Summer of Math Exposition

Not really a problem that many people think about, and sometimes that’s ok, but this was pretty uninteresting (maybe to me, i’m no combinatorist!)

The coloring is elegant, also the diagrams are beautiful. This topic itself is a really interesting, I’ve tried to draw a 4 set graph, and think about this topic, but I didn’t expect you can go this far. But if you can put more details like what the functions graph is in the descriptions will be better

Why is it still an area of research (i.e. why are the roadblocks that prevent new contributions to the field) ?

Now I want to see the tetrachromatic main color categories that I can see as a 4-set Venn diagram in the Smith construction style. Looks pretty handy, especially once the dimensions of e.g. color go up to pentachromacy (5-set), hexachromacy (6-set), and beyond.

This video is simple but effective. Its lack of novelty is outweighed by its clarity. Venn diagrams are so visually stimulating that they’re always memorable (for me at least).

Interestingly, set theory and Venn diagrams don’t just have to be theoretical. As I’ve mentioned, they’re also very useful in color theory. For example, a trichromat’s main (additive) color categories (red, yellow, green, cyan, blue, magenta, white) can be easily displayed and understood via a 3-set Venn diagram. For tetrachromacy, where there are 4 distinct color dimensions, you already need a 4-set Venn diagram to display its main color categories. I personally have an form of (non-retinal) tetrachromacy and I can definitely say from experience that a simple 3-set Venn diagram can’t be used to display all tetrachromatic main color categories.

Needless to say, I like this video, although I’m biased of course. The score isn’t better because I’ve already seen videos here that have a very firm production quality and really good visuals. Your video has taught me something new (Smith’s intersection diagrams), but it didn’t give me the same wow-effect like other, higher-scored videos.

Some very cool ideas mentioned, you could take a bit more time to explain each idea

The visuals and reaearch

I just happens that a few months ago I heard about this paper https://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r2, which has a constructive proof of existence for prime-numbered symmetric Venn diagrams, although they are not simple.

I haven’t actually read it in detail, but there’s supposed to be an algorithm along with figures up to n=17 posted to an author’s website. Unfortunately it’s no longer there because they retired, but I bet it could be found with some digging on the Internet Archive. Or you could look into implementing the algorithm yourself. It does seem like the n=17 case would require some zooming in to see the detail!

There’s also a followup paper https://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r86 where they try to get closer to simple diagrams, although I haven’t read it at all. And this is not in any way a thorough literature review, so maybe there’s been more progress since then.

As far as the video itself goes, I liked how many different ways to construct diagrams were shown, but despite having so many loosely connected ideas, the video felt cohesive and wasn’t overwhelming. The connection to Fermat’s little theorem is also really nice.

One possible improvement would be to focus a little more on one or two of the the results, like the connection to Fermat’s little theorem, since I found that I had to pause and rewind to really digest that.

I would never have guessed that Venn diagrams could have something to do with Hamiltonian paths. I really enjoyed the topic; personally, I found it engaging and original, and I watched it through to the end. One doubt: can it really be suitable for high-school students?

Nice video thanks!! Comment: Try Proofs instead of ‚usually works‘ statements :)

Nice visuals and animations. However, the video format could definitely be utilized better than just showing similar looking diagrams and equation. It gets the job done, but removes some joy in watching the video. Also, explanation was nicely done but not perfect in my opinion; The explanations moved smoothly, but it failed to answer some questions audience might have had while watching the video. Explanation format was also interesting where the speaker is acting like he is trying to solve a question themselves, while explaining at the same time. But overall nice animations and very interesting topic. Narration was flawless as well.

Interesting topic!

This was a fun topic with some nice visuals. The approach felt very mathematical and experimental, starting with Hamiltonian cycles then looking for more symmetry like the sine waves, then looking to refine the requirements and using those crossing diagrams. I liked that you cited specific historical names.

I would’ve liked to see at least a hint at how easy the problem is in 3D. I also think it would be nice to relate the Smith construction to counting in binary.

Overall, this felt like a cool fresh problem which you could attack from several angles, but I it would be nice to have some sort of take-home message.