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#p-adicnumbers#2-adicmetric#infinitesums

What does it feel like to invent math?

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

YouTube
  • Recommended by 7 people: 6 on Hacker News and 1 on Lobsters.
  • A classic. People kept recommending it from 2015 to 2024.
  • Presented by Grant Sanderson, creator of 3Blue1Brown

Intermediate. Assumes working knowledge.

4.6M views11 years ago7 recommendations

Computer scienceMath for programmersComputation and complexity

Grant Sanderson explores infinite sums and introduces the 2-adic metric, illustrating the creative process of mathematical discovery.

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. Home page: 3blue1brown.com/ Music: Legions (Reverie) by Zoe Keating Thanks to these viewers for their contributions to translations Italian: Marco Fantozzi Thai: @korakot, own doggoV●ᴥ●V ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: goo.gl/WmnCQZ Various social media stuffs: Patreon: patreon.com/3blue1brown Twitter: twitter.com/3Blue1Brown Facebook: facebook.com/3blue1brown/ Reddit: reddit.com/r/3Blue1Brown

Why it's here

7 people recommend this

What people say. Recommended for its excellent visual explanation of p-adic numbers and their connection to computer science concepts like two's complement.

JoeCamelon Hacker News • Recommends

On “Does 1+2+3+... Really Equal -1/12?”

I loved this video link to 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."

skadamaton Hacker News • Recommends

On “Communicating Advanced Mathematics to Kids”

…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": link to 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 w…

luizon Lobsters • Recommends

What does it feel like to invent math?

padicson Hacker News • Recommends

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: link to this video This article fills in some bits omitted from the video: link

piokochon Hacker News • Recommends

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: link to this video

krackerson Hacker News • Recommends

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 link to this video which motivates 2-adic numbers. There's also a neat connection between twos complement and 2-adic numbers.

8minfromsolon Hacker News • Recommends

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. link to this video