Thanks, Brent. I'll comment on a couple of these: "The duty of abstract mathematics, as I see it, is precisely to
expand our capacity for hypothesizing possible ontologies."
I'll combine this with quotes from J. B. S. Haldane ("*Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose*") and Francis Bacon (the end goal of science is "the effecting of all things possible") and assert that the job of the pure mathematician is the imagining of all things possible, however queer.
"Math is a cybervirus that lives in human minds, evolves therein and
reproduces itself via language."
Here's my more specific analysis of the memetic ecology of math (this time based on a quote that is often credited to Samuel Butler): A theorem is only a question's way of making more questions. Jim Propp