You know the feeling when there’s something that nags away at the back of your mind; something that just doesn’t fit. Like the Antikythera Mechanism.

Years ago, I read an article in Scientific American about a strange device with gears, that dated from centuries before clockwork was invented. Something astronomical.

At the time, I was a professional astrophysicist, working with the Ryle Telescope at Cambridge to study how heavy stars die as supernovae. The telescope relied on a state-of-the-art electronic computer, housed in a copper-lined room. Nothing to do with ancient gears.

Or was it?

Recently, I was tasked to write a chapter on the astronomy of the ancient Greeks. And that nag came back: what was it about the ancient gears, which had never seemed to mesh into the history of science?

As I mulled, I was discussing prehistoric astronomy - Stonehenge and all that – with an old friend, Clive Ruggles, the world's first Professor of Archaeoastronomy. He said "I assume you'll be going to the forthcoming conference in Athens, on the Antikythera Mechanism. There are going to be some interesting new results..."

Sad to say, my deadlines meant I never got to the conference. (You can find out what happened – including the behind-the-scenes stories – in an excellent new book by Jo Marchant.) But it rekindled my interest; and the Antikythera Mechanism took pride of place in my chapter on Greek astronomy.

While I'd always been taught that the ancient Greeks were the first great thinkers, the Antikythera Mechanism reveals that there were great engineers, too. For this device is not just a set of carefully hand-cut gears – but the world's first computer. As an astrophysicist in Cambridge, I was operating merely the latest – electronic – version of a device that had existed for two thousand years...

How did the world's first computer work? Read on to find out more...