If You Want to Learn Math, You Can’t Shy Away from Computation

by Justin Skycak on

Learning math with little computation is like learning basketball with little practice on dribbling & ball handling techniques.

If you want to learn math, you can’t shy away from computation.

Some people want to learn everything conceptually, without the need for computation. Wouldn’t that be easier, faster, and more fun?

Maybe, but you wouldn’t actually learn very much.

The problem is, mathematical concepts and computations are so tightly knit that you really can’t do either in proper depth without the other. You have to interleave between concepts and computations.

And typically, the most effective way to get an intuitive feel for an abstract mathematical concept, property, or theorem is to start with a concrete computational example.

Concrete examples are to mathematics as experiences are to life.

I’ll be honest, if you’re trying to avoid computation, then what you’re really saying is that you see math as a light hobby and don’t want to put in the work to learn it to the point of being able to use it professionally.

You want to read mystery novels and feel like a detective, but you don’t want to develop the skills to become a real detective and solve real mysteries yourself.

Learning math with little computation is like learning basketball with little practice on dribbling & ball handling techniques.

You might have fun learning some trick shots, maybe even three-pointers and slam dunks, but you’ll only be able to do those things in an artificially easy practice setting.

The moment you step on the court in a real game, you’ll be getting the ball stolen from you, bouncing it off your foot, missing open passes, running straight into opponents because you’re looking down at the ball all the time… all because you haven’t developed your dribbling & ball handling in tandem with the rest of your game.

Math resources that don’t give proper emphasis to computation end up having to water down their curriculum and cherry-pick problems, giving students the easiest possible problem-solving cases that don’t require too much in the way of foundational skills.

That can be exciting for students because you get enough conceptual understanding to feel like you’ve learned the material in proper depth even though you actually haven’t.

An extreme case of this would be full edutainment, e.g., a student spends a couple hours watching the 3Blue1Brown video series on Calculus or Linear Algebra and develops just enough conceptual understanding to think that they have actually learned the subject.

Many other math resources do this to varying degrees. For instance, the coverage & rigor on Brilliant isn’t really comparable to what you’d find at a top university.

That’s fine if you’re just curious about math and want to learn a bit without putting in too much time & effort, but if you’re serious about learning math well enough to make a career out of it, then Brilliant won’t give you what you need.

That’s where Math Academy comes in. We teach math as if we were training a professional athlete or musician, or anyone looking to acquire a skill to the highest degree possible, and we’ve designed the curriculum to go toe-to-toe vs any similar course you would find in the top universities and the most popular textbooks in the world.