The ancient Greeks' stories and achievements essentially taught the world how to think. That is, the Greeks recognized that there was probably a way to do something better, even if humans could currently not conceive of it.
Aristotle predicted that industrialization, e.g. in the form of what we would now call robots, would abolish slavery by making it uneconomical. The Industrial Revolution proved this prediction accurate about 2000 years later.
The Greek legend of Daedelus involved human-powered flight, and gave people the idea that they might indeed be able to fly one day. ("“The desire to fly,” wrote Wilbur Wright, “is an idea handed down to us by our ancestors who, in their grueling travels across trackless lands in prehistoric times, looked enviously on the birds soaring freely through space, at full speed, above all obstacles, on the infinite highway of the air.”")
The legends of Hercules literally transformed the world through Alexander the Great, who cited Hercules as his role model (and who was even depicted as wearing Hercules' lion skin). Hercules often had to solve problems by thinking about them, and he altered geography by diverting two rivers to clean out the Augean Stables. Alexander later altered geograpy by building a causeway or isthmus to attack the fortress of Tyre, and similarly came up with a very innovative solution to the Gordian Knot.
The Greek legend of Hephaestus said that the god of engineering and mechanical crafts created mechanical men (robots) to assist him in his work.
Greeks showed that steam could do useful work, and also (Archimedes) the value of mechanical advantage; he purportedly used machines to destroy enemy warships and, according to some stories, used an array of mirrors to direct concentrated sunlight against enemy ships to set them on fire. Modern solar furnaces use exactly that approach today.
The Antikythera mechanism is particularly impressive because it must have been hand-made, without modern machine tools and without modern metrology methods, but nonetheless performed its intended function
The ancient Greeks' stories and achievements essentially taught the world how to think. That is, the Greeks recognized that there was probably a way to do something better, even if humans could currently not conceive of it.
The Antikythera mechanism is particularly impressive because it must have been hand-made, without modern machine tools and without modern metrology methods, but nonetheless performed its intended function