This is one of my all-time favorite channels. It was started by Brady Haran in 2011. In the beginning, each video focused on a particular number and its interesting properties. However, the channel later expanded its scope to cover many fields within math, including abstract algebra, number sequences, geometry, topology, and so much more.

One of the things that makes these videos so enjoyable is the format they follow. A prototypical Numberphile video consists of an expert in some domain – typically an academician of some sort – teaching the audience about some concept within that domain. Further, the pedagogical devices employed are exceedingly simple: in most videos, the expert is armed solely with a large sheet of brown paper, a black sharpie, their voice, and their enthusiasm. Occasionally, they will have some props such as dice or coins. In more recent videos, Brady adds cartoon-ish animations to make the videos more engaging and entertaining.

Perhaps most importantly, however, is that each video feels highly approachable, and assumes little or no prior knowledge about the material being taught. The videos feel fully self-contained, with optional links in the description to extra footage or resources for learning more.

In addition to the YouTube channel, there's a Numberphile podcast which I really enjoy. In a typical episode, Brady interviews some mathematician about their life and their journey in pursuing math.

Computerphile is the sister channel to Numberphile, focusing on computer science as opposed to math. Although the videos are produced by a different person, Sean Riley, they feel similar in spirit to Numberphile videos in their format and goals.

The videos span many fields in computer science, such as security, networking, AI, type theory, functional programming, and more.

I first encountered Matt Parker, the man behind the channel, in a Numberphile video in which he talked about the number 3435 back in 2012. Matt has since appeared in many more Numberphile videos, and continues to do so today, though he also has a separate channel that I enjoy.

As the name suggests, the channel focuses on math(s) while injecting tons of humor (mostly in the form of puns) into the content, which makes the videos highly enjoyable. He covers a broad range of interesting areas within math. My favorite class of videos are those in which he takes on the role of an mathematically-inclined investigator looking into some real-world phenomena in a quantitative way (for example, here and here).

I've been a fan of Matt for a while, and I was pleased when my employer, Jane Street, became his YouTube channel's principal sponsor. Matt puts a lot of time and effort into his videos, and has also written a couple of books and performs talks.

Like Matt Parker, Tom Scott appeared in a famous Computerphile video about time zones many years ago which is when I first encountered him.

Tom is an eloquent and engaging speaker, who covers a wider variety of subjects than any of the channels I've mentioned above, including linguistics (in which he is formally educated), history, geography, computer science, and more.

He's also conducted a few game shows of his own invention, including Lateral (inspired by the great Only Connect on which Tom himself appeared), DISCONNECTED, and most recently Money.

There are many more series Tom has created which I haven't mentioned here. That's one of the things I like most about his content: they cover so much breadth and almost all of them are interesting to me.

This channel is run by Grant Sanderson, and focuses on teaching advanced (at least, relative to the content in other channels I've mentioned) mathematics while making heavy use of visualization as a pedagogical device. Grant uses a open-source, Python-based tool called Manim, which he developed himself, in order to produce the animations in his videos.

I find these videos to be extremely high quality. It is clear that a lot of time and effort goes into not only producing the animations in the video, but also in creating the script for the video such that the material is conveyed as best as possible to achieve Grant's educational goals.

Further, while the topics tend to be more advanced than those in Numberphile, Grant still assumes little prior knowledge and builds context up throughout the video or series of videos. As such, these videos tend to be slightly longer.

Grant has made some guest appearances on Numberphile as well, downgrading his visualizations to those that can be produced on the large brown sheet of paper.