Summer of Math Exposition

Phrases like "define the infinite expression as the limit of the finite expressions" should be broken up with visuals Maybe something like an infinite sum actually broken into component pieces and then shown slowly moving together to make the infinite expression. It's something that's better visually explained. Maybe even show lines of the length and how it can "add up" to be an infinite eg. 1 1+1 -- 1+2 --- 1+2+3 ------ N+(N+1)+N+2 ------ lim 0->infin(n) N+1 -------------------------

Really good, but kinda lack motivation else I understood really well the topic (maybe because i already covered it in class or smt) But in general it’s great

Good video, but the audio quality needs work. There were many instances where puffs of air hit the microphone and made scratchy static.

Watch your microphone a bit, you're breathing into it at times.

This is a rare find where people try to “explore” how to do math， rather than just follow math. After all, math was developed instead of being given. I wish more math videos take on this kind of spirit, really talk about how math comes into being.

Nice introduction to dynamical systems! A few comments: 1/ the blacks screens for more than 1 second are a bit awkward, even with sound; I would suggest putting something on the screen, even with low content. 2/ the last display with the [a1,a2, ...] expression does not stay on screen for long enough, I had to pause to parse it. And maybe you could have kept the sqrt(a1 + sqrt(a2 + ... )) notation on top to recall what you are formalizing. Cheers!

Goal Orientation: 4/10 Novelty: 2/10 Thought-Provoking: 3/10 Comprehensibility: 4/10 Technological: 3/10 Overall Average: 3.2/10

This seemed to just ramble with nowhere to go

The title doesn't seem to match well with the content of the video. The content was interesting, but I feel like it could have been clearer at times.

This video had an interesting beginning, but then seemed to meander off a bit, and it wasn't clear why. By the end, I still wasn't quite sure what I was supposed to have learned, and I was left confused. The visual aspects of the video were pretty good, but the audio was not. I recommend the author invest in an external microphone and a pop filter. The microphone need not be all that expensive, but it will result in a very large improvement in quality.

Always good to be reminded of the rules of infinite expressions!

to the first part: 1+2+4+... = -1 is on fact not nonsense, it's just understanding it as is needs 2-adic numbers, where you read from the right and not from the left. (in p-adic in general -1 is equal to (b-1) repeated infinitely and b is the base) in the limits (1:46) you swapped n and k, [limit as n->inf of Sk, and limit as k->inf of a0+...+an]