But if this is true, aren’t they using tools outside of mathematics already - that is, their aesthetic sense?
I know that sounds weird and round-about, but when I talk about mathematics having evolved to be useful in describing the universe, I think what I’d add to that is that it’s useful in describing the universe to us. It’s obvious there is an infinite set of alternative axioms and symbols that could be used to add apples, but the vast majority of them would require huge labour to work with. When you look at intentionally obscure coding languages (wikipedia has a list of some) it’s pretty obvious that even if you had been coding for 20 years in INTERCAL or Malbolge you’d switch over to JavaScript in a heartbeat if you realized it was an option.
The inner workings of people’s brains change from generation to generation as they are exposed to different ideas growing up, so it will become possible to consider ideas to radical to consider right now, but I think we need to fall back on our intuition about what’s useful to us now as that is itself a evolved idea that was calibrated to bring us to ideas like mathematics in the first place.
