Essential Maths For Beginner Gamedevs - Which Math is Useful?

There's plenty of tutorials on learning maths for gamedev, but why and where is this maths actually useful? Here, I try to give examples of how and when different types of mathematics pop-up, and how they are actually used when making a game. I have added links throughout the video and below if you want to learn these topics in more detail, but hopefully this will make you aware of the different areas of maths used in gamedev!
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Tutorials and Learning Resources for each topic covered (I have tried to include one video, one blog and one interactive thing to account for different types of learners!):

Numbers
+, -, x and ÷ are used frequently! The good thing here is that even if you aren't the best at doing sums quickly, the computer is! As long as you recognise when you should be using each operation, you'll be fine (e.g. subtract some health when your player takes damage).

Discrete Maths
You will almost definitely do a discrete maths course at university, if you do CompSci or a related degree. You could learn about any of these sub-topics for years.

Logic

Coordinate Systems

Trigonometry

Pythagoras Theorem

Vectors

Vector Normalisation

Dot Product

Cross Product (Advanced Topic)

Quaternions (Advanced Topic)

Graph Theory

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Timestamps
0:00 - Intro
0:30 - The Problem
1:15 - The Solution
1:52 - Calculus Not Needed for Making Games
2:19 - Numbers
3:38 - Discrete Maths
4:44 - Logic
6:40 - Coordinate Systems
8:09 - Trigonometry
10:17 - Pythagoras Theorem
10:58 - Vectors
12:51 - Vector Normalisation
14:31 - Dot Product
16:01 - Cross Product
16:51 - Quaternions
18:26 - Graph Theory
19:42 - Recap
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#math #gamedev #mathingames #indiedev #gamedevmath

[seraaron]

To add to your list: I would say *Probability* theory and *Statistics* are pretty crucial for system design and making the numbers work for you (and also for understanding the analytics once you release your game). *Physics*, or classical mechanics and galilean relativity at least, is definately up there too if you're making anything real-time. And by extension, *Calculus* : since like 90% of of physics is just multivariable vector calculus. *Matrices* are also useful, though typically only if you're working in the nittygritty parts of an engine. And this last one bridges the gap between maths and computer science, but it's been sooo useful to me in hindsight, and i rarely hear anyone ever talk about it: the very badly named topic of *Functional Programming* . A functional programming or operations research course will basically teach you how to take all of the maths theory you just learned and actually turn it into useful computer code.

[zambonni]

I am a High School MATH teacher. This is the most AMAZING video I've ever seen to explain WHY and HOW we use math in video games. Kids love video games so this appeals to them! SUPER AMAZING AWESOME JOB. Thank you for making this. I hope this gets a million views!

[viniciush.]

i had my journey of learning unity and going through my education alongside one another. As i progressed in maths, i became a better gamedev, and vice versa. I think it's fundamental to learn math in order to be a good gamedev

[TealComet]

I learn math on my own because I knew it was somehow useful in game development, but recently I was starting to lose motivation, asking myself when/why would I ever use this super complicated formula or that property. Thanks to this video, I understand better, and I'm ready to keep increasing my math knowledge and skills ! This is an excellent video :D !

[seraaron]

I did my undergrad degree in maths, so I've been delighted to learn through game dev that a bunch of the stuff that I learned there finally has a direct use for me! Although, I have to say, when I found the quaternion function I was initially disapointed that the unity function basically does all the work for you, haha, then I remembered how difficult it would be to *not* have most of that be automated. So yeah I mostly agree that you need to know how to use quarternions, but not how they work necessarily, unless you're building your own game engine from scratch.

[UnderfundedScientist]

This is the best explanation of normalized vectors I've ever seen

[GameDevArtisan]

Great video! I really liked the attention given to Vectors, as that seems to be where many people spend time spinning their wheels, so it's nice to see such detail given in consumable portions. Nice work!

[arvinsloane]

Thank you for this comprehensive video and for putting all that quality in it !!

[tauheedgamedev]

Great video, The learning never ends but vids like this make it so much easier.

[iambakuhatsu]

Found a video suggested by you yesterday and ended up binging about three quarters of your vids. I feel like you have a very unique perspective among youtube gamedev channels and you really clicked with me, thanks for all the work you put into your channel, there are a few things I'll definitely come by to watch again. Hope you're well!

[ccstudios]

Really helpful video man! Can’t wait for the next one!

[johntryl]

This was surprisingly refreshing. It often feels like there's too many disjointed tutorials, with no roadmap or motivation. You did a good job with this one. Glad I found this vid. Calc is more useful in controls and electrical engineering; if you want write software for airplanes and helicopter and you get the idea, that's where you'll use calculus, otherwise, study your linear algebra if you wan to make games. Basically exactly what you said. Nice work.

[tejaswithme]

Oh man... I'm shocked! For past 3 weeks or so I've been learning Godot from Heartbeast's old platformers video & i remember that he used *Vector normalizers* & finding that it's the same concept as he told just refreshed my memory!!!
Thanks for this amazing video Sir ❤
Love from India 🇮🇳

[MrZAPPER]

10:40 yes but also because the Greeks did it with triangles. Eastern math systems used arcs and strings before triangles. Super cool history to it

[kjmyer]

Great video. Well done on telling my why and how. So important!

[omaryahia]

❤ this is simple and to the point, you showed us in general, the usage of topix x in games is like this

[darrennew]

I will say I studied calculus for three years before I got to a physics class advanced enough that I needed it. Then I went "Oh! That makes so much more sense." It took another 20+ years to figure out why I read Great Expectations and Macbeth in high school. As for "numbers, " you need to learn the limitations of floating point too.

[vini_artist]

Fantastic! I’m learning game programming using Lua language and pico8. I limited myself in a small environment to focus on the fundamentals. Big engines can be really handy for those that know what they’re doing, but for me now, it’s like use a full car workshop to fix my bicycle. This video was everything that I needed! Thanks!

[notecolt]

Dude just summed up my high school maths and my first 2 years at uni

[titiksasanti]

that was exactly what I needed, thank you so much