Aint that is what mathematics attempts to do?
Mathematics attempts to explore or ``mine'' the space of all possible formal systems in which specific truths can be consistently formulated. It doesn't attempt to explain reality.
define "truth"
http://yudkowsky.net/rational/the-simple-truth
TL;DR - there is an objective reality outside of subjective idealism that can't be altered by altering one's perception of it, and there are certain truths that can be distilled from that reality.
Don't forget that your mathematics also just a religion, with its own rituals and idolatry.
The truths still remain if you remove the traditions and rituals.
Nope. It merely implies presence of "subjective experience". But that is obvious, as you can see the display of your PC, sense the keyboard keys, and listen to mp3 files.
Subjective experience requires conscious and deliberative thought processes. It appears you are trapped by the circular logic required to accept subjectivism.