I don't think I need to tell you that this subject is far too big to fit into the few paragraphs I have available. Don't expect what you read on "The Emunah Project" to be the definitive treatment of the Torah and science controversy. It won't even be a useful summary. Here's why:
I'm not a scientist. Not only have I not spent the years of intense study needed to develop intelligent and informed opinions in the many related disciplines, but even if I had, by the time I was done, the cutting edge of science would have shifted so much as to render my knowledge all but worthless. Science is a moving target.
There are all kinds of approaches to the conflict, many of which have already been adequately explored elsewhere (in books and on the Web). I don't see what the world stands to gain from my extra two cents.
The subject has, over the past decade or so, become badly politicized. Anything that is said or published can easily - and distractingly - be swept up in the partisan storm.
Still, scientific ignorance notwithstanding, simply in order to function as a Torah Jew, I do have to have an opinion...or at least an approach.
Here's how it goes:
There has appeared, over the past couple of centuries, what would appear to be some fairly robust classes of evidence from multiple fields of academic study, that do seem to raise sharp questions about the Torah's version of the origins and development of both the physical universe and of life.
It is unreasonable to simply disregard this evidence and the scientists who stand behind it (and all the more so to dismiss "all the scientists" as a group). Such broad and superficial generalizations generate far more heat than light. They would also require that their proponents withdraw from participation in much of the modern world - including most medical therapies - because much of modern technology is built on the same principles that underly the natural sciences they dispute.
Having said that, it is also unreasonable to blindly accept anything and everything coming from the world of science just because those producing it attended universities and wear white lab coats (with pocket protectors). The history of both academic fraud and honest error allows - requires - us to remain skeptical.
So I won't engage in any direct debate. But I also won't ignore the challenge. Where does that leave me?
Let's play a mind game. Imagine that Moshe Rebbainu, just returned from a forty day jaunt at the top of Mt. Sinai, ran into a modern-day multi-disciplinary science historian. During the course of their conversation, the historian presented accurate portrayals of all of today's most powerful scientific arguments against the Torah's creation narrative. He held nothing back. The latest data from anthropology, geophysics, biochemistry, cosmology...the works.
Now let's assume that Moshe, upon considering the evidence arrayed before him, concluded that it did, indeed, seem compelling (I'm not saying he necessarily would...remember: it's a mind game). How do you suppose he would respond? Let's consider the context. He's just come down from forty days spent in intense conversation with God Himself. God has just given him the Torah that includes the Beraishis narrative. There really is no room for doubt, right? But, on the other hand, the scientific evidence is still laying open before him.
Of course, I can't claim to know how Moshe would react. But here's a possibility. There can have been absolutely no doubt in his mind that God's narration of history is correct. What his senses recorded is so compelling that it pushes everything in its way off to the side. That leaves the evidence of an apparent conflict with scientific observations. Any explanation at all that claims to resolve the conflict - as long as it makes minimal theoretical sense - is really all that's needed. God created the world with a geological and biological history that only appears to be ancient? Maybe. The forces unleashed by the mabul played around with countless historical markers? Sure, why not? It doesn't really matter. Anything will do.
I'm not saying these theories are proven correct. I know they're not falsifiable and therefore they're not science. But who cares? I've got compelling evidence (which has been presented elsewhere on this site) that allows for them...or others like them.
Science and Chazal
There are certainly more than a few passages in the Talmud which seem to offer observations about the physical world. Many of these observations, if taken literally, conflict with current assumptions about the way the world works. Many of these current assumptions should probably not be ignored.
So what's up?
I don't believe in generalizing about the words of our sages. In fact, I don't believe in offering any opinions at all about even a single statement from Shas until I've spent time and energy trying to understand it in its context and explored what the classical commentators have written. Therefore the proper way to respond to these conflicts is one Gemara at a time. However, that being a rather big job, I'll meanwhile suggest one of a wide range of general possibilities.
It can certainly be said of most of the non-halachic statements in the Talmud that their real intent went quite some distance beyond the literal presentation. The rabbis had many important principles to teach us and they used a variety of tools (metaphor, exaggeration, analogy etc.,) to communicate. Considering the primarily oral nature of the Talmud, there was also a pressing need to subtly hide at least as much as was revealed. Therefore, it would almost be surprising if the Talmud did not include passages that employed mundane objects and processes - as they were then popularly understood - as a cover for the deeply profound ideas they wished to transmit. In other words, they weren't really talking about the natural world at all.
For some people, the products of serious philosophical study, while generally remaining relatively inconclusive and abstract, do sometimes present a challenge to emunah. As I have no interest in reinventing the wheel, I'll simply point you to an excellent overview of some recent literature concerning academic philosophy and religious belief. The page is the last of Rabbi Student's series on the subject. I chose specifically this one because it includes links to the previous four posts (and most certainly not because of any reference to a certain aged television show in its title).