Plimpton 322

Introduction: One of the oldest mathematical texts

Forms of mathematics are at least as old as the species homo sapiens. Older in fact, provided we agree to classify certain animal behaviors, like the ability to differentiate quantities, to count, or even to employ geometric design in the building of shelters, as evidence of mathematical activity. If we require material evidence to justify the claim that mathematics was being consciously employed by humans, we can cite the record of bones, dated to about 10,000 years ago, used as tally sticks to mark inventories of a certain commodity, and there are artifacts of craftwork and architecture which are roughly this old that sport geometric designs of considerable sophistication. Notice, however, that these records of mathematical activity do not differ much in substance from those cited above from the animal world.

 Once humans moved from hunting and foraging into farming and later into forming cities, new challenges of life required new forms of thought, including mathematics that looked much more like what we would today identify as mathematics. Certainly, the first literate civilizations known to us also provided written proof of their mathematics as well.

 An amazing example of this is the clay tablet Plimpton 322, so called because it is item number 322 in a collection of artifacts assembled by G. A. Plimpton in the 1930s and donated to Columbia University in New York City. This tablet dates to the 19th century, BC, and can be traced to the Old Babylonian civilization that flourished in Mesopotamia, the fertile valley of the Tigris and Euphrates rivers (present-day Iraq). The first urban civilizations had sprung up in this area of the world some 1000 years prior to the authorship of Plimpton 322 in the wake of improvements in agriculture, trading, organization of labor, and political structures that developed over centuries.

 The unknown author of the tablet, hereafter called the Scribe, lived within a century or so of two very famous Babylonians. King Hammurapi (1792?-1750? BCE) wrote a code of law well-known for its "eye for an eye, tooth for a tooth" directives in deciding personal injury disputes among his subjects; the Patriarch Abraham, another contemporary of the Scribe, led his clan from the city of Ur on the bank of the Euphrates west into Canaan where some generations later they formed the theocratic Tribes of Israel.

 Perhaps the most important development to come out of the old civilizations of Mesopotamia is cuneiform (literally, "wedge-shaped") script, an improvement over earlier, more pictographic styles of writing. This innovation led to more efficient means of recording ideas and information, and allowed thinkers to communicate their thoughts more easily.

View the tablet
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last modified 8/28/02
Copyright (c) 2000.  Daniel E. Otero