The 1+2+3+4+... = -1/12 video still seems a bit of a cheat, though!
The 1+2+3+4+... = -1/12 video still seems a bit of a cheat, though!
Because in that video they do invalid operations.
Compare it to how 3blue1brown handles this - https://youtu.be/sD0NjbwqlYw?si=js8taa28UcevI0Jg&t=1166 - the video is on the Riemann zeta function and my timestamp is on his comment about -1/12 at the end. But trying to explain something in a nuanced way doesn't get the same views as dumbing it down and coming up with a clickbait title (not that 3blue1brown is struggling for views).
I understand that the two channels have somewhat different objectves and approaches but in this case one of them strikes me as much better. The top comment under the 3blue1brown video addresses this too - you don't need to additionally mystify math.
3b1b is a channel with the goal to teach math topics in the clearest way possible.
Numberphile is about interviews with mathematicians telling stories which happen to be "in mathematics".
If you want to get a better understanding of a maths topic you're currently studying, 3b1b is the clear winner. If you want to get people to wonder about the diversity of maths topics out there, Numberphile is the better option.
Not to mention the part where it humanizes mathematicians themselves. Instead of thinking of Neil Sloane in the abstract as "the guy who started OEIS", I now have a picture of a nerdy, sweet grandpa who loves to talk about integer sequences.
I've also learned a lot about specific math topics from 3b1b. It takes me a few tries to get through any video since the soundtrack causes me to doze off. Would love it if he would release versions with just his narration.
[0]: https://www.bbc.co.uk/england/eastmidlandstoday/ican/index.s...