The end of 2001 has David Bowman as space baby starchild whooshing through hyper-awesome-whatever-space back to earth. The earth people say, this ending sucks, and they shoot nuclear missiles at him—or maybe they're shooting missiles at each other. Remember this was written back in 1968 when there was a Cold War between the U.S. and Russia, and everyone was worried about nuclear war and global incineration. In any case, no matter why the missiles are fired, nuclear weapons don't work on star children. They're too evolved.
Speaking of evolving, the last sentences of the book are about how star baby Bowman is master of the world, isn't sure what to do, and will think of something. That almost exactly parallels the last words we hear about old Moon-Watcher:
Now he was master of the world, and he was not quite sure what to do next. But he would think of something. (5.11-12)
So the end of the book loops back around to the beginning. It makes a parallel between Moon-Watcher, the evolved human who holds the future in his paws, to David Bowman, now a little moon himself circling the earth, who holds the future in his paws. The novel connects prehistoric man to future big head evolved man, and suggests that they both hold fate in their brains.
And more, they both hold fate in their brains because some aliens have pumped those brains up with super alien pumping intelligence juice (Can we get our hands on some?). Humans are getting on and transcending because someone is looking out for them. The future is in Bowman's thoughts, and his thoughts are alien. In 2001, humans are awesome because they aren't human—they're babies of the stars.