I once had a conversation with someone whom lamented how dull the world seemed now that everything had been discovered. I understood the sentiment from a perspective in the spirit of Aldo Leopold's rhetorical question: "of what avail are the forty freedoms without a blank spot on the map?". (Leopold was more referring to the sense of Wilderness, as opposed to geography). Even from this perspective, and the fact that this sentiment was echoed by many famous scientists in the 19th century, I still find this attitude very surprising.
If The Map is limited to Earth, I'd agree that most of the low-hanging fruit has been mapped, yet that still leaves most of the ocean floor as nearly a complete mystery. Satellites & depth sounders have made some rough topographical sketches, but as to the nature of what lies beneath is still mostly undiscovered. Amazingly, the most active research vessel, Alvin, predates the Apollo mission, and has yet to effectively be replaced. With the exception of petroleum surveys and military vessels, most of the abyss remains literally in the dark. We have better maps of Luna and Mars than the Atlantic!
And that's just on our own planet. The surface of Venus is another extrapolation by radar (most detailed resolution is 150km), with the sole exception of a few photos from the surface. Similarly, Titan is currently being mapped (next flyby May 21st!), but with mostly a rougher resolution and short swaths during flybys (despite 5 years in orbit, only 38% is mapped). We have nice photos from Europa, but only of the surface ice layer; what lies beneath the ice is still conjecture, although evidence is consistent with a global ocean! We only have educated guesses as to what Pluto and Ceres look like (stay tuned for New Horizons and Dawn). And this is just our backyard! We have just begun detecting planets (biased towards top-heavy), and it will be a long time before we can infer the actual surface of extra-solar terrestrial planets... and to actually explore one, even as fuzzy as a fast Pluto flyby, is only a crazy dream.
But that's only geographical unknowns. More fundamental is our lack of understanding, well, practically everything. Pick any discipline; biology, physics, psychology and ask some naively simple questions;
"how did life begin?"
"what is the universe mostly made from?"
"what is consciousness?"
Despite having 6.5 billion people roaming the surface like so many ants, and whizzing satellites, we still have only discovered about 10% of the living species (likely even less than that) -- and that's only counting those species that someone made a few sketches and published a quick paper. The number of species we have more than superficial descriptions are about 1%. It's likely a scoop of dirt from your backyard contains species of protists & fungi that are completely new to science. Now imagine how little we know of extinct species only preserved helter-skelter in the fossil record...
As Bryson noted in 'A Short History of Nearly Everything', "we live in a universe whose age we can't quite compute, surrounded by stars whose distances we don't altogether know, filled with matter we can't identify, operating in conformance with physical laws whose properties we don't truly understand."
A few questions I'd like answers to are:
1. Was there a Cambrian Explosion, or simply a fossilized manifestation of an existing progression? If the Explosion resulted in many new phyla, by what mechanism is DNA currently restricted to its form (or to rephrase this question, how rigid is DNA to evolving from any existing gene pool of a species?)
2. What are the causes of mass extinctions? For instance, what the K-T event caused solely by meteor impact, or was it a combination of impact that led to other calamities such as increased volcanism -> climate change -> sea level rise -> hypercanes -> ozone depletion & unstable climate regimes?
Why did some orders, such as turtles and crocodiles survive mostly intact, and other orders (mammals, birds) go through intact, but then radiated into many new species?
3. What is the climatic history of Mars and Venus? Why does only Earth exhibit Plate Tectonics?
4. How did life arise? Do other planets have complex organics (Mars, Europa, Titan, Triton, Ceres, Ganymede, Venus) that hint at events critical to prebiotic chemisty?