I make math art, amongst other things:
the online component of my math diary: Tsungfrūve
github (has a volumetric quaternion set visualizer and a Sprott attractor renderer, both written in C)
I am kind of skeptical of doing much in the way of symbolic nonsensica. The two dimensional symbol manipulation language we use is not itself mathematics (would the Vulcan learning pits in the first Abrams Star Trek movie actually use human symbols for math?) and is culturally and historically contingent. I like special functions and making phase portraits of functions on the complex plane. I don't trust the sort of mathematical writing which solely consists of pages and pages of category theory diagram scribble without alternate metaphor validation.
Long term projects briefs:
strange attractors are aperiodic. special functions have the exp on the unit circle as their keystone. what happens to the whole panoply of when we swap out the unit circle with something aperiodic?
How much of the content of Ramanujan's writing can be converted into animated phase portraits on the complex plane. For a demo, look at Borwein Cubic theta functions visualization (it's incomplete, I haven't gotten the script to the narrator yet.)
What families of functions on the complex plane correspond to zebra stripes/cuttlefish patterns/fingerprints?
If we were to associate a spring constant with every morphism of a category, could we use the vibrational spectrum from that to make (if Luca Turin's theory about olfaction is correct) an olfactory prosthesis for apprehending the odor of categories? (I admit, this one is pretty far out and is probably beyond current technology)
laser etched fractals as a way for the blind to apprehend things like the Mandelbrot set.