115 years ago, divers found a hunk of bronze off a Greek island. It changed our understanding of human history. One hundred fifteen years ago, an archeologist was sifting through objects found in the wreck of a 2,000-year-old vessel off the Greek island Antikythera. Among the wreck’s treasures — beautiful vases and pots, jewelry, a bronze statue of an ancient philosopher — was the most peculiar thing: a series of brass gears and dials mounted in a case the size of a mantel clock. Archeologists dubbed the instrument the Antikythera mechanism. The genius — and mystery — of this piece...