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Mathematics

Proofs, intuition and the odd unsolved problem, from calculus to linear algebra.

100 entries, about 33 hours of single videos. Bloom scroll this shelf

100 entries
22 min Group theory, abstraction, and the 196,883-dimensional monster3Blue1Brown

It involves the study of algebraic structures. I imagine you are likely familiar with groups (in the case you aren't, here is a good introduction), and perhaps with rings and fields as well. This subject can get very abstract. As for textbooks, I like Dummit and Foote for its comprehensiveness but it's quite dry. Haven't read any of it

Mentioned in r/compsci

32 min Visualizing the 4d numbers Quaternions3Blue1Brown

I have recently stumbled upon the concept of hyperbolic space, and was wondering if you could create videos related to this topic. I only know the basics, yet from your quaternion video(part1, around the 16 minute mark) I recognized an interesting fact on how the projection of a 3d sphere onto a 2d plane seemed to produce hyperbolic geometry. Could you create something more in depth relating to this phenomenon?

Mentioned in r/3Blue1Brown

17 min Are the real numbers... REAL?K-Theory

If I may be so selfish, I'd like to toss one of my own videos out there. Now let me tell you about some criminally underrated channels. Dr V. is undeniably the best place to learn about the proof of FLT of T

Mentioned in r/math

16 min Short proof of Abel's theorem that 5th degree polynomial equations cannot be solvedBoaz Katz

Impossibility of geometric constructions. This was covered by Mathologer in the following video: Mathologer managed to hide the actual Galois theory under the hood, which has its pros and cons. Insolvability of the quintic. This was covered by Boaz Katz: The proof presented there is due to Arnold, and it also avoids using Galois theory directly. Instead of Galois groups it uses monodromy groups, which I find even more enlightening.

Mentioned in r/3Blue1Brown

13 min Intro to differential forms (part 1)David Metzler

They seem to generalize a lot of complicated and hard to remember formulas from "regular calculus". I've been watching this series and it is helping a lot. I would love to see Grant's take on an intuitive way of presenting these concepts.

Mentioned in r/3Blue1Brown

21 min Outside Inssgelm

Outside In. This isn't from a content creator so it is unfortunately a one-off. It's an old educational video about how to turn a sphere inside out that I love watching whenever I'm high lol

Mentioned in r/math

Questions about mathematics videos

Where should I start with mathematics videos?

Good first picks here, chosen by the list’s editor because they build ideas up from the basics, are But what is the Fourier Transform? A visual introduction. (20 min), Why slicing a cone gives an ellipse (beautiful proof) (13 min) and Group theory, abstraction, and the 196,883-dimensional monster (22 min).

Are there short mathematics videos?

Yes. 34 run under 15 minutes, including Why slicing a cone gives an ellipse (beautiful proof) (13 min) and e^(iπ) in 3.14 minutes, using dynamics | DE5 (4 min).

Are there full mathematics courses or lecture series?

14 entries are full course, lecture or playlist, such as Summer of Math Exposition 1 video entries and Animated mathematical problems (Reddit-described playlist).

Where on Reddit were these mathematics videos shared?

Most came up in r/math (53), r/3Blue1Brown (35) and r/CasualConversation (6). A mention can be a recommendation, a question or an argument, and each video’s page says which it was.

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