A Layman’s Guide to Recreational Mathematics Videos
This is a crosspost from my personal website.
I have watched a lot of maths videos on the internet. The medium of YouTube is quite well suited to maths; maths books are frequently either boring or are really about maths history/psychology/sociology. People sometimes ask me for recommendations of maths channels and videos to watch, so I thought I would write this guide to have something to point them to. There are a number of channels that are good for formal education, like Khan Academy or Organic Chemistry Tutor. There are also other channels that upload high-quality lectures, like the Royal Institution and the channels of various universities. But I don’t even study maths at university, so here I’m only going to discuss channels I watch for fun.
3Blue1Brown (real name Grant Sanderson) is my favourite maths YouTuber. He animates his videos with a software he created called Manim, which is now also used by VcubingX and Reducible. Even if you didn’t understand anything he was talking about, 3B1B’s videos are still worth watching for the pure art and enthusiasm. My favourite videos of his are the ones about error-correcting codes, Dirichlet’s theorem and his interactive quaternion explainer. He has recurring series on deep learning, differential equations, linear algebra and calculus, all of which are excellent high-level overviews of the respective topics.
This is the most well-known maths channel. It’s possible that 3B1B’s new releases get more attention, but Numberphile has been going for longer and has a much larger archive. I enjoyed their recent series of videos featuring Neil Sloane, the founder of the Online Encyclopaedia of Integer Sequences. Some classics include the video on the Josephus problem, the interview with Terence Tao, and the videos with Ron Graham. It’s worth mentioning that James Grime and Katie Steckles, frequent contributors to Numberphile, also have their own channels.
Matt Parker describes himself as a stand-up mathematician: part comedian and part mathematician. He first received wide recognition from his Numberphile appearances and now he does live shows with his group Festival of the Spoken Nerd. His best videos are: his stand-up routine about spreadsheets, his videos about the hilarious superpermutation saga, and his investigation into whether “land area” assumes a country is perfectly flat. He also has a second channel, the highlight of which is the time he ran untested viewer-submitted code on his Christmas tree.
Another excellent channel. This one is of intermediate production value between the guy-with-whiteboard channels and the 3B1B cinematic masterpieces. He has a great video addressing the infamous Numberphile claim that the sum of all natural numbers is −1/12. Mathologer is strongest in animating proofs. I am especially pleased by his Simpsons-themed videos.
PBS Infinite Series (discontinued)
This is (or rather was) an underrated channel. I particularly enjoyed their exploration of voting systems and the Condorcet paradox (which I wrote about in my Beginning of Infinity review). Their video on the assassin puzzle is also good and it’s what introduced me to the idea of representing shapes as lattices. Finally, here is this post’s obligatory link to a quantum computing video.
This is probably the channel here with the fewest prerequisites, since Eddie is a maths secondary school teacher and his videos are just recordings of his lessons. But if you need to brush up on something needed for one of the other channels, I recommend him. He also covers some topics you may not know about, like how the RSA encryption algorithm works. He suitably has teaching awards and nominations for being really good.
Welch Labs (discontinued?)
This guy hasn’t made a video in over two years, but he comes recommended by 3B1B himself, and I recommend his series on self-driving cars, how science works, and a visual introduction to complex numbers.
Blackpenredpen is probably the channel I’ve watched the second most after 3B1B. While the production value is significantly lower, he makes up for it with sheer quantity. He’s particularly strong in algebra and calculus. Highlights of the channel include the time he livestreamed solving integrals for six hours straight, his videos about Oxbridge interview questions (which include a collaboration with Tom Rocks maths), and his recent conversation with Po Shen Loh.
Another channel with a simple style. I enjoy his videos about geometry. Like many of these channels, Penn has videos where he works through Olympiad problems and problems from other famous exams like the Putnam.
Flammable Maths is one of the most active members of the YouTube maths community. The level of assumed knowledge varies massively between videos and even within them. He also has a meme-y aesthetic and sense of humour that can become a bit much at times. His Christmas specials are good: these two videos featured many other well-known maths personalities, and he goes through problems every day during ‘Papa Flammy’s advent calendar’.
Presh Talwalkar, or MindYourDecisions, is the clickbait of maths on YouTube. Did you know that only 6% of Korean 11-year-olds could solve this problem?! All of his videos have the same basic format of working through some problem, animated with Powerpoint. Some random ones I liked: the 25 horses problem and some deceptively simple geometry problems.
Other channels that sometimes talk about maths
This guy really only has one video about maths, but it’s shockingly good.
Watching Veritasium videos was a not insignificant part of what first got 13-year-old me into science. Here are his videos about the logistic map, the Collatz conjecture and Gödel’s incompleteness theorem.
Vsauce is perhaps the most popular educational YouTuber, and he has touched on maths a number of times. I recommend his videos on the Banach-Tarski paradox, the napkin ring problem, and the brachistochrone. I have to say, I respect how much detail he goes into, especially in the Banach-Tarski video. It has so many views that it’s plausible that, of all people in the world who know what the Banach-Tarski paradox is, more than 50% of them learned it from Vsauce.
Andrew Dotson is a bit like the physics equivalent of Flammable Maths. A lot of his videos are vlogs, for people who want to see what life is like as a physics graduate student (hint: it’s shit). The videos of his where he does actual maths include finding the eigenvalues of a Möbius strip, integrating with Feynman’s technique and the “you laugh you differentiate” challenge.
Tibees became popular through her ‘exam unboxing’ series (see for example professors reacting to India’s JEE Advanced exam). Now she makes videos about what famous mathematicians and physicists were reading or writing, and occasionally she’ll make a video of her solving a problem herself.
Simon Clark studied physics at Oxford and is the messiah for physics A-level students applying to Oxbridge. He’s made a number of videos about admissions (playlist here) and if you’re thinking about applying then definitely watch his videos. The most explicitly maths-related videos he has include a brief history of pi and a video about the etymology of sin and cos. The videos of his I like the most are the ones where he talks about his favourite books (click here for the playlist).
TED-Ed has a puzzle series, which includes videos on the prisoner hat riddle, the Mondrian squares riddle, and a variation upon the blue-eyed islander problem. They also have videos about Hilbert’s hotel and where maths symbols come from.
Music and fun
You probably know Tom Lehrer’s periodic table song, and you may have even seen Daniel Radcliffe sing it on The Graham Norton Show. What you may not know, however, is that Tom Lehrer had an entire career as a mathematical musician! My favourites are ‘New Math’, ‘That’s Mathematics’, and my girlfriend and I are obsessed with ‘Lobachevsky’.
TheGermanFox has only uploaded three videos, but his musical proof of why e is irrational is actually really good and I can’t get it out of my head.
Vihart makes fun, usually short, videos, some highlights being this one about music theory and the Pi Day rants. Pi Day (March 14th) used to inspire a lot more enthusiasm, but I guess it’s sufficiently mainstream now that it’s no longer cool?
Bonus: podcasts about maths
This is a podcast hosted by the wonderful Steven Strogatz, an author and professor of applied mathematics at Cornell. I recommend his conversations with Janna Levin, John Urschel, Frank Wilczek, and Moon Duchin.
This podcast, hosted by Grant Sanderson, has just started recently, but I can already recommend the conversations with Steven Strogatz and Sal Khan (of Khan Academy fame).
Since it’s very difficult to communicate mathematics purely orally, maths podcasts are really more about the characters involved and their personal stories. This is no exception. The best episode is certainly the one featuring Roger Penrose, but I also enjoyed the conversations with Marcus Du Sautoy, Matt Parker and Grant Sanderson.
Thanks to Sydney for reading a draft of this post.
thanks for the excellent recommendations! I wasn’t aware of a number of these YouTubers :)
Think Twice is another good one for geometric proofs.
I also liked Epic Math Time’s video on the operation a^log b.
Zach Star has some great math videos as well.
I know it’s a decade old now, but I still love Vi Hart’s stuff on YouTube (less complex topics than the ones you listed though)