A bit late, but...

An example is

quaternions^{w}. I don't even understand what quaternions are or how they work. All I know is that they are 4-dimensional things that allow you to avoid something called

gimbal lock^{w} that occurs when rotating in 3-dimensions (and I can't wrap my brain around them). I'm not sure I understand exactly what gimbal lock is either

but I know it causes objects to not rotate the way you would think you are telling them to.

Don't feel bad. In the 1860's to 1880's the world of physics had only a few people that could understand the mathematics of Hamiltonian quaternions, which were a pre-requisite to understanding Maxwell's equations. Under pressure from other scientists and publishers, the equations were dumbed down to algebraic vectors so that us mere mortals could understand them. It had negative consequences in the same way that gimbal lock occurs and how Hamiltonian quaternions solve the problem. So, today we're stuck with electrodynamics that are partial at best. It's worse when in 1957 we discovered that we're doing everything wrong, and yet still plod on with flawed mathematics and physics. The problems that Hamiltonian quaternions solves echoes the same kinds of problems in the Einstein field equations and how they work by removing torque, which there echoes the gimbal lock problem of rotation. I'm still working on understanding the math for all of that myself, and don't expect to fully understand it for quite a while. The basics of a quaternion are pretty simple though, and very similar to how you might envision a complex number:

i^2 = j^2 = k^2 = ijk = -1

Still, it's a lot to wrap one's mind around, even in it's most basic formulation there. It messes with what one's idea of a square is.

On the game side, Monogame seems pretty decent. Still haven't given it much of a spin, but had a quick look at it. It covers a lot of ground.

http://monogame.codeplex.com/