As you can see I've been gone all weekend. If I have a choice between drinking and listening to a great rock band, or debating philosophy/science/theology, I think you know which one I'd pick!
nashmodeler gave a really good explanation of subjective reality. This is one of my biggest objections to the various logical arguments for God. Kant, Descartes et al were really brilliant people, well-versed in mathematics and philosophy, but every argument of theirs fails in the premise. Nearly every human being has certain perceptions of the world which agree closely enough with other humans as to make normal discourse and debate possible. However, one thing which must be made clear at the beginning of the debate is an agreement on the premise or assumptions that are to be made. That's where most arguments fall apart - the participants cannot even agree what basic assumptions must be made. Why? Because reality is subjective and based on our experiences. The only "a priori" knowledge one could argue for is the existence of our survival instincts, which are encoded in our DNA when we are conceived. Beyond that all knowledge comes to us from experience. One can have some really outrageous abstract thoughts, but unless they correspond with an experience of reality outside our minds, such thoughts are merely "mental masturbation."
Faith is one such abstract thought. I generally know two kinds of people with faith. The first type claims some a posteriori knowledge they gained which supports the a priori existence of God, and hence is the reason for their faith. The second type, which is more rare, recognizes that their spiritual experiences are purely subjective and they have no way to know whether they have anything in common with other believers. They have faith simply because it's comforting to believe in God, and they readily admit this.
The stunning differences in religions around the world is a strong indicator that knowledge is subjective, and suggests not that many gods exist, but that no gods exist. God was originally invented as a way to explain natural phenomena and, later, to give early societies structure and discipline. As we've seen over the centuries, the number of phenomena formerly ascribed to God have been reduced to virtually none. Similarly, many societies peacefully coexist on secular systems of law, including our own. For those who argue that the Constitution is based on Biblical morality, I strongly urge you to actually read the Constitution, and if you have time, the Federalist Papers. It is telling that the few laws actually based on Old Testament morality are being struck down as un-Constitutional, and rightly so.
That pretty much discredits the idea that morality can only come through God or an objective standard. I think some of you are referring to cultural relativism when you say, "subjectivism means that Hitler was doing what was best for his society." Cultural relativism follows from subjectivism, but it is only one of many possible conclusions. In my opinion, a subjective moral system benefits the entire human race, not just one culture. It doesn't take faith in God to reach this conclusion.
As for the objectivity of mathematical axioms, I've long wondered about this one. Yes, the axioms may exist without our experience of them, but do they exist anywhere outside our own minds? I'm not sure. You won't find a perfect circle or a right triangle anywhere in the universe. I would offer that the rules which allow us to think abstractly of a perfect circle are inherent in the physical laws, which are part of the fabric of space time and have existed since the beginning of the universe. We can discover these laws, but some of the conclusions we reach require circular reasoning. I.e., I define 'a' to be this, and it follows that 'b' will do this. That's great, but it rests on the premise, and we need to have some experience of the premise in reality for the reasoning to be more than a thought exercise. It's a very good question, though.
In conclusion, Jesus loves you Kevin! Have a doughnut.