I appreciate this piece, and it's helped me make sense of a lot of what's going on here. However, I have to part ways in calling for the Numberphile folks to be "congratulated." As a math teacher, and one who struggles every day to counter the deeply-ingrained notion that math makes no sense whatsoever, I can't stand it when that notion is spread across a wide audience and further ingrained into our culture. Sure, those who are already somewhat mathematically inclined are intrigued and want to know more. But those who are not see a video like this and say to themselves, "Further confirmation that math makes absolutely no sense." So I'm not about to congratulate them.