Linear Interpolation and a Clay Tablet of the Old Babylonian Period

In a brief historical note we look for the earliest occurrence of interpolation that the literature can provide. The search leads us to a problem of compound interest on a clay tablet from the Old Babylonian period (c. 2000–1700 BC), and to commentaries on it by Neugebauer in [5] and [6], and by Thureau-Dangin in [7] and [8]. The scribe who wrote this tablet does not give an explicit account of his method; nevertheless, after discovering and correcting an error by the scribe, the analyses of Neugebauer and Thureau-Dangin establish beyond reasonable doubt that linear interpolation must have been used to solve the compound interest problem. These commentaries are not easily accessible, and hitherto they have been known only to specialists in the field. Our present purpose is to draw them together in a review which may help to make an ancient mathematical episode more generally known, and place it at the historical beginnings of interpolation.