if u don't have a degree then Tom's advice on completing a degree is recommended (not mandatory but recommended)… some game coders today say “who needs a degree? look i can do this this this and that!”, i don't dispute such abilities, there's self-taught coders out-there who can really produce cool stuff in games, however the advice on having a degree is generally because you want to learn most if not all aspect of Software Engineering (SE) (not just how to make games). A lot of libs which end up in games are parts and components which come from other areas of learnin in SE.

For example, “the finite state machine” which we love to code in our games is used in many other areas even biology ?

A good CS degree course will also open your mind up to understanding the hardware you work with better (how to write better lib interfaces for your PS/XBOX/VR or even a TV settop box/Network Card/Graphics card/Sound etc…), it goes without saying that you will be opening yourself up to learning various coding languages as well such as csharp, c++, js, java, python, etc… i think u probably know all this, i just mention it to encourage you to take a degree ?

Now, in terms of maths, to be honest, the same CS degree course should offer Maths/Physics in various flavours and as you progress into Academia years, you would be having Advanced Physics and Maths, and these include -generally speaking- ALL the maths and physics that you need to understand game code maths & physics and more! : the big issue here is VERY OFTEN students don't know how to use (or when to use) ALL these maths and physics for game dev. A good course teaches you that.

In broad terms, games use all sorts of maths, u name it:

Algebra: for example for graph theory , A* and Dijsktra, u can use those for NPC path finding…right?

Geometry & Trigonometry: for 2D/3D/N-dimensional order object placements, vector & matrix multiplications, rotations, scaling, translations (this is where u learn on all sorts of coordinate systems space transformations, dual, triple transforms… and more…)

Analytical maths: a huge set of advanced equations can be taught here, curves, interpolations (which are bread-and-butter in games right?) and more…

Physics: all sorts of Laws here, Newton's, Faradays, etc… kinematics, dynamics, fluids, …. etc…

Some of these topics overlap, others don't… i mean there's a huge amount that u can learn with a good CS course (Programming techniques, Standardisations, ….)

When u have all this at your table, the key thing is knowing when and how to use a topic to solve a problem, “can I use binary trees to create a scene graph and store matrices in each node of the graph ?…”, u see the answer may sound obvious today, but there was a time when someone learned it the hard way and show everybody else how they did and today we have Behaviour Trees in AI, lovely ?

All this knowledge comes irrespective of whether you use Unity, Unreal or what not. The technical principles are the same for all, but we may code it in slightly different ways… Learning Unity or any game engine will not teach you these maths/physics fundamentals: it will teach you how to use Unity. You would have to self-teach yourself for anything outside of it;

To be honest, "you never stop learning until the day you die, and if you stop learning before it then you're dead" -lol- can't remember who said this, she's probably dead ?

If you don't want to go through the whole CS course, then some Unis and colleges offer Game degree courses, these are also good as the Maths in there could be dedicated and you would need to learn so much about all sorts of Applied Maths for other industries, however check on the diversity of such courses/topics to see what they offer… you don't want a course that it is too career limiting right?;

well i hope u find your path and i hope we help clear your confusion a bit;

All the best ?