The bedrock nature of space and time and the unification of cosmos and quantum are surely among science's great 'open frontiers.' These are parts of the intellectual map where we're still groping for the truth - where, in the fashion of ancient cartographers, we must still inscribe 'here be dragons.'
From a personal perspective, I am disappointed that we have yet to really achieve a full understanding of the origins of life on Earth. What was the spark that, billions of years ago, kickstarted the process of evolution that has brought us life as we know it today? I hope that we will get some answers to that in my lifetime.
And we should keep our minds open, or at least ajar, to concepts on the fringe of science fiction. Flaky American futurologists aren't always wrong. They remind us that a superintelligent machine is the last instrument that humans may ever design - the machine will itself take over in making further steps.
I'm a technological optimist in that I do believe that technology will provide solutions that will allow the world in 2050 to support 9 billion people at an acceptable standard of living. But I'm a political pessimist in that I am concerned about whether the science will be appropriately applied.
Scientists habitually moan that the public doesn't understand them. But they complain too much: public ignorance isn't peculiar to science. It's sad if some citizens can't tell a proton from a protein. But it's equally sad if they're ignorant of their nation's history, can't speak a second language, or can't find Venezuela or Syria on a map.
If you represent the Earth's lifetime by a single year, say from January when it was made to December, the 21st-century would be a quarter of a second in June - a tiny fraction of the year. But even in this concertinaed cosmic perspective, our century is very, very special: the first when humans can change themselves and their home planet.
It is mistaken to claim that global problems will be solved more quickly if only researchers would abandon their quest to understand the universe and knuckle down to work on an agenda of public or political concerns. These are not 'either/or' options - indeed, there is a positive symbiosis between them.
It might seem paradoxical that the biggest scientific instruments of all are needed in order to probe the very smallest things in nature. The micro-world is inherently 'fuzzy' - the sharper the detail we wish to study, the higher the energy that is required and the bigger the accelerator that is needed.
Most theorists suspect that space has an intricate structure - that it is 'grainy' - but that this structure is on a much finer scale than any known subatomic particle. The structure could be of an exotic kind: extra dimensions, over and above the three that we are used to (up and down, backward and forward, left and right).
The next humans to walk on the moon may be Chinese. Only China seems to have the resources, the dirigiste government, and the willingness to undertake a risky Apollo-style programme. If Americans or Europeans venture to the moon and beyond, this will have to be in a very different style and with different motives.
There are strong reasons for believing that space goes on beyond the limits of our observational horizon. There are strong reasons because if you look in opposite directions, conditions are the same to within one part in 100,000. So if we are part of some finite structure then, if the gradient is so shallow, it is likely to go on much further.