Summer of Math Exposition

The repetitiveness of the background music was somewhat distracting.

Perhaps fastforwarding some of the algebraic manipulations would have been nice.

Really good overall, I also left a comment on youtube.

I like the dodecahedron example. Great animation. Good video.

The three-dimensionalty of the dodecahedron wireframe with semi-transparent faces is a bit hard to perceive. (Maybe make parts that are further away from the camera darker or something similar?) Overall, a very competent explanation. Of course, when you get to algebraic topology it’s, well, just algebraic topology. The abstract algebraic manipulations could probably be cut down quite a bit.

I definitely did not manage to digest the entire video, having a bit of clue of most of the touched upon math but with large holes and a notable lack of practice left. But a couple of lessons and inspirations stuck, and I can definitely take that as a big plus from the perspective of someone who is probably a month or a few weeks of more targeted studying away from being able to absorb the entire video. The sound and editing was clean and I’ve spotted no issues.

Very good video! I like that you are not talking too fast. That’s important for these advanced topics. Explanations are very good and you managed to lead my thinking in the right direction.

Very good. This is what advanced math needs. A bit fast paced, but that might be just me being rusty with homology groups. Music is slightly too loud. The chat conversations between major players was a nice touch. As this is an advanced topic you might want to lay out prerequisites at the start. Also add timestaps.

This is the kind of video we need, thanks! Great job! Please made more video.

A question I’m often asking with SoME videos is: who is the audience? You obviously intended this exposition for a limited audience— your tags say graduate (and above) only— which inherently limits its value to the space. I agree. Most undergraduate students will not have the background to follow much of the discussion in 6:00–11:00, which is a long time to suspend disbelief.

This segment is really my main issue with the video. One of the things that I will remember is that, once the background machinery is dealt with, the rest of the proof is surprisingly simple. The problem is, if you don’t know this, you don’t know what’s coming after that 5-minute dense algebraic topology section. I think many people at the less experienced end of your audience, who would otherwise enjoy the last 15 of the video, would be justified in clicking away, anticipating that those 15 minutes would be even more technical.

I have some minor concerns beyond this (the explanation that P is a manifold didn’t really land for me; I didn’t like the choice to breeze over the fact that the relations you describe in the icosahedral group were all the identity; I’m not sure the algebraic manipulations at 10:00 were necessary given the geometry at 14:00).

I think some people might suggest moving the history at the end to the beginning to serve as stronger motivation. I’m neutral on that idea. It would be nice for the motivation, but it might set the wrong tone for what you are expecting of your audience. But then, pushing back the problematic segment another 2.5 minutes might give the “leavers” a little more confidence to hang on? I could see it either way.

Damn that was way too advanced for my algebraic topology rudiments

Very rich and in-depth, this is a subject I struggle with, and your video has definitely helped me make progress.

Visuals are fantastic

I was really lost in some of the non-visual parts. I think the audience that would get “enough” of this is very small. it would have helped to explain some of the things used, maybe hand wave some parts with a brief note if someone wanted the details, or try to explain using simpler language.

At the very least if the “main ideas” were explained in simplified language, then at least someone not following the details could at least get a glimpse of the true “aha” moments of the proofs

Still, even though a lot was over my head, this seemed like very good content. I’m sure a complete explanation that a high-schooler could understand would have to be quite a bit longer, but if that existed that would be a fantastic video

My algebraic topology is a bit rusty but I thought this was a great video. Well-motivated all along and very interesting.

Solid 9/9. One of the best low-dimensional topology submission for this game. Steady pace, well-calibrated animation, moreover an pretty unique perspective you barely see on textbook!