Summer of Math Exposition

It explored a variety of different mathematical problems which all by themselves seem to have nothing to do with physics. This was especially true for the part with the Cauchy-Schwartz inequality for which I have never before seen a non-analytic proof.

Beautifully done animations and renders, and the overall motivation of interdisciplinary work and/or research is a good takeaway. The music is a bit distracting sometimes, but the variety and simplicity of the results are fantastic to see.

This was an amazing video. The topic is unique, the visualizations very engaging. One suggestion I have is you included so many examples that it almost becomes too much to take in in one video.

These are all really cool proofs, and you present them all very clearly. The animations are helpful, although they’re all in different styles which is a bit distracting. Also, the background music is a little too loud.

I feel like there could be more Motivation in the Voice. It’s clear that you enjoy the topics but the tone seems a bit flat and even during sentences like “isn’t that incredible” the tone seems unexcited. It could also be the fact that it’s not your first language but maybe something that will get better with time. Also very nitpicking and no effect on score but during the first explanation you said AP and had PA written and then later as AP which made it take a few seconds to find what u meant. Otherwise very clear and understandable und well done.

I think their was a few too many examples before getting to the main idea.

no thoughts, it’s very good!

Nice video! Though I’m not sure if I would call most of these examples “cheating” in solving math problems using physics. For the first problem, the geometrical solution is rather simple and elegant, and the physics solution was more of an interpretation or application with further mathematical conclusions, instead of a “hack” for solving the original problem. So, maybe there is another way to brand this video that emphasizes how physics is being used to give further meaning and context to otherwise self-contained math problems.

A good collection of classic (and less common) exercises that connect mathematics and physics, very useful for cross-disciplinary work in class. Well animated. Suggestion: divide it by topics and provide more depth by accompanying it with theory to introduce the exercises more effectively.

That was awesome! Perfect choice of topic: the thought experiments are mind-blowing but still not widely known or commonplace (at least not for me). The effort that went into the execution must have been huge, I’d guess several times more than the rest of the videos I’ve judged, and those weren’t low-effort, either. The visual style was a bit incoherent, in my opinion, but that’s subjective, mostly explained by the diverse set of scenarios, and didn’t take anything away from the excellent content and execution.

Very solid through-line that connects all the topics covered

Most examples seem a little bit contrived. I majored in math+cs years back and I don’t even recall Cauchy Inequality, perhaps you should bring in the definition and why this matters on that one. It’s good to be able to make connections in different fields. Great, no, actually, awesome graphics. :)

The explanation of Pick’s theorem was my favorite example. I found myself deriving the theorem in concert with the video’s explanation and it served as a testament to how powerful a change in mindset can be to solving these problems. Cauchy inequality example was quick but after rewinding I understood the solution. Great topic and overall good execution.

As someone with a fairly weak physical intuition, I ended up pausing this video a lot while watching. Oftentimes I had some objection that I thought you had already explained and I missed— and equally often, when I pressed play, you immediately launched into the explanation I was hoping for.

I think this cuts both ways: while I was generally pretty satisfied with the video as a whole, the fact that I kept feeling like I was missing things speaks to perhaps some disorder in the arrangement of the ideas.

Probably my biggest complaint is your stated audience— this video is not going to hit middle-schoolers well, and although nothing is outside of an advanced high-school understanding, there’s a little too much going on for me to feel comfortable recommending it at that level either.

I don’t think that you’ve changed the way I like to think about Cauchy-Schwartz, the classic “dock problem” etc. but I was compelled by these alternative energy-focused perspectives, and I think these perspectives (or least the concept that they exist) will stick in my head for a while. You did I think overstate the case that “all” objectives can be represented as minima of energy functions— perhaps is true? i don’t know, but your argument seems wildly insufficient.