The mathematics to accurately predict or relay reality is still complex enough that it’s often beyond us. You’re right in that it’s a tool to understand, but if we’re using simplified math for simplified reality, is it really epistemological?
As you suggest, math isn’t outside the boundary of philosophic investigation. It never was in the past, and I don’t think better approximations change that calculation.
How can any perception be independent of mind consciousness? And how can mathematics reflect anything other than that consciousness?
"Within consciousness" doesn't belong here. Even if all sentient life in the universe died out tomorrow, the idea of triangles (and "triangluarity") would still exist.
this "the idea of triangles would still exist" statement looks very reasonable, but can we ever proove it? you can not remove ALL consciousness to verify. at least a bit consciousness must be in the system to do the experiment.
yes, it very much coincides with all of our understanding of reality, that abstract ideas like triangluarity is independent from any consciousness. at least any consciousness known or conceivable to us so far.
so my extension to this statement would be - admittedly supernaturally-sounding - that: Even if all sentient life in the universe died out tomorrow, the idea of triangles (and "triangluarity") would still exist, possibly because there is a consciousness above/beyond of the conceivable the universe to sustain their existence.
If so, then consciousness doesn't need to exist for information structures to exist.
A quadratic equation can be used to approximate the coordinates of the trajectory of a thrown object in a gravity field. I think the really interesting question is why that particular equation reflects that trajectory. Arithmetic operators - multiplication and addition in that case - in a particular order, are approximating the causal operations of existence that are actually at work. I think of this as the philosophy of mathematics and much more should be done to investigate it.