The central theme is the evolutionary development of humankind, as Animal says. And what does Clarke say about it? This is the understanding I've come to:
(I can't find my copy of "2001" at the moment so this is from memory.)
When one of the early humans begins to use his brain, he looks at a large, long bone, starts thinking about how the tribe on the other side of the watering hole is a problem, looks at the bone again, and begins to see a "(final) solution". He isn't sure yet exactly what he'll do, "But he would think of something." He throws the bone in the air, and in the movie it turns into a space plane, invented by his descendents a few hundred thousand years later.
That's us and we are soooo advanced and impressed with our technical knowledge! But something is missing. This is hinted at in the scene between the guy on the way to the moon and his daughter when he calls to wish her happy birthday. What's missing?--a certain humanity, replaced by technological substitutes. We must evolve beyond what we are today.
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After the astronaut, Dave, encounters the higher intelligence he evolves rapidly into the Starchild and returns to Earth, embryonic, yet mentally & spiritually light-years ahead of the humans he once was.
This is not in the movie, but is in the book:
As the Starchild nears the Earth, this unknown intruder is locked onto by every weapon available. The Starchild knows this, and isn't sure what do to next. "But he would think of something."
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Martin Luther King, Jr. understood this when he said, "We live in an age of guided missles and misguided men." Or something like that.
We must change how we deal with each other if we are to survive. Evolve or perish. Humanity has experienced the good and bad of the blessings of technological achievement. But our learning will be our destruction if we do not evolve wisdom to guide our use of it.
MRPLUTO