What would be the application of math (algebra, geometry, trigonometry?) to 2d game development?

I want to make a 2d RPG using monogame, a XNA framework.

I know math is necessary for 3d game development, but i am not sure how much math i would need to do a 2d game in a framework (not a game engine) and what benefits would it offer to manually do code stuff using math and a framework over using an engine.

Many game engines promote themselves as allowing the user to skip all the math parts and focus on the development aspect, for “faster releases”.

I am not sure:

1. How necessary will some branches of math be for 2d game development and what applications it would things like algebra, geometry and trigonometry have for a 2d game.

2. If trying to use math and do things “from zero” would be considered unnecessary and trying to re-invent the wheel when game engines allow you to skip that aspect. People choose to use frameworks to do games, so there must be a benefit.

Even a single moving sprite is already math because you have to take axis into acount, what about falling down, how fast can a character move and what about special effects. At least if you start writing Shader code, and I believe there will never ever be an engine or framework that always fulfills everybodies needs (if it will, we're getting unemployed at all) so you will more or less be involved in writing your own Shaders

Not all math is equal. Algebra is something you will use all the time. Trigonometry is only useful if you have free rotation, and even then a half-hour primer on trigonometry will teach you basically all you need to know. Geometry as it is typically taught in school is pretty much useless for game development - what you want is analytic geometry, i.e. geometry with numbers. But what you really want is a good foundation in the branch of mathematics called “game theory”.