Summer of Math Exposition

Nice visuals! :) And I like the narration, it’s very pleasant. The examples you showed didn’t really explain Bézout’s theorem for me, though. And after watching, I don’t really feel like I’ve understood Pascal’s theorem now. Got a little confused trying to follow the logic towards the end with the different polynomials. For example, what are common components? (Did I miss that?) What do the products of the lines look like? That might have been helpful to see.

The video is good, if a bit uninspired, but the audio is not great and in such a barebones presentation you really want the little stuff like that to pop. The quality is ok, it’s not terrible but not great; more importantly the tone is very flat, and it makes the argument harder to follow.

The video started off great with an introduction to a Bezout’s Theorem which I was unfamiliar with, and the intuition behind it makes enough sense that I could go without seeing the proof for this video. However, the proof in this video makes a giant unmotivated leap using lambda around 6:20 that made me confused throughout the rest of the video. I was too busy trying to figure out what lambda meant that the rest of the proof went over my head. Strong start, but I think the ending could use more substance to be a solid video.

Wow, really enjoyed it. Clear and concise. Very neat proof.

Motivation: Immediately starts the video, giving an in medias res feeling and keeps the video concise. Novelty: Interesting theorem chosen and the visual supports the verbal explanation of the theorem. There is no novel approach selected for the proof, hence, points docked on this criteria. Clarity: Algebraic curves was introduced too suddenly, giving almost no background or relation to commonly known topics. Later, introducing the “line” helped but the reordering of these concepts could have helped even more. Bezouts Theorem is just immediately used although it is in itself an interesting theorem that could have been proven. The proof moves too quickly giving no explanation and makes it very hard to follow. It suddenly just claims to have proven the theorem with the final figure not even matching the first frame of the video (“the motivation”) Memorability: Almost none, the video just told us what is happening in a series of steps.

This is really interesting! I’ve never seen a proof like this before. It really motivates me to learn more about Bezout’s theorem! I appreciate that you kept the video short and punchy by not trying to prove Bezout’s theorem and simply showing some examples to motivate it.

I’ve been really enjoying videos that cover a more complicated idea using a more intuitive and geometric worked example, and this is another great one to add to the list! Your animations were clean, you built up the ideas in a nice order, and I appreciate that the pacing of your exposition was thoughtful and calm. Great job!

Very good. Good quality. Maybe too hard for middle or high schoolers. Quality 9.5/10. Length 9/10 Easiness in understanding 8/10. Overall 8/10

I think an introduction, maybe a few words about the history of the problem or something else (maybe about pascal if it’s named after him) would be good to ease viewers in and give them some context; your start is a bit abrupt. Also, I do not think this video is at an appropriate level for middle or high school students; even most undergrads I know would be a little left behind. The mathematical notation, while perhaps not complicated for someone in the field, would almost certainly confuse a teenager. I did like the visualizations, and I think you gave a good explanation of Bezout’s theorem. However, the last bit of the proof was hard to follow (from when you added lambda onwards). But I have never heard of this topic, and the theorem itself is very cool, thank you for making this!

This is a very clever proof, and you do a good job explaining Bezout’s Theorem. One of the key steps in the final proof is creating a new curve, F, based on the polynomials for C and D and a new parameter lambda. Since that’s such an important construction, it would be helpful to expand on the intuition behind it.

The math content in the video is great. A very specific proof of a very interesting result that can be easily visualized.

The video would do much better if you improve the audio recording. I couldn’t hear you very well. Although I don’t have a good mic, what I do is to edit the video in audacity, and remove background noise with an AI plug in, and normalize the audio. I am sure there are other methods to improve the audio.

A potential cause of confusion is the fact that you use the same letters for some of the points and some of the lines. In the video, you use regular letters for the points and mathcal letters for the lines. However, when you speak you don’t differentiate between those. Perhaps, choosing different names would help people to follow the explanation more easily.

Besides that, it would be nice to relate this to the importance of pappus theorem in geometry. That would bring more attention to the importance of pascal’s theorem.

This is a very good choice of problem. It is an interesting theorem where the question being asked is very obvious.

The style of presentation is very clear.

The part of the solution showing the polynomials crossing was good .

however the algebra in the solution assumes some knowledge about polynomials. It would definitely be clearer if you explain what you mean by the product of lines.