Replica of a Babylonian Clay Tablet - Plimpton 322

Both written language and written tables originated in the ancient Middle East. Scribes kept lists of numerical data, such as the number of sheep and goats transferred on different days of the month. A few of the clay tablets on which they wrote survive to this day. A tiny number of these tablets have rows and columns arranged in tables.. The rows may give totals of number of various forms of livestock transferred over time, with a column for the animals that were the responsibility of each person charged with such matters. Such documents date from around 2020 BCE.

Those learning and teaching mathematics in ancient Iraq rarely displayed information in tabular form. However, in 1922 the American collector George Plimpton purchased such a tablet. This replica of that unusual object was made in 1957 by L. C. Eichner. Plimpton donated the original object to Columbia University in the 1920s. The original dates from about 1800 BCE, and reportedly was excavated in what is now Iraq at the side of the ancient city of Lasra. The portion of the tablet that survives has four columns of numbers written in the sexagesimal (base 60) system of numbers.

Otto Neugebauer and A. J. Sachs offered a modern mathematical interpretation of the tablet in 1945. They noted that the numbers in the second and third columns of the table might represent the squares of the length of the shortest side and of the hypotenuse of right triangles, and interpreted the table as relating to Pythagorean triples. As the name Pythagorean suggests, such numbers had previously only been associated with later Greek mathematics. Other scholars have suggested that this was a part of a larger table of reciprocal numbers and related geometric figures, compiled by a teacher wishing to have examples of such reciprocals available for use in assignments.

References:

A. Aaboe, Episodes from the Early History of Mathematics, New Haven: Yale University Press, 1964, pp. 30–31.

O. Neugebauer and A. J. Sachs, Mathematical Cuneiform Texts, New Haven: American Oriental Society and American Schools of Oriental Research, 1945.

O. Neugebauer, The Exact Sciences in Antiquity, Providence, R.I.: Brown University Press,1957, pp. 36–40 and Plate 7a.

E. Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322,” Historia Mathematica, 28 (2001), pp. 167–206.

E. Robson, “Words and Pictures: New Light on Plimpton 322,” American Mathematical Monthly, 109 (Feb 2002), pp. 105–120.

E. Robson, “Tables and Tabular Formatting in Babylon and Assyria, 2500 BCE–50 CE,” The History of Mathematical Tables from Sumer to Spreadsheets, eds. M. Campbell-Kelly, M. Croarken, R. Flood and E. Robson, Oxford: Oxford University Press, 2003, pp. 18–47.

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