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this post was submitted on 01 Jun 2026
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https://leightonvw.com/2015/02/05/if-you-add-up-all-the-positive-numbers-do-they-sum-to-a-negative-number-yes-they-do/
Oh, good. There's a Numberphile video on it linked at the end. That gives me much better odds of understanding this than just reading the article.
Actually, the Numberphile video is notorious for lacking mathematical rigor. Mathologer did a video on it. IMO, it's really really important to explain the difference between what's going on here (assigning a number to a divergent series) and what we ordinarily do (computing the limit of a sequence of partial sums).
There was a full on mathematical war on YouTube, with numberphile coming back later to show that most partial sum methods also end up at -1/12.
As a science nerd, mathologer basically just took the camp of "old concensus" and gave no other argument than "this is alien math, nope, I don't like it". It just felt like mathologer was Pythagoras fighting against irrational numbers...
I mean maybe in the first video, but not the one I linked. Here, he was very precise about the mistakes Numberphile made in the presentation, and the purpose and utility of standard summation of convergent series versus the other methods of summation. Like he's not dissing the idea or utility of summing divergent series literally at all, just Numberphile's oversimplified presentation of it.
Yeah that's fair! I didn't get through some of his videos, being more of a downer "grumpy style" ๐
I'll try to watch that again
There have been some claims that the numberphile video is very misrepresentative of the underlying math. But I never dug deep enough into it.
Feels like a risky click. I'm not sure my worldview can take any more shattering. It's already shattered I tell you. SHATTERED.