Not to nitpick, but I'm not sure the nature of time is so indisputably the greatest remaining mystery. The nature of consciousness, life, and death can all certainly give it a run for its money. Incidentally, would anyone happen to have a direct link to a version of this article that could be read without enabling javascript?
Yes. For me the greatest remaining mysteries are more in this order. 1. Nature of Life (we are still nowhere near understanding how it arose or how living organisms work in all their intricate detail). 2. Nature of Consciousness - what is consciousness, how can living matter instantiate it, how can we quantify it, etc? 3. Origin of the Universe 4. Why do we seem so alone in the Universe? 5. Resolving Quantum Mechanic…
Not only that, but do you have an existence before you are born?
This might be a religious question to some, or perhaps involve a religious answer, but religion need not be involved. It's possible that in some not yet understood way an individual might exist before they're born and are somehow incarnated or embodied in to matter or the world as we know it when they're born.
Sure, it might sound kooky or something that science might never be able to answer (or maybe it could, who knows?). But the point is that that's all part of the mystery of life, and the answer could be a metaphysical or ontological one, not necessarily a religious one.
Another question regarding the nature of life is what exactly does it take to go from a non-living substance to a living one. In some way this is a question of definitions (which is difficult enough and controversial enough on its own), but even given an agreed-upon definition of life, it might not be clear how exactly the process from non-living to living take place, or at which point the non-living becomes living.