Skip to content

Video Games and Math

So I’ve been mulling things over in my head quite a bit recently when it comes to school and relaxation, and I’ve concluded I enjoy mathematics and video games for the same reason: the real world kinda sucks.

Now I KNOW that’s such a basic r/im14andthisisdeep, Thanos-meme level statement, but the more I think about it, the more I find myself relating to it.

The real world is difficult and messy and complex and things don’t always go our way, which makes it very frustrating to deal with on a regular basis. In mathematics and video games however, that incalculable complexity is reduced to a few simple problems solvable by a few simple tools. The only reason I’m writing about this is I feel I’ve never read/heard/seen anyone discuss the similarities between mathematical reasoning and video game reasoning and I’d like to explore it.

Take Super Mario Odyssey, for example, one of my personal favorites. There’s this mission where you have to reach this trumpet player on the top of a building in New Donk City.

Now the game doesn’t tell you what path to go down (or up, rather) to get to him. You are given a set of tools in terms of Mario’s move set, the environmental structures you can manipulate, and the buildings themselves

Just by toying around myself I found 3 completely different ways to get to him: 1) you can use electricity to zap up an adjacent building and then flick yourself from that rooftop to the trumpter; 2) You can jump up to these fire escapes on the side of the building and then climb those and jump to the trumpeter’s rooftop; 3) You can jump up the fire escapes of a DIFFERENT adjacent building, and then press a button on a roof which unlocks this secret walkway and walk across to the trumpeter.

I went on to look at a walkthrough online of how it was done and they gave yet ANOTHER completely different route, by long-jumping from the tower in front of the trumpeter.

Now let’s take one of my favorite mathematical results: Quadratic Reciprocity. Basically you take this function of two numbers known as the Legendre Symbol, which is defined as follows:

Now if you don’t fully understand that, it’s not entirely important to the point I’m trying to make, although Michael Penn has an excellent video on the topic if you’re curious. Quadratic reciprocity is the theorem that, for any two odd primes p and q:

Now suppose (if you don’t already) you had a good understanding of mathematical reasoning and modular arithmetic. Just like the trumpeter, all you have is a destination you can see and a few tools to “move around” with. The theorems and concepts behind this field of math are your move set navigate this problem and arrive at the p(roof). And just like Mario Odyssey, there is almost never only one way to arrive at your destination. In fact, there are over 100 different proofs behind this one theorem, each similar in ways but utilizing different methods to arrive at the result.

It is this enthralling freedom brought that makes mathematics such a joy to me. I know I do these types of posts quite a bit where I talk about why exactly I love the subject so much but there are just so many aspects of it I feel are overlooked by the majority of the people who say they have a distaste for it. Mario games are designed to be accessible to everyone, but especially rewarding to players who take the time to learn the controls and master and apply them in creative ways; that is the genius of Nintendo developers. Unfortunately I don’t feel like the creators of math syllabuses across the word share the same genius – instead of showcasing the wondrous process of mathematical reasoning, students are just thrust upon by a 100 different problems of the exact same caliber and form. It’d be like if you were asked to do just a 100 of the exact jump again and again in a Mario game. No-one would want that.

Moral of the story is video game thinking is similar to math thinking so ask your parents for video games if your math grade is bad.