How did ancient Greeks build a computer over 1,000 years ahead of its time?

By turning astronomy into gear trains. The Antikythera mechanism, with what scans suggest were 35 meshing bronze gears in a wooden case roughly 34 by 18 by 9 centimetres, is a hand-powered device built by Hellenistic Greek scientists sometime between about 205 and 87 BC, designed to model the motion of the Moon and Sun through the zodiac, predict eclipses decades ahead of time, and even track the four-year cycle of the ancient Olympic Games. It is the oldest known analogue computer, and machines of similar complexity did not appear again until the 14th century, in western Europe.

Sponge divers found it in 1900–1901, pulling it from a Roman shipwreck off the Greek island of Antikythera along with bronze and marble statues and other treasure. The mechanism itself looked like nothing special, just a corroded lump of bronze and wood, and it sat ignored in an Athens museum for two years while staff worked on the more obviously valuable statues. It took until 1902 for anyone to notice that one chunk of 'rock' actually had a gear wheel embedded inside it. Even then, most scholars judged it too complex to have been built in the same period as the other finds.

It took decades of slow technological catch-up to prove them wrong. A science historian named Derek de Solla Price picked up the investigation in 1951, and by 1971 he and a physicist were using X-rays and gamma rays to image the mechanism's 82 separate fragments. A Cardiff University team pushed the imaging further in 2005, revealing a system of 35 meshing bronze gears, the largest about 13 centimetres across with 223 teeth, intricate enough to reproduce the Moon's genuinely irregular orbit, a motion studied in the 2nd century BC by the astronomer Hipparchus, who may have been consulted on the machine. Further reading of its inscriptions in 2016 found numbers tied to the cycles of Venus and Saturn.

Whoever built the Antikythera mechanism had compressed real astronomical theory into bronze, well over a thousand years before western Europe produced machines of similar complexity.