Summer of Math Exposition

Really loved the video idea and your delivery. Wished you went through two examples of the game, though. And actually showed how the contradiction of player 2 actually contradicts the established axioms. Also, I think more examples and arguments about why such a game is useful would be good. You stated that it is useful, but didn’t really illustrate it. E.g. you could show that group axioms usually contain both left and right neutral and inverses even though left neutral and inverse are enough. Seeing something like this would have really emphasized your point.

A fun video (also with the cat images^^). I liked the idea of the game, although it seems to be somewhat hard to play and also referee. The video was clearly motivated. Maybe you could have said in a few sentences what MathCamp is, although its spirit is conveyed.

You explained clearly how the game works by means of a specific example, so one could easily follow you along. The content was mainly static and could maybe profit from some animations to better maintain continuity and hook viewers. Especially, maybe some text elements could be shown rather visually with only the audio reading the full sentence.

Would have loved to see some link to a website that contains printable rules and maybe some more examples at the end of the video.

I feel clarity is well achieved, as well as motivation. Novelty may here refer to the novelty of sharing math as a game, which seems to be quite fun. There was no novel teaching style, instead a traditional click-through style of content. I didn’t find the video particularly memorable. Maybe one could weave some interesting mathematical statement into the game itself, but I don’t know if that would maybe overload the video.

On a technical side, I’d love to see such videos in at least 1080p quality (if frame rates are a concern, I’d rather go for 1080p with 24fps instead of 720p with 60fps). A better audio quality (with less compression artifacts and noise in the high-end) would also be appreciated. Bass/mids of audio seemed to be quite balanced. Some math-related elements seemed pixelated on screen, would love it to be sufficiently high-resolution (i.e. by using vector graphics during editing).

I thought this was an intriguing mathematical game and explained clearly. But the motivation wasn’t clear (other than simply for fun), and I am not sure what I should take away from it. I don’t think I learned much new from watching

I really enjoy the concept of this video and the game it presents. Games like this are valuable if they can help someone learn about the logic and philosophy behind math and even logic itself. I appreciated learning how the game works, and how it can help anyone understand more about axioms and theorems. Bonus points for cat pictures. LOL

Nice video. I think this video has novelty since a tiny “toy” axiom set up is fascinating, and this provides a good model.

A couple of notes:

• At 9:49, you leave the definition of a pidgin up for too short to read.

• I would maybe recommend explaining how the second “axiom” can be derived from the others. I don’t believe that is clear.

Love the tone of voice, very enthusiastic!

Love this idea for a game, totally something I could see math nerds playing. Very cool.

Also love the cats :)

nit: a bit too much preamble and formalism when explaining the game. breaks the flow of the video without adding much. when you say “we fixed the signature at the beginning of the game”, that totally addresses the operator stuff so you can cut that part out from before.

nit: not really relevant to SoME, but the title and thumbnail could be better. I actually saw this on my feed before SoME peer review and thought it was a video about what an axiom is vs what a theorem is, so I wasn’t interested. But this video is actually interesting, and I would’ve clicked on it if I knew it was about this! Maybe something like “The game where you try not to say a theorem”

with a tad less formalism, this could be brought down to be accessible to high schoolers without losing value for more advanced viewers. the core idea is you’re trying to say things that can’t be proven from what was already said. That’s something high schoolers could understand. You could gently introduce formalism as the game goes on, and maybe even make this video kind of an introduction to model theory/abstract algebra. It seems like you kind of wanted to do this based on the ending of the video, but by then you may have alienated a chunk of the audience with unnecessary and too-early formalism.

Overall great video!

I really want to play this game but look around me and see no one to play it with. Only criticism is that video should have come with friends :(

This definitely isn’t as mindblowing as some other submissions I’ve seen, but it makes up for that in engagement. The video is short and to the point.

Would have loved some expansion on other edge cases. I understand the rules of the game are simple at the end, but it sounds like there’s a lot of debate being swept under the rug here. And off the top of my head I can think of a lot of things, like, “should the scoring be based off of the number of independent axioms contributed?” I also got a little lost with the example as someone sort of familiar with logic but not with model theorist hijinks. About the closest I got to understanding the example round was when you compared it to the integers. I like the integers.

Decent video, but the audience is very niche. It was entertaining and engaging for an audience which already knows logic fairly well. However, you don’t come out learning much you didn’t know before.

This video sounds like a fun topic, but I think it should be clearer from the beginning what the video is about.

I think the video captured an interesting topic, as it was an original game that I would never have come up with, but definitely see why people at math camp would play it. I would also enjoy playing it probably. The visuals were very simple, but that had a charm, as it did not distract you from the information on the screen. I think some parts went a bit too quick. For example, the introduction of these axiom systems, I think all undergraduate students have had this, but still, a short refresher or showing one of the examples a bit more in-depth would have helped. Also, perhaps the problem that the maker asked (proving a contradiction) would be nice to (at the end maybe) show the solution to, in case students did not manage to work it out themselves. All in all, a nice video!

I come from engineering background so I haven’t encountered these axiom systems and structures. Sure I heard ‘for all x there exist y’ more than I’d like, but the idea of creatively coming up with an axiom system was completely new to me, and fascinating.

On one hand I feel inept, unworthy to judge this video, since I never even had a taste of Peano or ZFC mentioned in the video. But I came away with a vague sense that those might not be as scary…? Since it can just be a somewhat silly game.

So as a math exposition video, I think this is excellent.

At first, I was quite disoriented, but I eventually got hooked; it’s a really fun and interesting introduction to axiomatic systems. (I’m not sure if starting with the countries/colors games and the like is the best approach; it seems to me it would be more effective to get straight to the point. But that’s a matter of taste…) I do have one question left: the game clearly illustrates the relationship between systems and models—perhaps a word could be said about how this result can be generalized? In any case, it’s extremely original—well done!

“If I remember correctly the convention was to just laugh at the player and let them go again” absolutely made this video. Long-held slides with narration largely matching the content of the slides is about as standard a format as you could use. No problem with that, but it’s a serious handicap to making novel / impactful expository works. It means you have to lean all the harder on word choice and presentation style. This is a clever way of reinforcing the basic principles of abstract algebra and axiomatic systems, but has a significant flaw in implicitly assuming the viewer already is comfortable with (or at least comfortable with quickly learning) terms like “semigroup”. I personally enjoyed this video, but I think the circular dependency on basics of abstract algebra / model theory significantly weakens the presentation

I found this neither instructive nor entertaining.

Fun! I just sent this to some of my friends who I can imagine playing this when they were at math camp.

This was well explained and paced. Running through a game was fun and helpful. The elimination process at the end makes for an interesting bit of tactics.

I only wish this video could reach a broader audience. Unfortunately, it was necessary to assume the viewer is familiar with a fair bit of abstract math to follow along. I wonder whether a few more sentences near the beginning explaining what a “structure” is would help an uninitiated viewer.

Funny and entertaining, but I’m not certain of how informative it is. There’s a lot of gesturing at how model theory works, and the examples are useful, but I didn’t feel like I got a very concrete idea about what it is.

I would need more examples of this games playthrough to really get this