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Friday, December 24, 2010

NYU Exhibit: Babylonian Mathematics

New York University's Institue for the Study of the Ancient World has extended its exhibition, "Before Pythagoras: The Culture of Old Babylonian Mathematics" through January 23th, 2011.

From the exhibition's description:

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.”

The cuneiform tablets illustrate three major themes: arithmetic exploiting a notation of numbers based entirely on two basic symbols; the scribal schools of Nippur; and advanced training. Many of the latter problems were much more difficult than any that they would have to deal with in professional scribal careers, and their solutions depended on principles that, before the rediscovery of the Babylonian tablets, were believed to have been discovered by the Greeks of the sixth century BCE and after.

From a CNN article about the exhibit, "Pythagoras, a math genius? Not by Babylonian standards":

"They are the most sophisticated mathematics from anywhere in the world at that time," said Alexander Jones, a Professor of the History of the Exact Sciences in Antiquity at New York University.

He is co-curator of "Before Pythagoras: The Culture of Old Babylonian Mathematics," an exhibition at the Institute for the Study of the Ancient World in New York.

"This is nearly 4,000 years ago and there's no other ancient culture at that time that we know of that is doing anything like that level of work. It seems to be going beyond anything that daily life needs," he said.

Many scribes were trained in the ancient city of Nippur in what is now southern Iraq, where a large number of tablets were discovered between the mid-19th century and the 1920s.

Typical problems they worked on involved calculating the area of a given field, or the width of a trench.

These problems, says Jones, required the kind of math training taught to American Grade 10 students, but not in a format we would now recognize.

"It's not like algebra, it's all written out in words and numerals but no symbols and no times signs or equals or anything like that," he said.

This system, and the lack of recognizable Western mathematical symbols such as x and y, meant that it was several years before historians and archaeologists understood just what was represented on these tablets.

It took a young Austrian mathematician in the 1920s, named Otto Neugebauer, to crack the mathematical system and work out what the ancient Babylonians were calculating. But despite his advances, it is only recently that interest in Babylonian math has started to take hold.

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