Summer of Math Exposition

This video took a while to get started; it was relatively unrigorous where rigor was needed and extremely rigorous where this was not necessary.

Great video! you 2 did a great job with a clear, entertaining video. Motivation: 4/5 I like the introduction, but I think it could be improved on in terms of delivery, as the transition between the song, to the sum of squares feels a little shaky / rushed. tbf i would be too if I had to sing on camera. As an example, I think you could explore / summarize past uses or pascals triangle as well, or provide a more practical case of using the sum of squares (or anything else, these are just suggestions). Clarity: 4.5/5 The explanation of nCk terminology was the probably the most concise and clear I've experienced, you two do a great job maintaining a balance of clarity and depth in my opinion. This was maintained well throughout the video. particularly with the an excellent use of visual aids. However, there are a couple nitpicks I have throughout. For example, the animation / explanation at 7:40 could be slowed down, explained a bit clearer for the first 1/2 iterations, before speeding up. Novelty: 4/5 I enjoyed this topic quite a bit, I feel like this is an often glossed over / not often explored aspect of pascals triangle, and would be quite entertaining regardless of familiarity with the field. However, I do think there is room to go further in depth, and explore more niche uses and implications of these properties. Memorability: 4/5 Great video overall, and pretty memorable in a good way. However, I do think there could have been a bit more content. A good way to end videos, in my opinion, is often more open ended and points towards implications that could be futher explored by the viewer if desired. I do love the light hearted, funny atmosphere the video has, which brings the memorability up to a 4 from 3. Love the video overall, great job

Really good video, the ideas were well motivated and clearly followed onto eachother. It's also very nicely and clearly presented. Perhaps the only thing I would add or at least ellude to is the combinatorial relationships to the sums. (I do also have to add that mathologer has a very similar video to this from 4 years ago).

Fun, funny, well animated, engaging, clear. The only thing missing is novelty, but this video is a great explainer. Amazing sound FX.

That was incredible! The animations were soooo clean and well thought through. Such a great explanation and y’all made the alternating talking parts feel very natural which I’m sure is not easy to do. Hope to see more videos! I honestly don’t know of anything I didn’t like - maybe the fact that y’all haven’t posted in a year 😂

Very good exposition, though deducting some points due to lack of novelty of the topic / explanation.

Really cool, I haven't seen that way of deriving the sum of powers formulae. If you haven't seen it, this is another nice way of doing the same thing (not my video by the way) https://m.youtube.com/watch?v=D0EUFP7-P1M&pp=ygUPdW1icmFsIGNhbGN1bHVz

motivation 5/10 clarity 5/10 novelty 5/10 memorability 5/10

This work is well done... explanations are very clear and the animation is well performed ... The Pascal triangle is an old friend for the people who is familiarized with math but this video refresh some of the hidden properties ... I think this video is better than most ... keep doing that!!

This is one of the better ones. Very slick.

I enjoyed this quite a bit. The animations are very nice, and I thought the explanation of how Pascal's triangle works was really well done. In some sense I felt that the explanation of how Pascal's triangle is used to derive formulas for the sum of squares and the sum of cubes was a bit rushed, but otherwise the video was really solid.

This is a very good video, you start with an easy-to-state problem which could potentially interest anybody who knows just grade-school math, and you nicely show how it can be connected to Pascal's triangle to yield some cool formulas. I think one of your video's greatest strengths is that it can be appealing to people at different levels of math knowledge. The problem is simple enough that it can catch the attention of a math-interested amateur. Additionally, your presentation is sophisticated enough that it has things to offer to people pursuing math in college. In particular, I like that you show a method for how someone could discover these "sums of powers" formulas without knowing them already, which is something that bothers a lot of people who only learn to prove them by induction. Your audio design with the clacking of adding the two numbers together and so on was really nice and satisfying, and your visuals are very clean and easy to follow. You joke at the end about whether or not the problem has some greater significance, but I am actually glad you didn't try to reach for some hyperbolic statement about the importance of what you showed. To me, that showed a great deal of intellectual humility, and I don't think your video needed an emphatic "summary statement" in order to be impactful. Your video does what it says on the tin, and it does it well, and that's enough to make it excellent. I think my main criticism in your script writing is that you let a little too much "math speak" in for my taste. You use words like "thus" and "hence" pretty often, which are not used by most people in ordinary speech. To me, if your video is trying to be casual and approachable, this can come across as a little strange or off-putting, it feels like you're hanging out with your friend and all of a sudden they start talking like an Oxford professor. This is a minor nitpick If you're looking for follow-up videos, you could extend this method to talk about finite difference equations, or you could show how one could derive the same formulas using generating functions.

Best fish-produced maths-themed video I've ever seen. Also bonus points for getting it comfortably under a quarter hour. In hindsight I've seen quite a lot of videos that have taken well over 20 minutes to say no more than you say in half the time.

Eventhough the topic has been covered a lot of times, but your beautiful animations made it memorable. Good job!

I like how you've gradually built your results, guiding the viewer along. Some really neat visual proofs (of the numbers in Pascal's triangle corresponding to the number of paths, along with the binomial coefficients, and then ultimately the sum of cubes). The graphics are excellent and the humour between yourselves is also great. To make this even better (and this might be to do with my personal taste), I would suggest removing some of the music as it can be distracting. It was also a little off-putting to have a different voice appear the first time this happens; perhaps moving your interactive humour up to the front might help with this - so that the viewer appreciates that 'this is a two-person thing'.