Ancient people used techniques of measurement to build ships, houses and temples and developed methods of calculating financial transactions. For most of the civilizations of the ancient world, these mathematical conventions were merely tools used to help people accomplish short-term tasks or solve practical engineering problems. But some clever individuals comprehended a more powerful use for these mathematical tools. The Babylonians applied the techniques of measurement on Earth to measure the heavens. The Greeks embraced a daring concept, that even the deepest mysteries of nature could be understood by human beings through the study of mathematics and geometry.

It is hard to separate the general development of mathematics from that of geometry, which the Greeks called "earth measuring." Formulas for calculating areas and volumes of geometrical shapes were known to the Babylonians, but the original concept of "proving" a geometrical theorem is usually attributed to the Greeks around...