In case the previous post concerning concentration on the Boolean hypercube wasn’t enough for you, you can now watch a short, 20-minute animated video that I made for the STOC 2020 conference in theoretical computer science:
STOC is a large (by theoretical computer science standards anyway) annual conference, which was supposed to take place in Chicago this year. However, the organizers have decided that it would be unwise to pack hundreds of people into tiny rooms at this time of the year (not to mention getting them there), and the conference will instead be held online. All lectures are already uploaded to the ACM channel. Feel free to watch them, and then pop by and ask the authors questions during the online Q&A sessions.
I made this lecture using a Python package called manim, which is an “animation engine for explanatory math videos. It’s used to create precise animations programmatically”. The style is of course influenced by manim’s creator, Grant Sanderson, of 3blue1brown fame. I think 3blue1brown’s videos are amongst the best mathematical content I have seen on YouTube, excelling in pedagogy, structure, and visual appeal (I always point newcomers to this gem for a start). In fact, they are too good; channels like 3b1b and Mathologer have thoroughly shaken my faith in the traditional lecture hall. Why should lecturers put so much effort, year after year, into basic courses given to a small number of people (<1000 at a time), when they could be creating generational masterpieces like this? Judging from the comments, for example, 3b1b's analysis and algebra courses have made things "click" for many more students than a physical-world professor could ever hope for.
I know that some vital aspects of the classroom, such as participation and question asking, are still missing from these videos. But I foresee a time when technology will catch up. The video-lectures will be adaptive and responsive, and will able to handle input questions and clarifications, elaborating or speeding up upon the individual student’s request. Wouldn’t that be a neat time to learn (and teach!) math?
(Until then, though, you’re stuck with plain videos. You can find the code to generate the animations in my lecture here).