Numberphile v. Math: the truth about 1+2+3+...=-1/12
Why Hacker News recommends it
HN points to it as the in-depth rebuttal to the Numberphile video that explains why the 'proof' is wrong yet the result is meaningful.
What it is
Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.
Recommended by 4 HN commenters across 4 different months, 2020 to 2023.
What Hacker News said
Recommends stan_rogers · 2020-02 · on “Ramanujan Surprises Again (2015)”
Burkard Polster's (Mathologer) videos on the subject are probably going to be more useful than Numberphile. Numberphile merely presents a trick; Mathologer points out both that it's patent nonsense [0] and that it's useful patent nonsense [1]. [0] [this video] [1] [LINK]
Recommends cyphar · 2020-11 · on “1.5 is the midpoint between 0 and infinity in Ruby”
That proof (and the more general statement) is not correct because it makes assumptions about infinite summation of divergent series that are not true. There is a link between the sum of natural numbers -- namely, the analytic continuation of the Reimann Zeta function has Z(-1) = -1/12. But the Zeta function is only defined to equal the sum of inverse powers for Re(z) > 1. And under a specific definition of summation (Ramanujan summation) you can say that "the sum is equal to -1/12" but that isn't the same as normal summation. Mathologer did a fairly in-depth video[1] into why this proof is wrong and what the actual link is between the infinite series and -1/12. The upshot is that even if yo
Recommends crvdgc · 2021-10 · on “Conterintuitive facts in mathematics, CS, and physics”
I find a response video to it more enlightening. It's often found as the number one related video. [this video]
Recommends jonnytran · 2022-07 · on “Ask HN: YouTube Channels for the Intellectually Curious”
I know you're asking about Computerphile, but this video explains how one of the Numberphile videos is wrong: [this video]
Cites djaychela · 2022-07 · on “Ask HN: YouTube Channels for the Intellectually Curious”
Just spent 5 minutes making a script to find all the links in this thread and then 'score' them on the number of votes. Here's all the channels with 2 or more: 6 Votes: [LINK] [LINK] 5 Votes: [LINK] [LINK] [LINK] [LINK] 4 Votes: [LINK] 3 Votes: [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] 2 Votes: [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [this video] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LINK] [LIN
Critical t_mann · 2022-07 · on “Ask HN: YouTube Channels for the Intellectually Curious”
It's similar. Two issues with Numberphile videos I can remember: Their video on 1+2+3+... = -1/12 was so bad that another Math channel (Mathologer, which is highly recommendable btw) did a whole 40min video tearing it apart: [this video] In their video on fluid mechanics, they say that the Navier-Stokes equations describe all fluids on earth, while they only show the incompressible version (without clarifying). The examples shown on screen at that moment also include a Ketchup bottle, and they don't discuss non-Newtonian fluids either (Ketchup is non-Newtonian, that's why you can get a lot of it coming out at once if you shake a bottle too hard). It's a bit nitpicking though, because apart from t
Critical OldGuyInTheClub · 2023-09 · on “A Duodecade of Numberphile”
Yes, I kept waiting for them to "fess up" at the end but they didn't. Mathologer called them out on it. [this video]