Digging into the ancient cities of Mesopotamia, archaeologists have found about a hundred ancient tablets inscribed with mathematical calculations. Should you be really, really curious about such things, you can now see a dozen of the most famous tablets in one exhibit at the Institute for the Study of the Ancient World in New York. All of them seem to be practice exercises, or teaching aids; they show us the calculation of areas and volumes, but they give no formulas or theoretical statements. From these fragments of long-ago classrooms, a small band of scholars has for a century been trying to understand Babylonian mathematics. They have filled many books with speculations and interpretations, but what they agree on could be put down on a page or two.
For example, one famous tablet (above) shows that the length of the diagonal of the square is equal to the length of the side times a number that is about 1.42; was this worked out by careful measurement, or did the Babylonians understand the theory we call the Pythagorean?
One thing we do know is that Babylonian mathematics arose from the sciences of land management and irrigation, as practiced by scribes who managed the vast estates of temples and kings. Like writing, mathematics has its origin in bureaucracy: in the need to count, record, define, and control the world.