And to use your own philosophical principles against that: such things as "an invisible man who lives in the sky" could exist... whether or not any proof can be demonstrated. If there is a 'Creator' out there somewhere, he/she/it doesn't need **your** belief in order to exist. The real problems arise when mankind tries to politicize the debate with dogma (and dictatorship, and war, etc).
Indeed, such an entity could exist. And it is unquestionably true that if such an entity exists, it will continue to exist regardless of whether or not I or anyone else believes in it.
One of the fundamental axioms of science, though, is that one does not benefit from believing that something exists when one has absolutely, positively no evidence to support that belief. There are literally billions of things that could possibly exist--a secret alien base on the far side of the moon, a gigantic omnipotent sky-dragon that called existence into being with a flap of its mighty wings, a caterpillar with an infinite number of legs wrapped in a ball around space-time outside the bounds of the physical universe, a cloned reproduction of Elvis Presley sealed in a ball of lucite in orbit around Alpha Centauri...I could, if I wanted to, spend months coming up with lists of things that could exist.
Hell, I could posit that the entire universe was created just exactly as it was about three hundred milliseconds before you read this post by being sneezed out of the nose of a supernatural, all-powerful being with a bad head cold. That could be the case; all of our memories could have been created along with us just a scant instant ago.
But the point is, without any evidence, there is no reason that you should believe any of these things. And in fact, you don't. Even the most faithful person does not accept 99.99999% of all the things which have been accepted on faith throughout human history. When we're talking about beliefs which are not supported by evidence and for which no proof can ever exist, what tool do you use to decide which ones to believe and which ones to reject? How can you tell?
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Mathematical modelling of the physical world is bound to have a "faith" component. I'm not talking about an Old Man With A Beard, or the Flying Spaghetti Monster.
Not as long as you don't confuse the model with reality, nor believe that the model is a perfectly complete, perfectly accurate reflection of reality.
Models are useful precisely because they model only a portion of reality. As human beings, we can not understand the whole of the physical world all at once, so we create models that help us to understand specific bits of it at a time. The model E=mC^2 is useful in helping us to understand the relationship between matter and energy; the model Fg=g(m1 m2)/r^2 is a model that helps us understand the gravitational attraction between two bodies; the proton-proton chain is a model that helps us understand how hydrogen fuses into helium in a star.
None of these things is an attempt to completely model the physical world. Gödel's Incompleteness Theorem states that a formal mathematical system must be incomplete in terms of provable theses and internal consistency, but mathematical systems are not the same thing as models; models of the physical world are specific subsets of mathematics, and not all models are mathematical in nature.
