In the spirit of completeness and risking chronocentrism big time, I nominate Public Key Cryptosystems as something invented during the last two thousand years and which will remain useful long after the printing press will exist only in the (electronic) history books next to the steam engine. PKC has three incredible properties: perfect privacy, perfect authentication, and a reliable carrier of value and contracts — like gold used to be. All this in the digital environment where information can be easily and perfectly stored and copied. At a single stroke PKC transformed our vision of the asymptotic result of information technology from the 1984-ish nightmare to a realistic and ultimately attractive cyberspace where identity and privacy are not lost, despite of our (and Orwell's) commonsense intuition to the contrary.
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.