What do you use to animate your videos?
I create most of the animations programmatically, using a python library named "manim" that I've been building up, then use more traditional film-editing software to edit it all together (namely Final Cut Pro). If you're curious, this library is on github, but you should know that I developed it mainly with my own personal use case in mind. It's not that I want to discourage others from doing similar things, quite the contrary, but often my workflow and development with manim can make it more difficult for an outsider to learn than other better-documented animation tools.
The exception here is that for many 3d graphics in the past, I've been using Grapher.
There are aspects of producing videos in a software-driven manner like this that I find quite pleasing, but which are pleasing precisely because it's my own tool. It enforces a uniqueness of style, for example, which is by its very nature a benefit that can't be shared. There's also a certain freedom in being able to tear up the guts of the tool every now and then when I feel a change is in order, since backward compatibility needs are very limited when you only care about videos moving forward. Not exactly the best practice from a collaborative standpoint.
All that said, if you do want to try manim out, the github page has the information you should need to get started, and a small community has emerged that may be able to help with trouble points.
Will you please make a video on ______ !?!
There are so many topics I'd like to cover. And people seem to love writing emails/comments to make requests. Keep in mind, I will make judgments on what to cover next based on what I think has the best chance of deepening peoples' relationship with math, and what I am personally most excited to describe. Sometimes there's a worthy topic which I just don't think I have an original or captivating enough way to approach.
That said, I don't want to completely ignore requests, so your best chance of putting them in a place that I'll keep track of is the reddit thread linked above. This is not a checklist of what I'll necessarily do next, it's just a way to keep a pulse on what people are asking for, and how others respond to each request.
Also, if your request is one from multivariable calculus (e.g. Lagrange multipliers, the Jacobian, Stokes’ theorem, etc.), there’s a good chance I covered it in some of my work at Khan Academy, either in video or article form.
Note, requests I get through email are just about guaranteed to be ignored, since that reddit thread is where I look when considering what people are asking for and how others respond to each request with upvotes and comments.
What does the name "3blue1brown" mean?
I made the logo to be a loose depiction of my right eye color: sectoral heterochromia, 3/4 blue 1/4 part brown. It was a way of putting a genetic signature on my work, and the channel is all about seeing math in certain ways. The name, of course, is just derived from the logo.
What's the music playing in your videos?
Most music has been by written by Vince Rubinetti, which you can download on Bandcamp and stream on Spotify, Apple Music, Google Play, etc.. The piano song throughout the Linear Algebra and Calculus series, listed as “Grant’s etude” and “Grant’s Opus” on the album, are just little snippets that I wrote myself, not even complete songs really.
Can I translate your videos?
That’d be lovely, thanks! YouTube has some built-in tools to let people contribute subtitles, which is hugely helpful. Really, I can’t tell you what great affection I feel for those who take the time to do those translations. Once you submit a translated transcript, it needs to be approved, which also happens through the community. So reviewing submitted subtitles is also a great way to help.
Since YouTube is not available in China, there is a small team of volunteers that make them available on Bilibili with Chinese translations. You can find the means of contacting the team on that page if you want to help out.
Perhaps you’re wondering about dubbing content. This, unfortunately, takes significantly more time, which most people dramatically underestimate. Also, in some initial experiments with a Spanish channel, they don’t reach meaningfully more people than the subtitled versions on the original videos. Nevertheless, if you do want to put in all that time, and feel like you can commit to more than just one video, I’ll set up an alternate 3b1b channel where we can upload them. Just let me know once you have created one.
Current channels with some dubbed content:
You are not allowed to re-upload the content on your own channel, and such re-uploaded content will be taken down as a copyright violation. I know that might seem harsh, and that many re-uploaded dubbed videos are done in good faith trying to spread math around the world. However, I do need to be able to have some level of agency on how the lessons put out under my name and the 3b1b brand are presented. To take one potential problem, there is otherwise no mechanism for preventing the insertion of unwanted promotional or sponsored additions, or other sorts of edits I wouldn’t approve of.
Do you have an option for one-time donations?
The per-video model of Patreon is not for everyone, I understand that. There are some options here.
That said, just know that this sustained-support model makes it much easier to make plans for the future; imagine if your own salary/business took the form of unpredictable tips. Also, that Patreon page is where I concentrate all supporter-only benefits, such as early releases. In that way, if the same contribution you have in mind is spread over a pledge for several videos out in the future, it stands to be better for both of us. Well, except in that it means having to set a reminder to cancel the pledge when you intend to, but hopefully the perks in the meantime would be enough make that worth it. And of course, I’d be lying not to say that part of my motivation here would be that the videos I make in the interim are enough to earn your further support, but if they don’t, not a worry at all.
Either way, I’m extremely grateful to anyone who chooses to pay for the content which is otherwise free, in whatever form you are most comfortable with.
What resources did you use when learning math? Do you have any recommendations?
First of all, I should emphasize just how sparse the set of things I know is in the broader landscape of math, and the possible intuitions lurking in the shadows of that landscape. I'm still always learning, and moreover always trying to refine how I learn, and I have no clear answers on what is best. So take anything I say with the knowledge that it should be heavily supplemented with advice from other (wiser) people.
Much depends on what you want to learn in particular. As a high school student, I found the Art of Problem Solving website and books fascinating and transformative, and I think their resources would be just as good for any adult looking to learn more. In general, I do think the best way to learn is to emphasize solving problems, rather than reading/watching alone. Math is fundamentally about patterns, and solving problems is a good forcing function for immersing yourself in patterns.
Moreover, it's not enough just to get an answer to a question, ask yourself if you feel comfortable with the underlying structural reason why the problem you are working on should even be solvable, and if the pattern of its solution might carry over to other contexts.
Here's a handful of books I found particularly well-written (I'm sure I'll forget some):
"Vector Calculus, Linear Algebra, and Differential Forms" by Hubbard and Hubbard
"Linear algebra done right" by Sheldon Axler
"Ordinary Differential Equations" by Vladimir Arnold
"Chaos and Nonlinear Dynamics" by Steven Strogatz
"Visual Complex Analysis" by Tristan Needham
The expository papers written by Keith Conrad
"An Epsilon of Room" by Terry Tao
"Primes of the form x^2 + ny^2" by David Cox
"Topology" by Munkres
"The Cauchy-Schwarz Master Class" by J. Michael Steele
"Proofs from the Book" by Aigner and Ziegler
In reading, really try to predict what proofs will look like, and be willing to meditate on what the right way to think about a given object is. Ask yourself if each new construct feels motivated, or if it's out of the blue. If it is out of the blue, it's okay to move forward anyway, just keep note of the fact that there is a lurking question mark. Read with a pencil and paper by your side so you can sketch things out and scribble solutions to exercises as you come across them.
I hope that helps.
Can you answer a math question for me?
I’d prefer that you post it to the 3b1b subreddit. That way, even if I’m too busy to answer (or if I don’t know!), there’s a good chance someone else will help you. You should also post it to the the math stack exchange, or to Quora, where you’ll be exposed to many, many great minds who are eager to help you out.
I’ve solved a famous unsolved math problem/I’ve developed a novel idea. Will you check it for me?
Maybe that seems a little harsh, but there are two important things to note here. 1) I’m not a research mathematician, so I wouldn’t be the one to ask. 2) I feel I have too little time as it is to read and learn all the things I’d like to, so I have to be protective of where I focus that time.
Will you speak at my event?
Maybe! I tend to prefer focusing my time on videos, but will give the occasional talk. Feel free to share the details through the contact form below. If I say no, don’t take it personally, it probably just means I’m antsy to do more videos.
My organization would like to sponsor one of your videos.
Questions not addressed above?
(Pssst, gentle reminder that topic suggestions and questions about math are addressed above, so this is not the place to send those)
I do read all the messages I get, but I hope you understand that I just can’t respond to all of them.