Alister McGrath has two great articles up on the Austrailian Broadcasting Corporation's Religion and Ethics site, "Stephen Hawking, God and the Role of Science", and "Science, Belief and the Question of Proof". In the former McGrath, spurred by the recent flood of press received by Hawking and his new book, The Grand Design, argues persuasively that Hawking's claims in the book overreach the abilities of science.
In the latter he tries to pierce through the rhetorical clouds of atheist fundamentalists to show that science is not a question of proof, but is always subject to revision, and that that is of course okay. Darwin knew that his theory was not without problems, but he still thought it true, and this is typical of all scientific enquiry - indeed, that's the nature of hypothesis. McGrath:
As he remarked towards the end of his Origin of Species, "A crowd of difficulties will have occurred to the reader. Some of them are so grave that to this day I can never reflect on them without being staggered; but, to the best of my judgment, the greater number are only apparent, and those that are real are not, I think, fatal to my theory."
It is interesting to note that these words of Darwin could apply with equal force to Christian faith. Yes, it makes a lot of sense of things. Yes, there are some problems and difficulties. Yet the theory makes so much sense that Christians believe that they are justified in holding on to it.
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So what is the relevance of this for religion? For Christians, belief in God is the "best explanation" of the way things are. As C.S. Lewis once put it, "I believe in Christianity as I believe that the sun has risen - not just because I see it, but because by it I see everything else."
We can't prove that God is there, any more than an atheist can prove that there is no God. But all of us, whether Christians or atheists, base our lives on at least some fundamental beliefs that we know we cannot prove. That's just the way things are. And it's not a problem.
We humans are always working with our best guesses, giving our assent to a framework of belief that seems to match the data the best, that seems to most powerfully interpret our experiences. This framework always involves large swaths of contingency and less-than-sure certainty. This does not, however, make the framework irrational or necessarily untrue. In fact, without such frameworks we would be reduced to either a radical skepticism or a radical solipsism (though I think these are still just best-guesses, even if they are especially extreme ones).
And I would be remiss as someone who reads a lot of Karl Barth if I did not point out that Christians believe they can speak of God only because God has himself spoken. God is beyond the possibility of comprehension, and so anything that could be demonstrated within science itself (science being the most successful endeavor of human comprehension to date) by definition cannot be God.
But God is the God who speaks. Without that there is no Christianity, and without that science would undoubtedly be the deepest we could go. But way down, from beyond the depths of the infinite deep, God comes to us, dwells among us humans and shows to us what cannot be said - that which Paul calls pistis Christou, the faithfulness of Jesus Christ.