If I take the word "important" to suggest an invention that will have "the greatest impact on the next 2000 years" (after all, it is the future that counts, not the pa st!),then the invention of the programmable computer seems to me to be the most important invention of the last 2000 years. ( I am not including in my list of possibilities here ideas and concepts, since I don't think they qualify as inventions, and I suspect that the intent of the question is to explore technology, not ideas...). While the printing press certainly revolutionized the world in its time, computers will govern everything we do in the next 20 centuries. The development of artificial intelligence will be profound, quantum computers may actually be built, and I am sympathetic to the idea I first heard expressed by my friend Frank Wilczek, that computers are the next phase of human evolution. Once self-aware, self-programmable computers become a reality, then I have a hard time seeing how humans can keep up without in some way integrating them into their own development. The only other invention that may come close is perhaps DNA sequencing, since it will undoubtedly lead to a new understanding and control of genetic and biology in a way which will alter what we mean by life.
To arrive at the edge of the world's knowledge, seek out the most complex and sophisticated minds,
put them in a room together, and have them ask each other the questions they are asking themselves.