8.6M views · Aug 28, 2015 · 5:47 · 7 HN recommenders · 9 mentions · discussed 2017–2025
The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.
Why Hacker News points people here: HN commenters rate the series as some of the best visual teaching on complex numbers and recommend it for building intuition.
“The greatest audiovisual content on the topic I have ever seen”HN comment, 2017
“The greatest audiovisual content on the topic I have ever seen”
A multi-part audiovisual series on imaginary numbers.
The greatest audiovisual content on the topic I have ever seen: Part 1 - this video Part 2 - link Part 3 - link Part 4 - link Part 5 - link Part 6 - link Part 7 - link Part 8 - link Part 9 - link Part 10 - link Part 11 - link Part 12 - link Part 13 - link
“Welch Labs has a wonderful series on youtube on imaginary numbers”
Welch Labs' wonderful series on imaginary numbers.
Welch Labs has a wonderful series on youtube on imaginary numbers, "Imaginary Numbers Are Real": this video I like to tell my kids that imaginary numbers aren't really imaginary .. that in many ways they're more real than the Reals.
“Great explanations, engaging content and high production value.”
Great explanations and high production value on complex numbers.
Welch labs has an amazing series on complex numbers called “imaginary numbers are real”. Great explanations, engaging content and high production value. this video
“I really like this series on it by Welch Labs - loads of easily digestible videos, and a history lesson to boot”
Easily digestible videos on imaginary numbers plus a history lesson.
Yes, the name imaginary does it no favours. I was confused for so long about i, as it was never explained on classes, and it wasn't until 3blue1brown and other math youtubers showed me the light. I really like this series on it by Welch Labs - loads of easily digestible videos, and a history lesson to boot: this video
“I really enjoyed this video series on imaginary numbers. Went through the history as well as the math”
Video series covering both the history and the math of imaginary numbers.
I really enjoyed this video series on imaginary numbers. Went through the history as well as the math: this video
“I found this YouTube series really helpful to understand basics of imaginary numbers.”
Helpful series for understanding basics of imaginary numbers.
Regarding imaginary numbers, I found this YouTube series really helpful to understand basics of imaginary numbers. this video
“It is a great precursor to then thinking about quaternions”
Explains solving equations with no real roots; a precursor to quaternions.
I really like the welch labs series on imaginary numbers which covers the first part of what you talk about -- leveling up the notion of what a complex number is. Though his focus was more on solving simple equations with no real roots, but really detailing how/what is really going on. It is a great precursor to then thinking about quaternions this video
Example of math concepts easier to grasp when visualized.
I agree that for most of advanced math, VR won't help, however there are a lot of mathematical concepts that are easier to grasp when visualized. link this video link
“Here's a nice example covering complex numbers”
Example covering complex numbers in historical context.
For a small buffet of abstract math topics (with lots of exposition putting ideas into historical context and an emphasis on building geometric intuition) try Courant & Robbins "What is Mathematics?". Covers number theory, number systems, geometry, topology, optimization, algebra, and knots, among others. You could also play around with branches of math like Knot and Braid Theory, which are interesting in their own right, give insight into lots of different branches of math, and many interesting problems are still accessible to lay people. Number theory is also like this I think it can also be helpful to learn some things about the history of math and the historical context that different ideas came from. Here's a nice example covering complex numbers this video Maybe tangential to your ends, but the Crest of the Peacock is a nice book on non-European mathematical traditions, which provides some insight into how the process of establishing and validating mathematical knowledge works in other cultures. You might try books written by physicists or that are about mathematical physics (an author to look out for depending on your level is VI Arnold), since arguments will be of a more geometric or physical nature and appeal more to intuition. Stillwell is another author (not a physicist) that tends to write books that give context and geometric intuition You might like playing around with Pinter & Humphreys for Algebra, or Jänich for Topology (fantastic book for building intuition aro
