Grant Sanderson channels his passion for math into marvelously intuitive explainer videos
Published on March 04, 2021
How do you make a living in math? The obvious answer is to go the academic route, slog through a PhD program, and become a math teacher. But in 2021, is there another way?
For Grant Sanderson, the creator of 3Blue1Brown, the answer is a resounding yes! Since 2015, Sanderson has posted more than 100 beautifully animated and narratively compelling math explainer videos to his YouTube channel. In that time, more than three million subscribers have watched these videos over 180 million times. That’s a statistically improbable outcome for intellectually challenging content, which indicates this niche may be considerably wider than we might expect. Perhaps more significantly, he has almost eight thousand Patreon supporters who have become the dominant form of funding for his channel.
I can’t remember which of his videos I stumbled upon first, but I do remember the feeling it left me with. Despite 15 or 20 minutes of unfamiliar concepts (and lots of cute little animated pi characters) I felt calm and happy, as if the world made sense. Part of this is mathematical. 3Blue1Brown videos generally prove something, which is in itself reassuring. And part of it is the nature of good visualizations, which help you understand abstract things by making them concrete. But the other term in the equation is Sanderson’s voice itself. It conveys enthusiasm and curiosity, while also being encouragingly down to earth.
So how do you become an explainer, anyway? Sanderson credits his father with incepting math at an early age. “My dad would play these games with me,” he tells me, “they were clearly motivated by trying to make me like math.”
But it was really starting to program in college that hooked him on visualization. “A lot of programmers play around with math visualizations,” he says. “But I think I really resonated with that, because of the latent love for math and also how often certain things would feel a lot more sensible and understandable when there’s a nice visual behind it compared to when it’s driven by notation.”
Notation is to math what syntax is to programming, and in both cases, we generally teach students much more about how to manipulate these symbols than what they actually mean. This is good for passing tests, but bad for building intuition about what any of it means or what you might actually use it for. On the math end of the spectrum, this is the problem that Sanderson’s videos are trying to solve.
The name 3Blue1Brown is a sly self reference to the color of Sanderson’s right eye, which is blue with a wedge of brown slipped in. It’s also obviously a nod to the idea of visualization, but I think the personal touch also has a deeper meaning. Like other great math educators (Steven Strogatz, the author of Infinite Powers, comes to mind), Sanderson doesn’t just transmit information, he transmits his passion for discovery and understanding.
And to be an explainer in the 21st century, having an online presence is critical. “Because the internet’s only going to grow,” Sanderson reasoned, “and academia is not necessarily going to be the most stable place in the world.” So having a YouTube channel seemed like a good idea, but as he approached the end of college he wasn’t thinking about math videos as a full-time job.
One answer to the question of an alternate career in math presented itself in the form of Khan Academy’s talent search program. While getting his YouTube channel off the ground, he spent his days writing articles and making instructional videos about multivariate calculus. As worthy as he feels the Kahn Academy mission of open education resources is, his time there served to sharpen his focus for his own unique approach.
“3Blue1Brown videos take a lot of time,” Sanderson explains, “and Khan Academy videos, the whole point of them is that they don’t take a lot of time. It’s a little bit more like, Hey, we’re just sitting down with a student and doing a quick tutoring session, and then we post it.” There was no actual student in the Kahn videos, but playing the imagined role of tutor allowed him to make three or four videos in an afternoon. In contrast, his own animated videos can take a month or more to produce.
“It was probably healthy to have the forcing function of the day job, which was constantly thinking about students with their needs and where they are.”—Grant Sanderson
“It was probably healthy to have the forcing function of the day job,” he says, “which was constantly thinking about students with their needs and where they are.” Buts Kahn Academy didn’t provide the itch Sanderson needed to scratch. He doesn’t see his videos as a replacement for textbooks, classroom instruction, or tutoring but more as a “supplemental intuition builder.” Sanderson also feels the audience for 3Blue1Brown is broader than just students. “I think there’s always this unappreciated pent up demand from nerds for content that doesn’t just give a surface level description of what science is saying, but actually how would a scientist think about it.”
A perfect example of this type of thinking is his video that introduces the concept of the Fourier transform. He starts out, not with an intimidating equation, but with a the underlying visual idea that a complex wave, like the sound coming from a speaker, can be decomposed into a set of simple, oscillating waves. He then explains that this simple idea underlies a lot of math and physics, including, for instance, sound editing.
The classic Sanderson move comes with his introduction of a visualization that shows how you can actually pick these simple sine waves out of the seeming complexity. He shows how you can wrap the ups and downs of a wave around a circle, revealing flower-like patterns. This transformation is not only beautiful to look at, but also useful, because the center of mass of the wrapped wave moves dramatically at the repeating frequencies. This moving center of the rotating wave, Sanderson demonstrates, is the Fourier transform of the wave when you graph it over time.
By the end of the video he has explained the fairly small amount of notation that generates the different parts of the graphics. Instead of your head exploding with all kinds of arcane examples of notation (see Wikipedia page on Fourier transform to experience said explosion) you have a simple and surprising idea, elegantly expressed. From there, you might feel better-equipped to take on Wikipedia (and the world).
A great 3Blue1Brown video is about, “finding the right balance where the substantive point that you’re making is distinct, but the way that you’re getting at it is approachable. It’s got to have some connections in the person’s mind.” An interesting visual that looks good on the screen isn’t enough. It also has to address what motivates someone to want to know about the topic in the first place. “That bit of curiosity is the hook of the video, and the story explains what is this picture? The visual is heavily intertwined into the story, it is the prompt, it is that mystery that needs to be addressed.”
A big part of what makes it possible for Sanderson to express original mathematical ideas that spark understanding is that he’s written his own animation software, Manim. When I asked him about his production process he pointed out that one of the big variables was whether he needed to write additional code for a new type of visualization. The Fourier transform video, with its spinning wave rosettes, was one such case. Having such intimate control of his means of production gives him freedom, while also lending his videos a distinctive and highly intentional visual style.
Finding the story
The narrative style of 3Blue1Brown is also distinctive, and almost diametrically opposed to how the same topics are covered in most educational settings. The secret, he says, is “making sure that you resist the temptation to start with the general abstract thing and then populate it with examples to explain later.” Instead, Sanderson inverts the scheme to start with a motivating example before describing the abstraction. To learn a challenging concept, he believes, most people need that motivation to want to understand the underlying generalization. “Pretty much all textbooks and explanations do it the other way around,” he says. “And it’s because that’s so tempting to do once you understand a topic.”
During the pandemic, Sanderson felt compelled to stretch himself and try some new things. From April through May of 2020, he did a series of ten livestreamed lessons he called Lockdown math. Not only did he figure out all of the tech behind livestreaming, but also incorporated realtime feedback working with a startup run by a couple of friends from Kahn Academy called itempool. He admits, “The lesson planning itself was pretty all consuming.” His goal wasn’t to replace the classrooms students were shut out of, but to provide a different kind of learning opportunity because, as he puts it, “Zoom classes kind of suck.”
On the animation side, he found himself drawn to some of the mathematical concepts behind epidemiology (Karl Friston felt a similar pull). His videos from the beginning of lockdown on exponential growth and epidemics and simulating an epidemic are among the channel’s most popular. The one on simulations in particular answered that latent need many of us felt at the time to ask scientific what-if questions in the absence of certainty.
“The best thing to do is make content that’s not related to what’s timely, but instead, just go back to the roots and make more stuff that just explains things that people want to learn about.” —Grant Sanderson
But the messages of solace that he got from his viewers were more about topics that had nothing to do with the pandemic. “The flavor of the most warm lockdown-related feedback was one of the things pushing me to realize, actually, the best thing to do in this case is make content that’s not related to what’s timely, but instead, just go back to the roots and try to make more stuff that just explains things that people want to learn about,” he says. “Not because it’s topical, but because of the fact that people are at home in an environment where learning is otherwise kind of a painful process. Just give them a better option.”
Thousands of true fans
When Sanderson left Khan Academy at the end of 2016, he had to figure out how to fund 3Blue1Brown. By then, it had become much easier to monetize YouTube videos with influencer marketing and crowdfunding services like Patreon. He experimented with both, but soon realized that the Patreon model where passionate fans “directly contribute to the creators that they consume” made the most sense.
“Influencer marketing is great for short-term content, where most of the impressions happen within the first month or two,” he explains. “But then, a lot of the content I want to make, I want to be evergreen. I want it to be relevant 10 years from now.” Crowdfunding, he continues, “usually plays at least some role in a lot of educational channels, because there is this public good component, and people often just want it to exist in kind of a goodwill sense.”
Fortunately, the people who like this content consume a lot of it! What’s the secret of this success? “I think it’s it’s always hard to know why people watch a channel, you can make a billion speculations,” Sanderson say, “but I suspect part of the reason that the channel has garnered the audience that it has is that there is something that it’s offering they’re not finding elsewhere.” This lines up well with Kevin Kelly’s advice to creators to do the work that only you can do and then find 1,000 true fans for that work. Sanderson has exceeded that goal exponentially, by any measure.
This doesn’t mean he’s completely given up on academia, but he seems more interested in working through his growing list of interesting math concepts than in playing the long game for tenure. He reflects now that, “the ten years that would have been spent in a PhD, doing apprentice research, were instead spent doing apprentice creation.”