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.  If you're curious, you can find it 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, 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 backwards 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, never hesitate to let me know about things that can be improved.

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 judgements 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.

Note, requests I get through email are much, much more likely to be ignored, since that reddit thread is what I look to when considering what people are asking for and how others respond to each request with upvotes and comments.

What does the name "3blue1brown" mean?

When I started the channel, I knew that I wanted 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 find here  The piano song throughout the Linear Algebra and Calculus series, are just little snippets that I wrote myself, not even complete songs really.

Who are you?  What's your background?

My name is Grant Sanderson.  I studied math at Stanford, with a healthy bit of seduction from CS along the way. For a while, my job experience was pointing me in the direction of software engineering/data science, but ultimately the primary passion for math won out at the expense of the mistress.

I've loved math for as long as I can remember, and what excites me most is finding that little nugget of explanation that really clarifies why something is true, not in the sense of a proof, but in the sense that you come away feeling that you could have discovered the fact yourself.  The best way to force yourself into such an understanding, I think, is to try explaining ideas to others, which is why I've always leaned towards the teaching/outreach side of math.

I was fortunate enough to be able to start forging a less traditional path into math outreach thanks to Khan Academy's talent search, which led me to make content for them in 2015/2016 as their multivariable calculus fellow, and after that began focusing my full attention on 3blue1brown.

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.

Questions not addressed above?

(Pssst, gentle reminder that topic suggestions 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. Especially anything with a long and meandering math question.