I always have #6 on my list and I always put it off. /sad
3D maths and game development worked out somewhat in the past (I forgot most of it though, and as that was the DOS days it wasn't really more than high school level geometry). But I doubt that I could find enough real noticeable application for e.g. category theory.
(Just being the basis for something often isn't enough. You don't need to know much about physics to hop on a trampoline.)
I'd love it if people had suggestions for other engaging ways to apply math while programming!
My current job has me messing around with linear algebra and statistical analysis on occasion, though I've found the cobwebs in that part of my brain are rather thick :)