The Mathematics of Egypt, Mesopotamia, China, India and Islam

The Mathematics of Egypt, Mesopotamia, China, India, and Islam:  A Source Book.  Victor J. Katz, Editor, 2007, xiv + 712 pp, illustrations, tables, $ 75.00 hardcover.  ISBN 13: 978-0-691-11485-9.  Princeton:  Princeton University Press.  http://www.press.princeton.edu

The instructive introduction to this monumental contribution to the company of source books in mathematics, while recognizing deficiencies in general histories of mathematics published as late as 1972, concisely summarizes the import and impact of the five civilizations.  Each culture has its own chapter with common format:  preliminary remarks and/or introduction, selection of texts with historical and mathematical commentaries, and appendix including sources and references.  An index of mostly proper names ends the book.  The editors of the respective chapters, in order, are Annette Imhausen, Eleanor Robson, Joseph W. Dauben, Kim Plofker, and J. Lennart Berggren, each an expert in the field offering their own translations from original sources.  Imhausen, Robson, and Berggren comment judiciously upon the art of translation.  Seriously missing are maps to accompany each section.  I recognized only 25 of the at least 72 place names mentioned.  Despite this single deficiency, the volume offers much material to be explored.  A few of the gems I found are these.

Imhausen, noting the few but rich resources for Egyptian mathematics, presents extracts from non-mathematical works (letters of officials) that give cultural perspective to the math texts (Rhind papyrus and fraction tables). Robson, besides offering new translations of some sixty Mesopotamian tablets that deepen the history of the field, informs us that people who would become professionally literate had to be proficient in both numeracy (use of numbers) and mathematics (development of concepts and skills).  Dauben not only clearly explains and exemplifies the Chinese algorithms for the four arithmetic operations, but details and contrasts with other texts the oldest extant yet recently discovered (1984) Chinese mathematical treatise, Suan shu shu (Book of Numbers and Computation, ca. 200 BCE). After explaining the tenuous origins of ancient Indian mathematics and discounting the book Vedic Mathematics (1965) as without foundation “in the traditional study of the Vedas,” Plofker observes that the mathematics needed for astronomy and prosody were often versified, emphasizing “the close intellectual ties between Sanskrit mathematics and grammar . . .”   In addition to explaining Arabic names and arranging his selections in a rising hierarchy of math topics, Berggren introduces many of us to the “perfect compass” for drawing conic sections.

The book belongs in the library of every person and place interested in the history of mathematics.

Barnabas Hughes, O.F.M., California State University, Northridge

See also the MAA Review by Fernando Q. Gouvêa.