This is a belated Rosh haShana post, but I have been thinking about this question ever since the rabbi of the synagogue I was visiting raised it in his speech. How can we say "this day is the birthday of the world" and simultanously agree with science that the creation of the world was a process over billions of years? Then there was no specific day on which creation was finished, it just evolved continuously. We still of course did the whole liturgy with this passage in it and so on, but if you think about it, it is a bit schizophrenic.
The Tora says that the earth is five-thousand-something years old. Science says it is much older and points to evidence such as fossils. Fundamentalists answer that G-d has created fossils ready-formed and "backdated" at creation. Of course, I am not going to argue that G-d has the power to create ready-formed fossils. It should not be too difficult if you compare it with the creation of everything else. But why would he do it? As a trick, to test our faith in the Tora? I would like to point out a problem with this approach:
But, he [Louis Jacobs] notes, such positions still require us to believe that God has given us the power to reason, and the ability to uncover compelling evidence, but nevertheless expects us to resist the obvious conclusions. (Dr. Daniel Jackson: Torah min haShamayim: Conflicts Between Religious Belief and cientific Thinking)
The G-d I believe in is not a G-d that would trick us like that. My G-d wants us to use our powers of reason and intellect to do research. To discover the secrets of this earth. And to marvel at the amount of detail and balance we find! Fortunately for me, accepting that the earth is more than 5773 years old does not destroy my faith and I do not think it should.