A Layman’s Guide to Recreational Mathematics Videos
“When in doubt, do more maths”
Note: This was originally posted on samenright.com.
I have watched a frankly obscene number 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.1
Explainer channels
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 a more advanced channel called VcubingX. Even if you don’t understand anything he is 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 overviews of the respective topics.
This is probably YouTube’s all-time most popular maths channel. 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 excellent live shows called An Evening of Unnecessary Detail. 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 chap-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)
I particularly enjoyed their exploration of voting systems and the Condorcet paradox. Their video on the assassin puzzle is what introduced me to the tool of representing higher-dimensional shapes as 2D lattices. Finally, there is the obligatory 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 snippets from 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 lots of teaching awards and nominations for being really good.
This guy hasn’t made a video in over two years, but I recommend his series on self-driving cars, how science works, and a visual introduction to complex numbers.
Well-produced videos about computer science, for example a rundown of the travelling salesman problem.
Problem-solving channels
Blackpenredpen is probably the channel I’ve watched the 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, 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.
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 problem.
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.
Other channels that sometimes talk about maths
This guy really only has one video about maths, but it’s a masterpiece.
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 respect how much detail he goes into, especially in the Banach-Tarski video. It’s plausible to me that, of all people in the world who know what the Banach-Tarski paradox is, more than 50% of them learned it from his video.
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 crap). 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. His book videos are decent.
Music and fun
You probably know Tom Lehrer’s periodic table song, but he had a whole career as a mathematical musician; my favourites are ‘New Math’, ‘That’s Mathematics’, and ‘Lobachevsky’.
TheGermanFox’s musical proof of why e is irrational is incredibly catchy.
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 at Cornell. I recommend his conversations with Janna Levin, John Urschel, Frank Wilczek, and Moon Duchin.
This podcast, hosted by Grant Sanderson, only has a few episodes, but I 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. 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.
The preview image for this post was taken from this video; the problem is a lot of fun.
I love Elliot Nicholson's playlists for subject tutorials: https://www.youtube.com/watch?v=O4plQ5ppg9c&list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_
Thank you!