Summer of Math Exposition

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Excellent video! The math is interesting, and you’ve managed to pack a lot of ideas into one video. And the visuals are clear and helpful. My biggest issue is that the intro is really long. It’s more than 17 minutes before you get to the problem you solved, and the leap of faith which is the central theme doesn’t show up until almost halfway through.

The video could be improved:

1. The motivation for the video wasn’t very clear in the beginning. Further, the overall goal of explaining the “ground state minimization” was not clearly explained
2. The example in the beginning seems a bit contrived which didn’t smoothly segue into the big picture. For eg, I didn’t make sense to me why are we modelling tensions between people that way and what do we hope to achieve/understand
3. The video makes some jumps in explanations which felt rushed. For example, for the Hamiltonian formula, how did we go to single summation to double summation? Would have been helpful to get deeper explanations

Nice visuals

It’s cool to have researchers post videos explaining their work to the public! Your enthusiasm really shines through!

I did think the music was a tiny bit loud and distracting, and it did seem well past the level of high school.

I think it would’ve been nice to include a few small example problems and talk through their solutions. The one example you had with just Alice and Bob didn’t have enough complexity to represent the difficulty of the problem yet. Primarily working with general equations and not concrete examples made it hard to appreciate why the problem is interesting.

I think the commentary on rich-vs-poor was interesting, but I think it would have been helpful to start introducing more of that earlier in the video and including it throughout.

A great video. My main gripe is that it wasn’t really motivated why I should care for solutions of this kind of Hamiltonian. It’s nice to have analytical insights, and particularly if you know what they are good for, though I understand that is inherently difficult for recent research. I found the application to a society rather artificial and wasn’t convinced by that comparison.

Congratulations for your work, first of all! It is a very nice idea. Here are a few things that I noticed from the point of view of SoME4:

1. Be very careful what your target audience is. Once chosen, all explanations should be understandable for the lowest level. In your video, there is a bit of a tension between explaining on the one hand what exponential growth means and using many very high level tools (matrices, differential equations, …) rather quickly without many explanations. I feel as if this should either be targeted only at undergrad/grads or you should be a bit gentler on the level of math tools used.

2. The very beginning of the video is rather confusing. You start with an interaction of +1 being agreement and -1 being disagreement. This makes the HIGH energy state preferable. But without underlining the change in notation, you then continue with the physical interpretation of searching low energy states. This might be worth pointing out more clearly.

3. You spend a large amount of time on the introduction which is good. But it might have been nice to leave a bit of the time to the comparison with the other topics (closer to the reality of large parts of the audience) that are connected to the Ising model. For the number partitions, it might have been nice to have multiple examples. When you mention the other topics, people unfamiliar with them have no idea of what they represent. I would suggest either to at least give a very short explanation or simply leave them out.

4. Although the contribution is clearly from the physics side, one might want to be a bit more careful with the word “proof”. The final bit in which the discrete Hamiltonian is replaced by a continuous version is a very nice and clever bit of research which gives a lot of insights for the discrete version. It is, however, not a proof that the discrete systems behaves exactly the same. It is, at best, a strong suggestions of it.

5. A last general piece of advice: Although it feels very satisfying to show the full computations, it is often more useful for the audience if all the technicalities are swept under the carpet. Most people (especially if this video targets highschool students) will not be able to follow them anyway. Instead, one might be able to find either visuals or heuristics to give the audience the right intuition.

On a side note: a) “Ising” is not pronounced with an English “i”. Instead, its transcription (from Wikipedia) is [ˈiːzɪŋ]. b) You should use $\DeclareMathOperator*{\argmax}{arg\,max}$, so that the constraint is correctly formatted.

Wow !

I think it is wonderful the way this video thoroughly explains the concept and shows … The video has a wonderful storyline. I think this is the best video I have seen so far.

Initial Thoughts

The concepts and math in this video were way over my head. I won’t be able to speak much to the content, but the presentation.

What Went Well

Your animations and verbal presentation were very well done. Everything looked and sounded really good.

Ideas for Improvement

I think narrowing your target audience here would be appropriate. I applaud any high schooler who understands a tenth of this video. My undergraduate was in engineering, not math, but I’d guess this would be difficult to follow even for most undergraduate students. The one improvement I can suggest in the presentation is toning down the music in a few place. The music in the background became a distraction at times.