Summer of Math Exposition

I think the video balances a well balanced between rigorous proof and geometric intuition as well as some interesting extensions of here. I especially liked that we had a geometric intuition, which then went to a rigorous definition that allows us to generalize to higher dimension. The animations are a very good way to help visualize what the different k homotopy groups are and how we can build on them. I think we can try to give a bit more intuition on homology groups which would help to give an idea of what the differences between the two groups are.

Very clear explanations on an important but relatively undocumented (on YouTube) topic! I love it, and hope you continue to keep making things!

The visualisations in this submission are exceptional. This is by far the best video on topology I have ever seen. Well done.

The submission was well structured and I liked your style of presentation.

Beautifully explained there is nothing left for me to say.

Run the script by someone who is part of your target audience, and have them help you keep in the things that are at their level, and cut out the things that are not at their level, just to make for a shorter video. Amazing animations! Lot’s of detail, and rigor

Very nice!

Absolutely outstanding. As someone who just learned manim, the animations are not only elucidating, but extremely impressive on a technical level. I didn’t study math in undergrad, but luckily I have enough background knowledge in group theory and measure theory from self study to understand the more technical definitions (although it did lose me in the end, but the last section was definitely for a different audience).

I might finally have understood in what way homotopy and hology are different for a second

The day by day analogy isn’t really necessary. The relationship between the animation and the voice over is not always clear.