Summer of Math Exposition

Interesting topic and a great introduction! The voice-over clarity could be improved. The conclusion where you leave the viewer to read the quote (although a great one) falls flat. I enjoyed the video, but I did not gain any new insight from the visuals or story, hence the grade

This reminds me of this TedEd video from a couple years back about this one portal riddle. Otherwise, good animation, niche topic, good method of teaching, and I thought the outro was funny. Forgive me if it’s obvious and I just can’t see it, but I would like it if you broke down how you got the numerical value for the individual chance of K being monochrome at 5:51, and how the upper bound got raised from n to 2^{k/2} at 6:21

Good explanation, the audio could be improved.

Using the party problem to motivation the probabilistic method is a great hook, and also historically accurate, so I was already pleased at the beginning. But given the name of the video, I was surprised that the conclusion focused on that Ramsey theory motivation rather than the probabilistic method itself (For instance, highlighting some of the other results that the probabilistic method used, showing papers that cite the original Erdos work, etc.) Maybe if you had just swapped the “two conclusions” it would have felt better to me?

The explanation and proof of K(3,3)=6 were respectable. Some minor nitpicks:

• The formalization at the beginning is not quite correct: “monochromatic subgraphs of size 3” could also be (unions of) paths
• The first explanation of n=4, talking about the “trap” could have used a few graphics.
• Since you don’t talk about non-diagonal Ramsey numbers, I would rather have seen you define R(s) rather than R(s,t). But since this is all I have to complain about, you did pretty well!

I spent most of my watch time convincing myself that the inequalities ran in the correct direction. In particular, taking a little more space to breathe on why this gives a lower bound would probably be useful for the audience. (Introducing the concept, for instance, that to lower-bound a minimizing “for all” statement, one needs to ‘construct’ a counterexample for smaller values.) Since the video was fairly short already, I don’t think you’d run much risk of losing audience interest.

These criticisms are fairly minor to me. I think you’re showing promise as a math expositor, and hope to see more from you!

Short and punchy, gets to the point and says no more than it needs to say. It’s nice to see methods from probability theory used in unexpected places. I’m guessing that this video is supposed to be for people who already know a bit about graph theory, and it seems fine for them in that case, but it could probably stand to be more welcoming to newcomers with just a few extra minutes of explanation. I mean, it’s already a pretty short video, so no harm. It is true that this video is fairly memorable, but the main contributor to that is the bombshell ending quote, so I dunno if that’s cheating. There’s not a whole lot to say about this video: it has one goal and it achieves it. That’s about it.