There are, it seems to me, just two fundamental scientific questions that, for very different reasons, we may have no possibility of answering with any certainty.
One question is so fundamental that it is arguably not a scientific question at all: It's the big how and why question of existence itself. Although there are many technical questions still to be answered, as a mathematician, I find myself broadly content with science's explanation of how the physical universe — including time itself — sprang into being: the symmetry breaking, primordial fireball we call the Big Bang, followed by the subsequent evolution into the universe we see today. But that is simply an explanation of the mechanics of the universe of our experience and perception. It leaves us with a lingering question of how, and perhaps why, the framework arose in which the Big Bang took place in the first place — be that framework one in which our universe is the only one there is and has ever been, or one that cycles in "universe time" (whatever that is), or maybe some kind of multiple universe scenario.
I accept that this is not really a scientific question. Science only addresses the how of our own universe, starting just after the Big Bang. But my curiosity, both as a scientist and more generally just as a thinking person, cannot help but dwell from time to time on the biggest question of all — the question that for those having a deep religious faith seems to find an answer in the phrase "God made it that way." (An answer that I find even more incomprehensible in a world where millions of human beings believe that that same God authorizes his chosen emissaries to fly jet airliners full of humans into buildings full of other humans.)
My second fundamental question is clearly a genuine scientific matter. In fact, it is a technical question about evolution by natural selection. Exactly how and why did a species (namely, us) develop that has the capacity to think abstractly, that possesses language, and that can reflect on its own existence? Like the big existence issue, this is a question that has enormous significance for us, as humans. And that makes it the more frustrating that we may find ourselves unable ever to answer it with any certainty.
In my recent book The Math Gene, I summarized arguments to show that the possession of language (i.e., a symbolic communication system with a recursive grammatical structure allowing for the production and comprehension of meaningful utterances of unlimited length) and the ability for "offline" thinking (reasoning about the world in the absence of direct input from the environment and without the automatic generation of a physical response) are two sides of the same coin. Implicit in that argument is that this ability also brings with it the capacity for self-reflective, conscious thought. (I also argued that such a mental capacity also yields the potential for mathematical thought.) Thus, we are talking here about the capacity that makes us human, and in so doing makes us very different from any other species on Earth.
The best evidence we have from anthropology is that our ancestors acquired this capacity some time between 75,000 and 200,000 years ago. (The evidence is in the form of manufactured artifacts that early humans left behind, which indicate such a level of abstract thinking and communication.) But how — and in terms of natural selection, why — did our ancestors acquire this capacity? All we know for sure is that it came at the end of a three-and-a-half-million year period in which the average brain size of our ancestors grew to roughly its present level, approximately nine times larger than is normal for a mammal of our body size and about twice that of a present-day ape.
What makes this question particularly hard is that, at least in terms of functionality (as opposed to brain structure), the acquisition of syntactic structure (i.e., the structure that enables us to create complex sentences or to reason abstractly about the world) is an all-or-nothing event. As linguists have pointed out, you cannot have "half a grammar". True, in theory you can have grammars without, say, passive constructions, but there is no chain of gradually more complex grammars that starts with protolanguage — simple subject-predication utterances — and leads continuously to the grammatical structure that is common to all human languages. The chain has to start with a sudden jump. Although the acquisition of language was a major functional change in brain capacity, there is no reason why that jump was not the result of a tiny structural change in the brain. But what propelled the brain to reach a stage where such a change could occur? And what exactly was that small structural change? This would surely be a minor technical question about one detail, among thousands, of evolutionary history, were it not for the fact that it was this single change that made us human — that made it possible for us to ask these how and why questions, and to care about the answers.
One oft-repeated suggestion for the natural selection advantage that language provides is that it enabled the communication of more complex thoughts and ideas than was previously possible. But that suggestion falls down immediately when you realize that such communication can only arise when the brain that is doing the communicating is able to form those complex thoughts and ideas in the first place, and that capacity itself requires a brain having grammatical structure.
It seems likely that the two sides of this particular coin, thinking complex thoughts and communicating them, arose at the same time, and indeed it could have taken both aspects together to spur the development that led to their acquisition. But we are still left with the tantalizing question that the obvious natural selection advantages this capacity provides only came into play after the capacity was in place. Just what led to and prompted that jump remains a mystery.
There has been, as you might imagine, no shortage of attempts to provide an explanation, but so far I haven't seen one that I find convincing, or even close to convincing. (I mention some in The Math Gene, and give pointers to further reading on the matter.) And even if someone produces a compelling explanation, it seems we will never know for sure. When our early ancestors died, their brains rapidly rotted away, leaving nothing but the skulls that contained them. And even if, by some fluke, we found an intact brain from some early ancestor, buried deep in the ice of a glacier somewhere, how could that help us? Dissecting an object as complex as the human brain tells us virtually nothing about what that brain did — how it thought and what it thought about.
Our higher brain functions could just have been an accident. Of course, all evolutionary changes are accidents. What I mean here is that it may be purely accidental that the structural change in the brain that gave us language and abstract, symbolic thought did in fact have that effect. It might just be, as some have suggested, that the brain grew in complexity as a device for cooling the blood, and that language and symbolic thought are mere accidental by-products of the body's need to maintain a certain temperature range. (Certainly, the brain is an extremely efficient cooling device, as illustrated by the fact that putting on a hat is an extremely efficient way of staying warm when we go skiing.) Personally, I don't buy the cooling mechanism explanation. But unless and until someone comes up with something more convincing, I see no way we can rule it out.
For all our huge success in telling the story of how life began and evolved to its present myriad of forms, it seems likely that we may never know for certain exactly what it was that gave us the one thing we value above all else, and the thing that makes us human: our minds. If there is one question I would like to answer above all others, it is this one.