Once you realize that even science sets its own axioms and is quite limited- you can happily be just as enlightened and rational a human being for choosing to believe in G-d and the literal interpretation of His Torah with no need for any apologetic theories.
That is basically the approach of the Lubavitcher Rebbe (not last Thursdayism like someone mentioned before, that was just mentioned by him in passing).
Science and Torah operate on 2 different planes. Torah deals with absolutes, where the creator tells us how things are, while science is a human construct, where, based on the evidence and the data we have so far so-and-so is the theory that makes the most sense.
The Rebbe's approach can be summarized as follows (to see it more in depth see the book "Mind over Matter" jj1000 linked to earlier):
1) Instead of bemoaning the "conflict" between science and Torah let's look at what science actually says and, more importantly, with how much conviction science (as opposed to scientists) actually says it.
2) As mentioned before, Torah deals with absolutes while science offers the hypothesis that makes the most sense given the data we have.
3) There is a great difference between the certainties in empirical sciences (like chemistry and medicine), that deals with things we have direct access to and can be tested in the lab, and observational sciences (like astronomy), that deal with things we can only observe yet we can't test and experiment. On the third level (the one with the lowest level of certainty) are the speculative sciences that deal with things that are so far removed from us (either by vast space or by vast time-frames) that we can not observe them directly and only infer them from their effects.
4a) In the speculative sciences there is a big difference in how we infer things. There are 2 main methods interpolating (where we have data for 2 points and try to infer what would happen in a point in between) and extrapolating (where we have data for 2 points and try to infer what would happen at a point beyond those 2).
4b) Between the 2, obviously hypotheses inferred by interpolating have a higher level of certainty then by extrapolating (if I know how water behaves at 1 degree Celsius and at 99 degrees I would assume that at 100 degrees it would just be more of the same, not realizing that there's a phase transition at 100 degrees where the properties of the water change DRASTICALLY).
4c) When extrapolating, obviously, the farther you get from observable data the less reliable your observations get (if your data set goes from 0-100, extrapolating to 101 will be a lot more reliable than extrapolating to 200, 1,000, 10,000 etc.).
4d) Extrapolating from cause to effect is inherently more reliable than extrapolating from effect to cause (the equation 1+1 can have only one outcome, 3, but if I give you the number 3 and ask you how did I reach it there are in infinite number of paths I could have used to get there (1+2, 2+1, 1*3, 9/3, 6/2........)).
5) All the above applies even if all the external factors remain the same, put in different variables and things can change dramatically and often-times unpredictably (ask a chemist how long it would take milk to separate into whey and curds the answer would be a a few weeks, put in some enzymes and the process is reduced to mere seconds).
6) Based on all the above we can easily see that the theories about the age of the universe are amongst the ones that have the smallest level of certainty. Even science will agree that we are dealing with events that happened in the far distant past, under very different conditions with a very limited data set (~150 years of direct observation and a fossil record that can at best be called spotty).
7) The point of all of the above was NOT to say that "scientists don't know what they are talking about" (or worse that "scientists are phonies" like others will say), scientists are doing the best they can under the circumstances. The point of it all is just to point out the INHERENT weakness of these theories and that, although they may be the best and finest that modern science has to offer, they are still not strong enough to use as a basis for changing the meaning of Pesukim in the Torah.
ETA: wow that came out way longer than I expected...
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