Move over, Archimedes. A researcher at Harvard University is finding that ancient Greek craftsmen were able to engineer sophisticated machines without necessarily understanding the mathematical theory behind their construction.
Recent analysis of technical treatises and literary sources dating back to the fifth century B.C. reveals that technology flourished among practitioners with limited theoretical knowledge.
“Craftsmen had their own kind of knowledge that didn’t have to be based on theory,” explains Mark Schiefsky, professor of the classics in Harvard’s Faculty of Arts and Sciences. “They didn’t all go to Plato’s Academy to learn geometry, and yet they were able to construct precisely calibrated devices.”
The balance, used to measure weight throughout the ancient world, best illustrates Schiefsky’s findings on the distinction between theoretical and practitioner’s knowledge. Working with a group led by Jürgen Renn, director of the Max Planck Institute for the History of Science in Berlin, Schiefsky has found that the steelyard — a balance with unequal arms — was in use as early as the fourth and fifth centuries B.C., before Archimedes and other thinkers of the Hellenistic era gave a mathematical demonstration of its theoretical foundations.
‘Craftsmen had their own kind of knowledge that didn’t have to be based on theory,’ explains Mark Schiefsky, professor of the classics in FAS. 
