THE AGE OF THE UNIVERSE
The solution to the contradiction between the age of the earth and the universe according to science and the Jewish date of 5755 years since Creation is this: the real age of the universe is 5755 years, but it has misleading evidence of greater age. The bones, artifacts, partially decayed radium, potassium-argon, uranium, the red-shifted light from space, etc. - all of it points to a greater age which nevertheless is not true. G-d put these things in the universe and they lead many to the false conclusion of a much greater age.
I said the evidence is misleading. Does that mean that G-d is tricking us? Not at all: He told us the truth! Only someone who [perversely] decides to ignore the statement of the Creator and rely only on what he can investigate will be lead to a false conclusion. Only to such a person is the evidence misleading. And note that this policy of creating the world looking different from its true nature is an inescapable Jewish idea. For, we recite twice every morning that G-d constantly recreates the universe, even though this is not observable.
Let's first understand that G-d certainly can do this if He wishes. There is no logical impossibility in imagining such indicators of false age. Furthermore, something like this is part of the naive understanding of Genesis. Adam was created as an adult. Observing him a few minutes after he was created, we would assume him to be at least twenty years old: he was created with misleading symptoms of greater age than he possessed. The trees created in the Garden of Eden presumably had tree rings. Tree rings usually indicate the age of the tree, but in this case the rings are misleading evidence of age the trees did not possess. So the idea is not inherently absurd.
The usual response to this idea is: "Why would G-d do that? Why would He want to mislead us in that way?" Now strictly speaking we don't have to answer that question. Knowing why G-d would do it is not a prerequisite to asserting that He did it. Often we don't know why people do various things; that does not lead us to doubt that they did them! Nevertheless, even though we don't need to answer the question, we can. Briefly, the purpose of the physical world is to hide G-d's presence so that we can exercise free will. In fact, the Hebrew word for "world" - olam - means "hiding". So evidence which hides the true age of the universe since Creation would be part of the general policy of hiding G-d's presence.
A more sophisticated objection to the second solution is this. Can we not defend any arbitrarily chosen age for the universe by this logic? If we said the universe is 50,000, or 500,000, or 5,000,000 years old, we could always say that the evidence of greater age was due to misleading evidence put there by G-d! Doesn't this trivialize the whole project? It means that there is no objective standard at all for deciding how old the universe is!
The answer to this objection is as follows. Indeed, if we were to use this logic without any limits, it would trivialize all investigation in the age of the universe. But we are suggesting that it be used to resolve a contradiction between two generally reliable sources of information. Under these conditions it is wholly appropriate. I will give you an analogy. Suppose George is accused of murder, and we have his fingerprints at the scene of the crime, the murder weapon at his premises, and he has a motive. Suppose the only argument put forward by the defense is that George is being framed. That will surely not be taken seriously. To take it seriously would undermine almost all attempts to convict, since almost always it is possible that the defendant is being framed. But now suppose we have a witness who claims to have seen George 100 miles from the crime at the time when it occurred. Now we have a contradiction in the evidence. Now it surely would be appropriate to suggest the possibility of a frame-up and to investigate that possibility. After all, frame-ups do sometimes happen. Our case is strictly parallel. To suggest that G-d hid the true age in defense of any arbitrarily chosen age is wrong. But to use that suggestion to solve a contradiction in the evidence is perfectly appropriate.
Of course, this solution assumes that the Jewish tradition does have enough evidence to be regarded as generally reliable. I believe that this is true, but defending it requires a much larger effort. In the mean time, given that premise, the analogy with prosecuting crime holds. Therefore it seems to me that this solution is perfectly adequate to reconcile the two ages of the universe: the Jewish date gives the real age, while the scientific estimate is the result of reading misleading evidence.