What does it feel like to invent math?
Why Hacker News recommends it
Recommended as a favorite Grant Sanderson video and a visual introduction to p-adic numbers and sums like 1+2+4+...
What it is
3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.
Recommended by 6 HN commenters across 5 different months, 2016 to 2024.
What Hacker News said
Strong rec JoeCamel · 2016-07 · on “Does 1+2+3+... Really Equal -1/12?”
I loved this video [this video] "An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math."
Strong rec skadamat · 2017-12 · on “Communicating Advanced Mathematics to Kids”
So many things I could say about this, but I"ll let Alan Kay speak for me - [LINK] Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up: - at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y). - as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there - closer to early teens, symbols were m
Recommends padics · 2021-05 · on “Mathematicians Find Long-Sought Building Blocks for Special Polynomials”
3lue1brown has a great visualization of constructing p-adic numbers and calculating their metric through the lens of 2-adic numbers: [this video] This article fills in some bits omitted from the video: [LINK]
Recommends piokoch · 2021-05 · on “Mathematicians Find Long-Sought Building Blocks for Special Polynomials”
You add infinite number of positives numbers to each other and you get -1 as a result. p-adic numbers are adding some sense to this seemingly contradictory result. Great intro: [this video]
Recommends krackers · 2023-10 · on “Marvelous Arithmetics of Distance”
It's also not a full introduction, but for those who want to have a taste of p-adic numbers, see 3b1b's video [this video] which motivates 2-adic numbers. There's also a neat connection between twos complement and 2-adic numbers.
Recommends 8minfromsol · 2024-10 · on “2-adic numbering for binary tilings”
3blue1brown has an earlier, kind of meta, video about “What does it feel like to invent math?” where Grant tries to show how one might invent, and so by define, p-adics. Complete with the customarily excellent visual aides. [this video]