# Recommendations

If there’s one thing I hope 3blue1brown videos do, it’s to inspire people to spend more time playing with and learning about math. In a separate post, I lay out some recommendations for books on math which I've personally enjoyed. Here I thought I'd list some of the other places online you might enjoy exploring, should you find yourself with an itch for more math.^{1}

## Practice

Passive consumption, say by watching videos or reading books, is certainly the lowest friction way to expose yourself to new math. But if you care about long-term retention and deeper understanding, there really is no substitute for practice. So before getting to other YouTube channels and books you might enjoy, here are a few places you can go to learn more actively.

The first is brilliant.org. I know a few of the people there, and I can vouch for the fact that they are extremely thoughtful about what makes for good learning. It shows in the product. Rather than putting lectures and videos front and center, problems and puzzles take precedence, all presented in a structured progression. The site also benefits from an active and helpful community of users.

Another good reservoir of problems with a helpful community surrounding them is the Art of Problem Solving. In particular, they have an extensive archive of contest math problems, ranging from more approachable ones like the AMC8 to extremely hard ones like the IMO, all with excellent surrounding discussion from the community.

The original Art of Problem Solving book by Richard Rusczyk, by the way, was one of the things that made me fall in love with creative math as a young student.

Mathigon is a very beautifully done set of interactive articles on all sorts of fun topics in math. The experience sits somewhere between reading and playing a game, with a really wonderful blend of artwork, technology and pedagogical clarity. One small feature, but which adds a ton in my opinion, is that you have to answer questions in order to continue reading. It's a nice way to force the reader to be honest with themselves about whether they're being passive or not.

For building up your fundamentals, say starting with algebra, take a look at Khan Academy. They are probably most famous for the videos Sal does, but arguably the site is most valuable as a source of problems you can drill on, starting from the very basics if necessary. I may be biased, though, given that I used to work there!

## Other YouTube channels

Mathologer, by Burkard Polster. Half of the appeal here comes from the delightful bits of math this channel covers, often with novel ways of presenting otherwise extremely complicated topics to make them easier. For example, he has a video showing why $\pi$ is transcendental, which is a famously difficult topic, but which he skillfully boils down into an approachable step-by-step presentation. The other half of the appeal is watching Burkard delightedly laugh at his own jokes every 2 minutes or so.

Numberphile, by Brady Haran. I’m guessing if you’re here, you already know about Numberphile. If somehow you don’t, it’s a great channel full of interviews with mathematicians. As a result, you see a wide array of the types of topics which different mathematicians find exciting to showcase or teach, and a little more of the human element behind this subject. There is also an associated podcast, less about the math, and more about those human stories.

Standup Maths, by Matt Parker. This channel is more whimsical and comedic, but that’s not to say there isn’t a lot of serious math it covers.

Looking Glass Universe, by Mithuna Yoganathan. She covers ideas from physics and math explained simply and unusually honestly. Start with the one on spin, it’s great. She also places an emphasis on doing practice, often assigning “homework” at the end of each video.

Also, can we just step back to appreciate that the four channels above are all run by people either from or based in Australia? What’s going on over there? And that’s not even counting Tibees, Eddy Woo, James Tanton and countless others.

Welch Labs, by Stephen Welch. Perhaps best known for his series on imaginary numbers, this channel is full of high production quality and well-written videos. There are also several series on machine learning, the topics underlying self-driving cars, so this is certainly one of the more applied math channels out there.

Black pen red pen, by Steve Chow. If you like seeing how to work out integrals in all sorts of crazy ways, boy is this the channel for you. Steven is a math teacher, and the videos have a feeling of being in office hours, honestly working through problems with a very skillful and enthusiastic teacher. Many of the problems covered are the kind you might come across in school, and many or just for fun.

Patrick JMT, by… well… Patrick. If you want good, honest worked examples of practice problems, especially for calculus, it’s hard to find a deeper well of examples than what this channel provides.

Needless to say, there are countless others. But often less is more when it comes to recommendations, so let's leave things here for the time being.