Speedrunning Calculus

Harys Dalvi

September 2021

We sometimes see video games as a major productivity drain. They're addictive, and take away time that we could spend doing other things. But there is also intrinsic value in the enjoyment gained from video games, and there is even an entire culture and community centered around them: gamer culture.

Gamer culture has many facets, but the one I am most interested today is the speedrun. In a speedrun, veteran gamers go beyond merely completing a game (an impressive feat on its own) and complete it in the shortest amount of time possible.

I looked at how fun and addicting video games can be, and how speedruns add a new exciting layer of challenge. Then I looked at my calculus homework, which involved vectors and 3D Cartesian coordinates. These disparate ideas combined into something that would dominate my first few weeks of college: speedrunning calculus. I set out to finish all the homework for my 15 week semester of Calculus 3 as quickly as possible. I ended up finishing the Friday of my third week of school.

Inspiration from Gaming

There are countless examples of beauty in math, notably \(e^{i \pi}+1=0\). There is also a deep sense of satisfaction that comes with completing a challenging math problem. Despite this, even the most mathematically-inclined people would probably agree that video games are more addicting than mathematics.

The question behind my speedrun is this: if video games are so fun, how can we learn from them to make work more fun too? Here are some key characteristics of video game speedruns that make them so captivating.

Let's look at what these mean and how they relate to academic work.

Time pressure

In a speedrun, the time pressure is obvious: you have to finish the game as quickly as possible. This means you have to avoid pausing the game and stepping away; you need to give your full attention to the game.

Time pressure in academic areas usually exists in the form of deadlines. This leads to the common cycle of procrastination: we put off work until just before we have to do it, because there is no time pressure. Then, once there is time pressure, we finally give our full attention to the work.

The speedrun concept eliminates the opportunity for procrastination. Although there is no clear deadline, time pressure is present from the first second. You have to finish the game not before a certain time, but simply as quickly as possible, whenever that may be. This means that you can't wait for a deadline to approach, and waiting will only hurt you.

By speedrunning calculus, I was able to change the type of time pressure from an externally motivated deadline to an internally motivated challenge. This made me give my full attention to learning calculus even when I could afford to be lazy, just as gamers put other things on hold when doing a speedrun. It's an easy way to create your own time pressure beyond what a deadline can do.

Well-defined goals

The goal of a speedrun is to complete a video game as quickly as possible. What it means to complete a video game is usually well-defined by the game. For example, it may be killing the Ender Dragon in Minecraft, or defeating Bowser in Super Mario Galaxy.

But the goal of a speedrun is actually defined even more precisely than that. Along the way, there are “checkpoints” of some kind that serve as their own dopamine boosts within the larger context of finishing the game. This might be finding diamonds in Minecraft, or collecting a star in Super Mario Galaxy. These “checkpoints” keep the gamer's motivation high even before reaching the final goal.

The other part of a speedrun is the as quickly as possible part. This is setting a goal above and beyond the bare minimum, or a “challenge” goal. Like setting smaller “checkpoint” goals, setting this kind of larger goal helps keep up motivation.

In academics, each class has a set of content to cover, often divided into smaller topics or units (“checkpoints”), and an ultimate goal of becoming knowledgeable about a certain subject. But usually, I just do the homework and studying as it comes because I have to. I don't always consider how it fits into the big picture of learning about the subject of the class, or how that fits into my life. Considering these “checkpoints” or making our own can be a fun way to think about how our work fits in on a broader level. In my calculus speedrun, I celebrated a “checkpoint” after finishing all the work for each month.

Classes don't usually define “challenge” goals for the students to go beyond what's needed. In quantitative subjects like math and physics, it's often possible to do well in a class simply by learning equations and procedures to solve problems. A common “challenge” goal is to go beyond this and understand the content conceptually, often with mathematical derivations and thought experiments. I find that this way of learning is a fun challenge that also builds a stronger foundation for later classes. In my calculus speedrun, however, my challenge was the same as that of an actual speedrun: finishing as quickly as possible.

“Gamer attitude”

Gamers choose the games they play, and when they speedrun a game, it's because they choose to. They don't play a game feeling like it's a chore; instead, they go in with what you could call a “gamer attitude”. They are ready for the challenges of the game, and they are hopeful that they will do well. Obstacles are not seen as obstacles, but as opportunities to overcome problems.

Students don't always choose the classes we take, and when we do, there are still times we don't feel like doing the work. We don't always go in with a gamer attitude, and instead feel like we are getting through a chore. To use gamer slang, this is not pog.

But in my calculus speedrun, I found myself adopting a gamer attitude. By the time I was a month ahead, I no longer had to do calculus homework in the way that most students have to do homework. I could have taken a break from calculus, or continued working at a slower pace. But for the sake of the speedrun, I chose to put other things on pause (including actual video games) and work through calculus lecture quizzes for hours a day as if they were boss battles.

In class, we are often frustrated by challenges; but a video game with no challenges to overcome would hardly sell. This is not just an intrinsic difference between gaming and the real world; a lot of it has to do with attitude. Even if you're not doing a speedrun, adopting a gamer attitude to work is an effective way to “gamify” learning or work in a similar way that many apps do.


Although the speedrun gave me a productivity boost and helped me focus on calculus, there was one major drawback. Earlier, I mentioned conceptual understanding beyond what's necessary as a good challenge in a quantitative class. Unfortunately, since I went through the material so fast, I found myself memorizing formulas and techniques without understanding them, just so I could do the homework.

Looking back, I've already forgotten some of the formulas from earlier lessons. This is another reason why I prefer conceptual understanding to rote memorization: it's much harder to forget. I learned the second derivative test in three dimensions about two weeks ago, and I'm already a little shaky on it. But I still remember stoichiometry from my chemistry class about two years ago, because I spent much more time understanding it and practicing it until I was able to explain the concept behind the mathematical procedure.

Now that I've finished the speedrun, the rest of the semester will be review for me. I hope to use that review time to develop a deeper understanding of the content so I'll have all the benefits of a speedrun without the drawbacks.