3Blue1Brown
6 HN recommenders · recommended in 7 months, 2017–2023
22:11 · 5.4M views · Dec 9, 2016
3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.
HN praises its visualizations, its handling of the -1/12 result, and its ending, and often prefers it to other explanations of the topic.
8 comments from Hacker News
Appropriate juncture to repost this: this video "Visualizing the Riemann zeta function and analytic continuation" (Watch the last 30s or so if nothing else. You'll not regret it.) There is a kind of 'real' Ural spiral [or really a kind of chaotically decaying 'orbit'] related dynamic that gives the prime numbers (assuming the RH.) Conceivable that OP's pattern might have some relation to this dynamic, and fun pondering to boot.
I don't think it comes close to 3blue1brown's video on the same topic - this video Still nice of the video in the original post to give a bit more of a historical context, instead of focusing entirely on the mathematics. It could have done without the building analogy around the beginning though, that didn't come up later and was just distracting.
> 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 - this video - 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.
That was a fantastic video. I was left wondering a bit about the difference between the Riemann Zeta function and the original Zeta function, but I found this 3Blue1Brown video which explains exactly that: this video
3Blue1Brown recently did a video on the Riemann zeta function: this video It's not as in depth but it has some helpful visualisations that I've never seen elsewhere.