Summer of Math Exposition

The proofs themselves are really clever. The important equations flash by a bit too quickly, and it would be helpful to slow down a bit for the audience to follow them. Also, hearing about why you're doing doing the second proof, then seeing the first, might be a bit confusing. Move the motivation for each to the start of that proof.

The key ideas are interesting but first the video was quite short and particularly, rushed. A more detailed exploration of the proof or a clearer explanation of momentum conservation, tailored for a general audience, would have made the video more engaging. A math enthusiast might feel unsatisfied, At least that's how I felt.

It is proving pythagorus theorem using pythagorus theorem ...

The proofs were interesting but the equations flashed over a bit too fast sometimes. Also a delay between the statements would be nice so viewers can keep up with the video

I would advise adding text to the screen to reinforce what is being said

This video was somewhat odd, in that much of the beginning was simply a black screen with the author speaking. Once we get to the proofs, I found the first one to be somewhat opaque, and not as simple as other proofs I've seen, so it's not clear that this is represents something useful. The second proof uses conservation of momentum to "prove" the Pythagorean theorem. I'm not a mathematician, but I suspect many people would object that this is actually a proof because it assumes conservation of momentum to begin with, which, in some sense, depends on the Pythagorean theorem.