If you are an autodidact, you have most likely tried Duolingo (a free language-learning app). And if you’ve watched educational videos on Youtube the last few years, you’ve definitely heard of Brilliant.org. I finally tried out the latter.
I have a few project ideas that would be well served by a working knowledge of calculus.
I happened to have learned basic calculus in school, but that knowledge is long gone.
There was finally an excuse to try Brilliant.
Overall impression: mixed. It hasn’t worked well for me for math learning—although the reasons why won’t apply to everyone. It has been great fun on math-adjacent subjects, though.
To elaborate on the Duolingo comparison: Brilliant is designed around ~10-20 minute sized lessons. The frequent prompts definitely force you to concentrate on the material. Concentration is a pre-requisite to learning any subject deeper than surface level, so that is good. However, the idea is that you fit these 20 minute lessons in during your daily routine, maybe when you first get up, maybe before bed, maybe in the middle of the day on a break from something else. Borrowing directly from Duolingo, Brilliant has frequent prompts about trying to keep up a “streak.” Switching context during my day to learning for 20 minutes works fine for practicing a new language, but it does not work for me for math. If I had to guess why, it is that language is largely memorization, which requires concentration, but only so deep, while learning new math concepts engages a part of the brain that goes deeper.
Going deeper on my unfounded theory of learning, I see 5 levels of learning:
- You don’t even know what the subject is about or why you would learn it
- You don’t know the basic terms and concepts of the subject ← Brilliant is great for this
- You recognize the terms/concepts easily enough, but aren’t practiced at executing/applying them
- You’re generally comfortable with the subject, but could use review to aid retention and fill in gaps ← Brilliant is great for this
- You’re an expert on the subject, to proceed you have to go back to level 1 or 2 but a layer deeper
The sweet spot for Brilliant is if you are at level 2 or 4 on a given subject. In the interest of keeping the lessons engaging and bite-sized, Brilliant gives you 1, maybe 2, question prompts on a given concept before moving on. This is great if you are trying to pick up the concepts for the first time—you don’t want to get bogged down practicing just one or two things—it is more important to move quickly and get a map of the concepts in the general domain and how they fit together. Moving quick is also great if you are at level 4, since it lets you skip quickly past all the stuff you already know.
Why I run into such trouble with the math lessons is I am level 3 in so many subjects. I get bored reading the explainer text, but then I mess up the prompt question, I get the explainer but don’t internalize it, then it snowballs and I mess up subsequent prompts because I haven’t internalized the previous prompt knowledge. Messing up like this is not a big deal if it is your first pass through the knowledge, you still pick up a lot, but it is not productive if you mostly get the concepts but need to practice more to force internalization. It is not as exciting, but honestly what I need to do to proceed is pick up a used textbook and work through more practice problems. Then I can come back to Brilliant as a complement for the review phase.
I don’t regret getting a paid subscription to Brilliant. I’m level 4 on a bunch of other subjects they cover. The chemistry course was fun (too short—I hope they release more soon!). Working through “Physics of the Everyday” now. Will do CS courses after that. Maybe stick with a month-to-month subscription though—there are only so many math-adjacent course offerings currently.
Have you tried Khan Academy?
As fun as Brilliant is, if you want to learn math, look into Khan Academy first. There may be not as much buzz around it—owing to it being a 501(c)(3) without a huge marketing budget—but if fills an awfully similar niche: bite-sized lessons, practice prompts, and great explanations. Oh, and Khan Academy is completely free.
You can donate money if you like, that is what I do
Not free in the sense there are some free lessons, like Brilliant. All of Khan Academy is free.
I plan to use both going forward. The autodidact space is still small enough
If you include all the possible learning material available, the space is impossibly large, books alone will get you there. But my focus here is more limited—all the high-density, interactive learning opportunities available on demand.
that I haven enough attention to divide between all the offerings. Although I look forward to the future when there is so much available content that I will be forced to be picky.
Advice for Brilliant
Keep expanding your approach into material that isn’t already a well covered school subject. There are already industries that pump out good material covering subjects that undergrad students are forced to learn. Like it is cool if your material can help students, but as I see it the underserved market is autodidacts. You can hit both if you cover emerging fields—like you are doing with machine learning—but there are only so many of those.
There are plenty of established subjects that are underserved: transportation, building things, and any form of engineering come to mind. I mean, there is highly technical material aimed at people who are entering any of those fields, and there is more than enough “general interest” material, but the latter is all fluff. There is little in the way of interactive learning material that goes to the depth of introducing the relevant equations while keeping it all engaging for someone who can’t focus on learning the material like it is their full time job. I haven’t run the numbers, but all the subject areas I mentioned have proven interest as judged by the number of magazines in the rack at the book store—multiply that number by the rate of autodidacts in the population and I bet you have a pretty good sized market.