Joe Traub already nabbed the invention I would have chosen; empirical method. So I'll stake out a different claim. For present purposes, I'll claim that the most significant invention of the last 2000 years was the human ego.
The ego I'm talking about is the self-concerned human that Harold Bloom credits Shakespeare with having invented. It's the thing that William Manchester finds definitively missing in the Medieval mind. Jostein Gaarder, in his children's philosophy novel, Sophie's World, blames St. Augustine for inventing it. It's what the fuss is about in Nietzsche. It's what exists in existentialism.
In truth, I'm not entirely convinced that I don't find good evidence of this creature in pre-Christian/Common-era texts. (Thomas Cahill thinks it was a gift from the Jews.) But it does seem that the sense of individual self, outfitted with moral responsibility, free will, consciousness, and — most importantly — neurotic self-obsession, at one time did not exist, and then did.
That same sense of self is now being challenged by AI-ish members of the EDGE community. Perhaps it will disappear, just as it once appeared. So it is reasonable to think of the ego as a natural inhabitant of approximately the last 2000 years.
One could argue that the ego had to precede empirical method. The shift from pure rationality to empiricism relied on an acknowledgement of differing perspectives of observation (while pure rationality was thought to be independent of personal perspective). So the self was needed in order to have a starting point from which to pose theories and to make measurements in order to test them. Only an ego can have imperfect enough knowledge to make mere guesses about what's going on in the universe, and the hubris to test and improve those guesses.
I personally hope the ego survives the computer.