mainly dedicated to videos, but most easily transfer to blog posts. I want to preface this by saying that I understand that my criteria are weird and strict, but this comes down to personal preferences when watching YouTube educational videos. So you can have an objectively good video, but if it doesn't satisfy the criteria, it wouldn't be my favourite video. and it doesn't feel authentic for me to shout out videos that I don't like, even if they are objectively good.'

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The main weird criterion is novelty. In short,

• Is your video covering a topic that has been explored before on YouTube, and is popular on YouTube?

• If yes, is it using an approach that has been explored before on YouTube, and is popular on YouTube?

If both answers are yes, then I'm sorry that your video just fails this criterion.

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Just to be clear, when I say “approach that has not been explored”, I don’t mean just adding better visuals or clearer explanation. If you simply add visuals to a very traditional textbook or a lecture recording on YouTube, explaining what each step means visually, that doesn’t count as novel to me. It needs to approach the topic from a different angle. To other people, there is value for a video to have similar arguments in the topic, just with better visuals or clearer explanation; but to me it feels like the same video. I know I am very weird in this regard, and you shouldn’t feel that your video is not good if I haven’t shouted you out at the end. It really needs to pass this strict test in order for me to even like the video.

To be clearer on what I consider as a different approach, I am taking examples from my channel.

Negative examples:

• The video on the notations SO(n) and SU(n)

• The video on general complex number manipulations

• The older video on combinatorics

They do not satisfy the criterion of novelty, because they are at best compilations of arguments others have said on YouTube. I made them as prerequisites to topics whose approach have not been explored on YouTube before. (Respectively: Lie algebras using vector fields, visualizing complex functions, and Catalan numbers in the context of deposit / loan calculations)

Positive examples:

• The video on geometric interpretation of Taylor series of sine

This satisfies the criterion of novelty because when I search for the geometric interpretation of the sine series on YouTube, nothing else really comes up, so it really is novel in this regard.

• The video on visualizing matrix transpose

This satisfies the criterion of novelty because I have really never seen anywhere on the internet a visualisation this direct. Most likely they would rely on singular value decomposition, which is really complicated visually. At least this is an independent discovery (maybe even original!).

If you want some examples of blog posts, I have previously been on Quora, a question-and-answer site answering maths questions. Here are some examples that illustrate novelty. They are mostly from answers (with one proper blog post), but all answers can easily be repackaged into blog posts (and have indeed been repackaged into earlier videos on the channel):

• Exploring mathematical elegance with a simple problem

• Finding an area under the curve with physics (and geometry)

• Geometric proof of Heron’s formula slightly improved from the original from Heron

Anyway these examples hopefully illustrate what I mean by novelty. Again, I know this is such a strict criterion, but it is really how I myself feel when I watch educational videos on YouTube. I just have weirdly strong opinion that if the same concept is packaged differently, however different it is stylistically, it still counts as rehashing content. 

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After the video passes the first criterion of novelty, the second is to be well-motivated. Basically:

• why do YOU care about this?

• why should OTHERS care about this?

• is there a final goal in the video that we will reach?

I think this is more important than novelty, but novelty serves more as a prerequisite before I even consider the video seriously. Sometimes, the reason why you care about the topic you cover is just that it is interesting, and may sometimes be quite esoteric; but you want others to relate to your passion as well - even if it is “just interesting”, the motivation should be easy for the general maths enthusiasts to understand.

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These two criteria are the most important ones in my mind. What I don’t care about is your style - it could be using Manim, or GeoGebra (like my channel), or black/whiteboard, or basically any tool you think will convey your message best. Again, I want to stress that your entries can be objectively good and enjoyed by many people and still don’t pass through these admittedly weird and strict criterion. In any case, do start planning your entries - I can’t wait to see them!