It is a shame that mathematicians have divorced themselves from philosophy.
It is clear that some of mathematics has to do with interpretation.
The words that we all write here are not mathematics.
We each have our own interpretation.
If your words exactly matched those of, say, Euler, or any other great, then you would be accused of plagiarism.
To admit that we each must have our own philosophy; our own interpretation; our own internal representation; would be mature.
Otherwise we would be bound mimics with no further freedom to explore.
That we ought here on this medium to cover the ground more fully by filling out these interpretations is a valid pursuit I believe.
Even in no human ever reads them some AI will one day digest the entirety of USENET and come to understand the human race that much better by it.
Sadly that AI's conclusions on the human race will be rather desolate relative to some of the assumptions that past philosophers have made
such as humans built in God's image, fully conscious beings with free will, the ultimate intelligence...
These assumptions are clearly wrong. We are limited and we are inhibited.
Simply partake of some alcohol and witness the reaction.
We are tamed animals; tamed by our society.
We are programmable humans.
Far more programmable and operable than our machines that we have created.
Sadly the programs that we run are dubious and such programs as
Christianity, Islam, Judaism
are simply shards of what was an exclusive branch to whom all the land and all the women were presumed by the local power known as Abraham who exteded his grasp to foreign lands and destroyed local cultures and imposed a book of law onto all.
That one book is now under the process of accumulation and variation rather many versions of exclusionary principles.
The ambiguity of this situation especially with their insistence on propagation is problematic to the human race.
That communists have formalized atheism into their system of thought (or at least did back in time) would explain quite a lot of the anti-communist and anti-socialist rhetoric here in the U.$.A. where capitalism is eating us alive and we waste more than we can even consume because it is good for the economy.
While we lay waste to the planet one might wonder...
W T F I G O H ?
We can return from blaming nations (though this does appear to be relevant in that the relative performance and behavior of nations to their people and to other nations and to other nations' people; a place where my nation has provably done great wrong) to tribes and witness the source of conflict from a very early time in history before even a word was uttered. Simply consider one bad year when the berry crop was poor in all the hills but for one fertile valley where the water runs clean. As all the tribes arrive there for berries what will we do?
As mathematics forms an escape chute from such human considerations ought we really to further split mathematics from philosophy? From reality?
This is I am afraid where academia has landed the mathematician. It is a lie.