I do not know if you know this but you are talking to a mathematician.
If you have a mathematical education, then use it to think through 'proofs' logically, you should know as well as I do that the demonstration of a specific does not constitute a general proof. BTW, I also have an undergrad Mathematics; however, one is NOT a mathematician without either being a Ph.D. or well published in the field (and I dont just mean three or four journal articles). Surely you should understand as a 'mathematician' that proof in no way implies truth.
But if by your heart, you mean the seat of your emotions, then you are also on shaky ground for emotions are tossed about by the winds. But if you faith is intellectual, then you are on solid ground. The intellect is the "part" of the soul that knows. It is that through which we know anything, including God. Whether we know something by reason or revelation, it is the intellect that knows these things.
Let's talk about this reason devoid of emotion; as much as I hate to admit it, I am by no means a rational person, my philosophy and reason are driven by my faith, I accept God's existance by faith, I accept his omnipotence by faith, and I accept that he is infinitely merciful by faith. No logic or reason can demonstrate these things to me and from these assumptions I can then use intellect to reach other conclusions, but they are not rational conclusions for they are based on assumptions of faith rather than logic; your conclusions cannot be any more valid than your assumptions.
However, though I am not a rational person, I am capable of rational thought (if, for one reason or another I decide to be rational). Logic tells me first and foremost that it is absurd to assert that God exists (as it is absurd to assert the opposite, or to assert as valid anything that cannot be proven); it also tells me that even if I can prove something, this has no bearing on whether or not it is 'true,' as GÃƒÂ¶del proved, proof is a lesser standard than truth. However, if I am compelled to take a step away from pure logic for the sake of life and sanity that step should reasonably be towards empiricism, is this a rational step? From a perspective of absolute truth, of course not, any assumption is inherently irrational; however, as a means of evaluating our experience, it is reasonable to use our experience (then our evaluation of our experience would only be screwed up if our experience itself is screwed up). Thus we arive at the reasonable conclusion that the most useful and way to evaluate our experience is by using our experience, there is no reason to go beyond this unless it is absolutely necessary to explain some unexplainable phenomena within our experience.
Here, I fear, there is no place for your god. There are accounts of the beginning of the universe that are consonant with our experience and do not require the introduction of unobservable complexity; that is to say, it is reasonable to describe the origin of the universe without an invisible man in the sky going 'poof'. Likewise, there are reasonable understandings of the development of life and intelligence (if we dare call homo sapiens intelligent) without some omnipotent being making adjustments or, again, going 'poof'. As for the additional conclusions of saying that this invisible man in the sky is omnipotent? Unobservable Omnipotence? So now this guy not only exists, but somehow has unlimited powers behind our imagination, yet there is still no observable proof of this guy. I guess at least you can explain him away now by saying he's so smart and so powerful that he's just tricking us. But that is something of a problem when one then makes the claim that he is merciful...in our observations and experience we do not see mercy in the world, ever watch a cat hunt? There is no mercy. Yes, there are convenient stories to explain away these things, that somehow everything is tanted by sin (our fault, but we can't reverse it, and god just sits back and laughs; he made a half hearted attempt to fix things with this whole incarnation and resurrection deal, but truth be told things didn't really improve much after that); however, this lack of mercy is not a moral judgement, in the animal world it's merely survival. The universe is a cold and chatoic place, governed by randomness, a randomness that doesn't care about your survival a randomness that has no mercy. If you get struck by lightening and die, there's no personal force, no mercy or wrath, it's merely chance, it would have struck were you there or not, it simply does not care, it is incapable of caring. This is the logical reality of the universe, not some caring, loving, merciful, personal god; our experience with the universe simply does not show mercy.
However, inspite of these reasonable conclusions, we choose to believe in a merciful God not because he must exist for the universe to make sense; he must merely exist for the universe to have meaning, for us to have meaning. It is because of this emotional need for meaning and purpose that leads men to seek after gods. Not so much out of a need to know how as out of a need to know why, a yearning of the heart, an emotional desire. So perhaps it would not be right to say that God is rational, for our very belief in him is based on emotion and irrationality, no rational necessity is there. Does this make God's existance any less true? Of course not, for proof has no bearing on truth. Returning to our discussion on pure logic, unpolluted by observation and experience, I may not be able to prove God's existance, but it doesn't matter for even if I were able to submit such a proof (as I essentially did against the existance of a god), it would have no bearing on truth. For, once again, I reiterate, proof is a lesser standard than truth.