Summer of Math Exposition

This is my favourite topic to learn about in university :) It could really use some additional explanation on quantifiers, equivalence classes, division by an equivalence and more if it is meant to be comprehensible for a high-school audience. The video could have used 40 additional minutes

For high school students this is too abstract, and for graduate students this is the standard way of construncting number sets.

This video doesn’t seem to add much to the discussion on this topic, except for maybe at the end, although for that part it’s not clear how it’s helpful for students.

I’ve always loved this topic, even having implemented all of these constructions in the Rocq proof assistant. Maybe I’m not your intended audience because of that since I won’t know if it wasn’t clear. But I still think it was a good video. One minor nitpick: when defining addition for the natural numbers, you wrote 0 + n = n and k + S_n = S_k+n. However, you need to ensure that the 0 in the first case is on the same side as the S_n in the second case. In proving that 1 + 1 = 2, you ended up assuming that n + 0 = n when all we know is 0 + n = n, so maybe that’s what you intended to write. There were some mistakes in the rational number addition as well but I see you already noticed those.

I really enjoyed this video! It progressed really nicely through the each set of numbers. Each step felt quite natural. I especially enjoyed the distinction between an equivalence class and an arbitrary representative.

I loved your hook that the naturals are not a true subset of the reals. It caught my attention and made me think deeper about how those numbers are defined.

The video was well-motivated and had good visuals, but it presents standard concepts without novelty or innovation. The title is interesting but the video doesn’t explain well enough that it’s not literally true according to standard mathematical convention.

This one’s tough to grade. The video targets a very abstract topic in a digestible way. The visualisations that you employ are good, but I don’t think they are novel. There was no particular motivation given why we need a rigorous definition of numbers, nor did the video build up to a climax. In that sense, I am not sure how much the video adds to the international math explainer ecosystem. Of course, the video is targeted at the French-speaking ecosystem where this niche may not have been covered, but I grade this from the international perspective. When you gave the exercise of decoding a rational, I didn’t understand how to distinguish between a pair denoting a subtraction and one for a division. The remainder of the video was clear, though I can’t really judge that because it wasn’t new to me. All in all, the video was well made, but I subtract points because I’m not sure how much it adds to existing material with respect to the criteria of the guidelines.

Your video wasn’t very original, but it was a nice summary that I enjoyed watching. I think it would be too difficult for a high school student to follow to be honest. The animations for the equivalence classes were very well done.

Its in french. Not a very interesting topic either to be honest.