Summer of Math Exposition

Nice hook, I like the combination of animation and live whiteboard work! Also it's a great introduction and explanation of the L1 and L2 norm. I think this video is best for the general public who might not have thought metrics before, since it's pretty visual and doesn't go through verifying the properties of the L1/L2 or p norms. The explanation is clear, but I don't see much novelty in the video. Some ideas could be providing intuitive explanation of other norms, like L_inf norm or observing what other traditional Euclidean shapes look like in other norms.

Here are few random notes and some interesting question I had during watching the video that didn't get answered: - You started to read the definition at the beginning, you said metric is about distance. It would make more sense to have this in opposite order. Showing the things on real number line and "discovering" the definition of metric is way better for video format. - You were using x1,x2,y1,y2, then proceeded to define it. Either everyone understood that at the beginning or you lost some people. - You have unnecessarily repeated the function for L2 metric and other things, padding the runtime. - Why are we talking about metrics? What about the definition is so special? Euclidean distances make sense, but what about the other functions satisfying the definition? Are there more metrics I should know about? Can defining some metric help in some algorithms? - The video is too long for amount of information it provided. This could easily be cut to half and be still understandable. - The audio is quite bad. - The rounded square from the beginning of the video is nowhere to be found. That one looked at least interesting, although I don't know how useful it is.

This would have been better as a written document and not a video. The video format is not very good for long passages of written text. It felt less like an explainer video and felt more like the reading of a formal proof.