Summer of Math Exposition

The moment the probe was reduced down to that of one vertex at 18:10 is where the idea of probabilities clicked!

This has been an incredibly educational video to watch, thank you for taking the time to make it, thoroughly explaining your amazing breakthrough.

The visuals were helpful, and the script was clear, I just found that at a few parts they didn’t time exactly right with each other, like around 6:17 where the translation of the set was introduced.

I also think the timings could be improved for some scenes, in the duration of some animations and the wait in between for some others. I felt that some parts went a bit too quick for me while others waited unnecessarily.

Those issues hardly subtracted anything from the clarity and overall impact of the video of course! I hope we get to see more of your work in the future!

The Guidelines are quite clear on what they want - and this is it. I cannot describe it differently than outstanding. Even though this is an active field of research, you never leave the user behind. I’ve had more than one moment while watchingvthe video where I was just thinking “ohhh how cleanly it all comes together”. A pure pleasure to watch, and I’ll just have to pull a 9.0 when it is a 9.0

The result is interesting, and the video builds it up in a way that makes sense. And you do a great job making it clear where the proof is going. I would have liked to see more of the details of the equivalence between the single point and the collection of probes, since that’s such a key part of the proof.

Making the whole video in Manim is cool, but the AI generated voice was off-putting. Video was interesting but lacked motivation. Could have also used some background music.

The content and premise was super interesting, and I was curious to learn about the result. My favorite math problems are ones that are simple to pose, but complex to solve. The script and animations were very clear, and easy to follow. But I was turned off by the artificial voice narration.

Super cool to see how the problem of continuously coloring the plane turns into a more discrete graph theory problem. If it was explained to me by someone other than Siri, it would be one of my favorite videos I’ve seen in the competition this year.

I especially liked how you avoided very technical definitions, like the measure-theory formulation of density, which would have gone over my head. I would love to see more videos in this style, where mathematicians present their work in a way that the average undergraduate can understand, but I appreciate that it is very hard to do.

Amazing quality content!! I never expected to see a recent math discovery explained by the authors themselves, and it was also so easy to digest!

I would get rid of the AI voice and use natural voice, this makes it more memorable.

So I think the first half of your video is beautiful, the connection between what feels more like a measure theory problem to concepts in graph theory is both unexpected and very elegant. That said, the back half starts to get pretty unclear - the connection to probability that you talk about is only something that I got a few minutes into you explaining it, then you talk about linear programming solving systems of inequalities but you never actually demonstrate the inequalities in question, and I think the very rigid presentation style doesn’t help matters. You also say that your search came up negative for finding any probes beyond a 25% bound, but then your timeline of bounds over time shows a graph from 2023 that has a 24.2% bound, which is from when you said your team proved the conjecture? And you promise a connection for why the number 1/4 is important, but you handwave it at the end by bringing up Bessel functions out of the blue.

The first half of your video has a real clarity to it, even if it doesn’t really give a reason why the problem is important it shows a real beauty in it. I almost wish I had only seen that part of the video, because the back half really robbed me of that clarity. But you do have something here, and congratulations on the proof.

Impressive video! My main concern is related to the topic and its relevance for a larger audience.

Very cool to see authors create more understandable videos alongside their research!

The video seemed to go a bit fast in some places, but that is probably preferable to getting too bogged down in fiddly details. The narration seemed sort of monotone — was it text-to-speech?

Nevertheless, this was a really cool peek into this problem, with lots of beautiful and helpful animations.

The AI voice takes a lot away from the video quality. If I encountered this on Youtube, I would promptly click off the video assuming it is regular AI slop.

The visuals are clear and entertaining, the problem definition at the beginning is interesting, and the first examples are well presented, all ideas following nicely each other.

The second part is also clear, except for the very end where the introduction of the Bessel functions and successive proof of the conjecture was rushed.

Very interesting and nice animations. It went a bit fast on how to use graphs to provide an upper bound on the density, and I had troubles understanding exactly how the probabilities were computed afterwards. The video could benefit from more details on these parts but otherwise very nice.

The video is otherwise clear and well motivated and memorable.

I think this is definitely not a video for highschool student but undergrads and graduate students in pure maths could be interested in it.

This is an interesting problem that I believe has many practical applications. Though I do wonder why shapes of constant width don’t help satisfy this problem (granted, this is not my field of expertise as it is yours). This video feels over packed and quite long. The voice actor used does not help, her constant vocal range makes it difficult to pay attention over the full length. As well, I think that this is novel enough that you wouldn’t need to dive into the results of the paper. I think high school is a bit of a reach for this as the ideas quickly become specialized to the field of the problem. It’s not that a highschooler couldn’t understand this, but the style is a combination of lecture and conference presentation. I’m not sure it does a great job of teaching a concept. If you divided up the video into more focused blocks, changed to a different presenter who was able to speak enthusiastically about the subject, and chose an audience to hone the information density, I think you’d have a winning video. Right now, it seems off.

Not a real voice, I think.

Really interesting even though I didn’t understand all the reasoning on the first go I’ve seen the Moser spindle before as a solution to a math puzzle (“Find seven points such that…”), but I didn’t know it had a practical use like this

A fantastic summary of high-level research in an approachable way. I loved how you slowly walked us through the development, introduced the clever method of probes, and concluded with an organizer of the currently known results. All beautiful and very clear!