What does it feel like to invent math?
What does it feel like to invent math? on HackerTube: recommended by 6 Hacker News commenters across 5 separate months, 2016–2024.
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.
What HN commenters said
6 Hacker News comments link this video. Each one links back to its thread.
skadamatDec 2017Strongly recommends
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 much easier to grasp and relate to, etc. With this context in mind, there have been some cool efforts to mix the second and third channels I just mentioned to communicate advanced math concepts. Vi Hart and Grant Sanderson's youtube channels come to mind. Here are my favorite videos by Grant: - "What does it feel like to invent math": ▶ this video - On the visual intuition behind a hard problem on the Putnam exam - "The hardest problem on the hardest test": [link] - From vectors to matrices to vector spaces to higher-level ideas like the link between linear algebra and calculus: "Essence of linear algebra" series: [link] What I especially like about Grant's videos, is that he often walks through what a mathematician would do, the questions she would ask, etc.
in “Communicating Advanced Mathematics to Kids” · View on HN
JoeCamelJul 2016Strongly recommends
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."
in “Does 1+2+3+... Really Equal -1/12?” · View on HN
8minfromsolOct 2024Recommends
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
in “2-adic numbering for binary tilings” · View on HN
krackersOct 2023Recommends
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.
in “Marvelous Arithmetics of Distance” · View on HN
padicsMay 2021Recommends
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]
in “Mathematicians Find Long-Sought Building Blocks for Special Polynomials” · View on HN
piokochMay 2021Recommends
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
in “Mathematicians Find Long-Sought Building Blocks for Special Polynomials” · View on HN