Summer of Math Exposition

The proof itself is pretty clear, and I can follow all the steps. But it's not clear where those steps come from. For example, you jump straight from the problem statement about primes to the graph of 1/t, and only later connect the two. It would be helpful to add a transition explaining why someone working with primes would even think to look at that graph.

The video is extremely hard to follow, in part because of heavy accent, in part because of it's structure. It's not very clear what we are going to do. We are obviously going to prove that there are infinitely many primes at the end, but there is no indication of how we are going to get there and why we are doing what we are doing. The part where you explain how integral works feels like random thing that came out of nowhere. The rest of the video is mostly sequence of algebraic manipulations that, to be honest, lost me in the middle. (I've tried to re-watch parts when I got lost, but it got tedious after a while.) Content for videos needs to be structured differently to be digestible in real-time viewing. This videos topic or form is not novel in any way. Instead of watching this video, it would be easier to just look up some standard proof on Google in text form an follow each rigorous step at your own pace.

In manim, you can change the runtime of an animation using the run_time parameter. This would help speed up long animations like the one between 3:00 and 3:30, which really doesn't need to be 30 seconds long. Also, doesn't the expression you got at 5:48 already finish the proof? If there were finitely many primes, then the right-hand side would have a finite limit, but the left-hand side tends to infinity.

It was a bit difficult for me personally to follow the explanation, I was unsure about the purpose of the area under the function 1/t. But the visuals look very clean and well thought out.

I haven't seen this particular proof before. I think it is presented clearly and carefully. I liked the video a lot.

1. Good length 2. Too many formulas on screen 3. Lack of motivating examples 4. Manim overuse 5. Unclear concepts