Summer of Math Exposition

The last part was genuinely mind-blowing, and nice graphics

The concept is very simple, and I enjoyed the video’s style. The only issue I have with it is that there’s just not really much to it. Dirac’s solution immediately solves it before I have the chance to become fully invested in the problem. However this is a relatively minor complaint, and overall I thought the video was quite good.

Motivation: 7 / 9 – The main challenge is presented and explained well. Seems counterintuitive to think that it could be possible to make any number out of four 2’s, which makes one interested – just by thinking that the answer can be found in 5 minutes. But it lacked a bit of motivation to look forward to the answer other than the answer itself. Maybe some historical background, some foreshadowing about Paul Dirac in the first 30 seconds would be good?

Clarity: 7 / 9 – Everything was explained fairly well. I would try to state the problem maybe a bit clearer – you refer to “rules” a few times in the video (something is not against the rules for example), but they were never explicitly stated (like, in your face stated, with saying words “the rules” and showing them on the video itself)

Novelty: 4 / 9 – It’s a classic challenge, that some people might’ve never seen in the infinity version. Also, for me it lacked a bit of content. Maybe a deeper dive into the topic would be better – what other solutions have been found (infinite solutions), maybe there’s one that’s better than Dirac’s (Paul Dirac’s solution uses square root, which hides an additional two in it). Maybe there’s some mathematics that shows that, under certain conditions (like only finite set of functions u can use) there’s a negative answer to the problem? I see a lot of potential in such topic which wasn’t used up in my opinion.

Memorability: 8 / 9 – nice illustrations, quite original style of presentation, I liked it a lot. The technical side was actually quite nice – especially audio, which I really appreciate. The only thing I will pick on is the thumbnail, which, for me, is just boring and doesn’t tell me what the video is about.

Overall: 6.5 / 9 – I liked the video a lot, very cozy and chill. The rating would be a lot higher if it was just a bit longer and more novel. Good job!!!

Thought this was cool, I have seen similar game but didn’t know that it had been solved. I think I was a nice short duration which fit nicely with the topic. Overall I think I is quite a good video.

The video didn’t have the catharsis moment for me. I didn’t feel enough motivation, but the visuals were cool

Very good. Well structured. Good puzzle

This is adorable! Just a perfect little bit of recreational math. Love the art, love the font.

A bigger meditation on what consitutes an elementar/simple/basic operation would have good; especially since you allow Gamma/Ackermann/etc. If you — seemingly — allow all functions, everything is possible in a trivial way. But otherwise, very nice video!

And that’s why games need rules… so that mathematicians can break them.

This was a very fun and interesting video, many thanks! I rarely have learned something complex in such a playful way. If you’d started with Dirac’s result, I might have been intimidated by the equation. But since you built up the video with simple examples and added the “Someone ruined it”, it felt more like watching a fun story than rigorous math. The video’s pace is perfect, the music fits well, the colors are well-chosen and the cat is cute. I throughly enjoyed it :) Just for the sake of finding something to critique, I’m personally not a big fan of cynicism, but I think this is very personal taste and nothing objective to change.

Very good video! The presentation style is calm, clear, and easy to follow. One of the rare math videos where the background music actually fits well.

That was a really fun watch, not too long, not too short either. I appreciate the unique animation style, it really makes this stand out from the rest. I also appreciate the cute cats of course!

The audio quality seems solid, the voice over is good and the music fit perfectly.

It was interesting and the animation, while minimal, was nice. However, I think that it lacked motivation somewhat. This could be exapanded by providing more variations of the problem with more limitations or by providing historical background (was this a widely known problem before Dirac?)

A fun little mathematical puzzle, very hooking but unfortunately lacking in some depth. Visuals and music were also great. There are some controversy about square roots introducing a hidden 2 much like cube roots, which should’ve been addressed as. There is also another way not involving square roots that generates positive integers: sec(arctan(x)) = sqrt(x^2+1), repeating this n times gives sqrt(x^2+n), which I’m a bit disappointed in not seeing. Since complex numbers were mentioned, I thought I would also see rational results.

I remember a numberphile video about this.

I have not heard of the game before and while watching the video it was difficult to understand how it is a challenge to create any natural numbers by using only the number 2 and any mathematical operations. For example, the number 7 was used as a pesky number but can’t it be represented as 2+2+2+2/2? Was the challenge to find the most convoluted way to create any number and that is why the example from Dirac was mentioned in the end? Also, the reason why Dirac ruined the game is not really clear from the video.

Good video.

Nice neat video with good presentation that’s a good breather. Enjoyed the whimsical nature of it.

I think it’s pretty neat that we could express something like this with finite states. I think it’d be interesting to look at other things that we could do with other combinations of numbers and number of arguments as well, while still maintaining the tone of the video.

we can also use 2^3 - 2^0 to get 7 right?. though like the story telling approach.

Cute !

It can perfectly well serve as a recreational activity or a break between two classes—or as a puzzle to be solved at the end of a lesson.

A whimsical video that has a fun puzzle and some neat math. Though it is short it does a great job at keeping you engaged. For the scope of the video I don’t have much criticism. Great job.

Short, sweet, and very well explained with helpful visuals! It was clear, easy to follow, and got my interest quickly. Nice work!

My favorite thing about the video for sure is the art, I really liked the art style. I also enjoyed the background music, narration, and the dig at physics majors. The resolution for the question involving arbitrarily—nested square roots is a satisfying answer to me. It is also impressive that he manages to explain a problem, attempts at solutions, and the actual solution in 4.5 minutes.

I didn’t enjoy how often he referred to the rules when the rules are self-imposed and very open. If it really is any mathematical operation, I could just define an operator psi_n that sends 2222 to any natural number n. I also feel like allowing i is cheating, but again the rules are self-imposed so maybe that’s on me. This isn’t my favorite type of math, so I may be biased against it.

Very fun video and great animations!