The Antikythera Mechanism is an artifact found on a sunken boat a century ago. It's a device that has bronze gears and apparently was used to do some sort of calculation... by ancient Greeks, because it's about 2000 years old.
Its specific function has always been a mystery because of the deteriorated condition of the device, but new techniques (including advanced X-ray imaging) have revealed writing on the back side of the mechanism, indicating it was used as an astronomical tool. The names of the 12 months are inscribed, and other markings indicate it was used to predict solar eclipses and the timing of the four-year Olympiad.
You can read the NYT article for details, which are very cool. But I want to add something here. Ancient people weren't stupid. They were just as smart as we are, but they didn't have the tools we do now, including computers or even algebra and calculus. Their knowledge was derived almost solely through observations. Sometimes, such as with Aristotle, they simply decreed things to be true that weren't (Aristotle said a lot of things that obviously didn't jibe with very simple observations), but in many cases they took painfully detailed notes of the night sky, timing events over centuries to such a degree that they were able to predict eclipses and other phenomena.
Don't forget, they knew the Earth was a sphere, and Eratosthenes was able to measure the circumference of the Earth to remarkable accuracy. These guys weren't fools.
It's easy to forget that. But one thing they lacked that gave them a huge advantage in astronomy was light pollution. Many ancient civilizations had unfettered access to the night sky, and agricultural peoples were tied to the sky as firmly as they were to the ground, using astronomical events to time their farming activities. Nowadays, fewer people can see stars at all, and we've lost something precious and wondrous.
So it shouldn't be a surprise that 2000 years ago, the Greeks had a fantastic knowledge of the sky's behavior, and built devices to help them measure it. The surprise is that we're surprised.