Since the nineteenth century, thousands of cuneiform tablets dating to the Old Babylonian Period (c. 1900-1700 BCE) have come to light at various sites in ancient Mesopotamia (modern Iraq). A significant number record mathematical tables, problems, and calculations. In the 1920s these tablets began to be systematically studied by Otto Neugebauer, who spent two decades transcribing and interpreting tablets housed in European and American museums. His labors, and those of his associates, rivals, and successors, have revealed a rich culture of mathematical practice and education that flourished more than a thousand years before the Greek sages Thales and Pythagoras with whom histories of mathematics used to begin.
This exhibition is the first to explore the world of Old Babylonian mathematics through cuneiform tablets covering the full spectrum of mathematical activity, from arithmetical tables copied out by young scribes-in-training to sophisticated work on topics that would now be classified as number theory and algebra. The pioneering research of Neugebauer and his contemporaries concentrated on the mathematical content of the advanced texts; a selection of archival manuscripts and correspondence offers a glimpse of Neugebauer's research methods and his central role in this “heroic age.”
Highlights from the Exhibition
University of Pennsylvania Museum B6063
This multiplication table was written by a student named Gan-Gal as a demonstration of his skill as a scribe. Click here to learn more.
Image by University of Pennsylvania Museum. All rights reserved.
Yale Babylonian Collection YBC 7289
This famous tablet is a graphic witness that Babylonian scribes knew Pythagoras' Theorem and could calculate accurate square roots. Click here to learn more.
Image by West Semitic Research. All rights reserved.
Columbia University Plimpton 322
Plimpton 322 reveals that the Babylonians had a method of finding sets of three whole numbers such that the square of one of them is the sum of the squares of the other two, a classic problem in Number Theory. Click here to learn more.
Image by Christine Proust. All rights reserved.
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Plimpton 322 consists of trigonometric tables in a very condensed form to economise on cuneiform space. The angles are from 30 degrees to 45 degrees, though for cotangents this gives the information for 45 degrees to 60 degrees. The great mystery as to whether the first column does or does not include 1 is explained by sec squared exceeding tan squared by 1, so this coluimn can economically show both. Finding the square roots gives secants and tangents for which there are columns from which sines or cosecants can be calculated. We are not told this, but the other degrees can be calculated by the half angle formula cotu+cosecu equals cot u/2.
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