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WebGL: can't help you there, I'm learning that one as I go and am prepping some stuff for a big update.

3D engine math: being able to utilize different normal vectors can allow you to do really cool stuff. tangential vectors, I believe, need to be manually calculated and there isn't a nice little code block to use in this case, so HLSL must be utilized or you can just capture the normal and utilize a perpendicular. one of my FAVORITE shaders I've ever made used a sphere calculated around a single point to control either saturation within sphere (inside = colorful, outside = desaturated) or alpha/opacity (inside = transparent, outside = opaque). I used the backface of the mesh to then give it a big emission on the inside. Looks like a hole was punched by a laser cannon.

John Carmack stuff: I know of the fast inverse square root he used, though tiny efficiencies like that are much smaller fish with the technology we're using now, nowadays we  try to optimize on larger sets of components/features and reduce the scale and complexity of larger sets of calculations. 

What I want to learn: I'm very functionally minded and I have been told (in nicer words) that my UI is ugly/unprofessional and that my game doesn't really aesthetically pop or stand out in terms of visuals. I kinda have a checkmark system in my head (i.e. does it work? then great!) and there's little space for thoughts such as: it may work, and may run fast, but it doesn't look *pretty* or *cool*. I want to learn how to make things look cool, really.