Summer of Math Exposition

Absolutely phenomenal video.

There was a lot I really liked.

• The introduction did a great job of motivating the topic by showing how it is an open problem and setting the scene for how the rest of the video will go.
• The topic was novel and explained very well. The questions asked throughout the video gave the viewer a chance to ponder.
• All visuals and animations assisted with the clarity. Building up to the higher dimensions from a simple problem also made it clear.
• It was fun and memorable! It taught concepts which can be hard for students by tying them to a simple understandable game.

Perhaps the only “criticism” is that I felt the topic involved keeping track of a lot of different ways to count things, so I got slightly overwhelmed by the end due to the video format (as opposed to say a written down format). I feel that I would have to rewatch it.

But amazing job.

I like the topic of this video quite a bit, but I must admit that I eventually got really bored. I think the presentation is simply too “monotone.” Both the narration and the visuals were too similar throughout, so by the time I was halfway through the video my mind was wondering quite a bit. I suspect the target audience would get bored and “click away” from this video. I think part of the problem is that the proof here is presented as a lengthy number of steps, but none of those steps are particularly well motivated. So while I could follow what was happening, I never really felt like I was learning anything profound. In the end, I finally through in the towel after 26 minutes. I just couldn’t bear watching any further.

The introduction was great , but as the video progresses I can’t really get the things

I love set!

The problem is very interesting, and the proofs by contradiction too. I found a little difficult to understand some intermediate results, such as the number of hyperplanes in different dimensions.

Incredible work and beautiful visualisations! Also explained really thoroughly! I just think it’s slightly tiring after a bit, which is why i didn’t put a full score, but other than that it’s perfect!

I liked how you strung together a story with these complicated combinatorics arguments that made them easier to absorb. You had exactly the graphics you needed. I liked the bipartite graphs with ”…”; those got the point across better than words alone would.

I still had a hard time conceptualizing exactly what you were double-counting, so it might be nice to have that information linger on the screen longer.

All around, great video!

The repetitiveness and use of leitmotifs seems to be a very conscious choice here, but it didn’t work for me. For those already familiar with the concepts, the pace is too slow. For those less familiar, it’s easy to lose focus when encountering all the calculations. The video is enjoyable and the topic is fun, so I mean this sincerely and without sarcasm: I would genuinely recommend this video to friends who watch math videos when they struggle with falling asleep.

I really appreciate you bringing up George Polya’s advice in problem solving. I’ve read his book before, and it’s really helpful in becoming better at problem solving.