If you thought that the room-sized computers from the sixties were old, try watching this video by Apple Engineer Andrew Carol. Using only LEGO pieces, Carol rebuilds the Antikythera Mechanism invented by the Greeks in 100 B.C. to predict celestial events and eclipses.
The video explains how the Apple engineer built this ancient analog computer out of LEGO pieces and how the age-old system actually works. Math is certainly part of the equation in this construction and its amazing to imagine this kind of technology being invented in such an archaic era. What's even more incredible is how Carol manages to rebuild this invention entirely out of LEGO.
Although not digital, this age-old invention still counts as an analog computer and demonstrates how the Greeks were ahead of their time.