Thesis Statement: The development of mathematics in the ancient world, at one time traced back to the ancient Greeks, is now understood to have originated with the Mesopotamians and Egyptians whose mathematical systems reveal both striking similarities and important differences in form, usage, and cultural significance.

Campbell-Kelly, Martin, Mary Croarken, Raymond Flood, and Eleanor Robson. The History of Mathematical Tables. NY: Oxford University Press, 2003.

From primary sources, the authors ascertain that the ancient Mesopotamians rarely expressed their mathematical equations and information in tables though the form has existed in writing for over 4500 years. Rather, they typically wrote them in the form of lists. They relate this to the fact that the sexagesimal place value system had not yet been developed. Even upon its development in the eighteenth century BCE, it is estimated that it was still only used in a small percentage of documents. By contrast, in scientific and mathematical developments over the last 500 years, tables have been instrumental in advancements and communicative styles.

Friberg, J. Unexpected links between Egyptian and Babylonian Mathematics. Hackensack, NJ: World Scientific, 2005.

Friberg explains the modern sources of information regarding both Egyptian and Babylonian mathematics and she discusses their similarities in depth. Ancient Mesopotamian texts include a very well established number of texts recorded from clay tablets which had been carved using the cuneiform script, dating from the second millennium B.C. Ancient Egyptian texts stem from a lesser number of original sets of papyrus texts from three different time periods. Friberg then explores the extensive similarities between particular texts, such as the presence of geometric progressions in both Babylonian and Egyptian sources. The presence of metric algebra, similar division reasoning, other types of geometry, and the mathematical roots of economics are all addressed with thourough analyses of the various texts.

Katz, Victor J. and Annette Imhausen. The Mathematics of Egypt, Mesopotamia, China, India, and Islam. Princeton: Princeton University Press, 2007.

Katz begins by discussing the former Western bias regarding mathematical history and the more recent advances in understandings as a result of archaeological finds in different parts of the ancient world. In chapter one, the history of Egyptian mathematics is discussed with the emphasis on both the mathematical understandings revealed in particular texts through problems, and the theoretical communications but the ways the Egyptian used mathematics. The author includes a section on the administrative usage of the Egyptian mathematics system for the government of their civilization. In chapter two, the Mesopotamian mathematics history is addressed, specifically on the various periods of mathematical advances in the region. The advances of the Uruk, Shuruppag, Nippur, and Umma civilizations of the third millennium BCE are explored as well as the old Babylonian period of the second millennium BCE.

Kline, Morris. Mathematical Thought from Ancient to Modern Times. NY: Oxford University Press, 1972.

Kline begins with a discussion of the origins of mathematics in general, detailing the development of number systems, arithmetic, algebra, and geometry in both Mesopotamia and Egypt. He argues that mathematics, as a discipline, did not exist before the ancient Greeks, but that the groundwork was set by earlier civilizations for their innovations relating to mathematics. Specifically, he provides the history of Mesopotamian and Egyptian mathematics as it is known from primary sources. He connects the rise of mathematics to the formation of agricultural civilizations, and to the Mesopotamians of the fertile Nile River valley. He points out the different connections between the political activities in the region and the resulting spread of mathematical knowledge across larger regions.

Selin, Helaine and U. D’Ambrosio. Mathematics across Cultures: the History of Non-Western Mathematics. Boston: Kluver Academic, 2000.

Extending the body of work compiled on the history of ancient mathematics, Selin’s many articles address the connections between mathematics and culture, the transmission of intellectual capital from East to West, and the individual mathematical achievements of many different ancient cultures. The mathematics of Mesopotamia is explored in an essay by author Eleanor Robson entitled “The Uses of Mathematics in Ancient Iraq: 6000-600 BC,” including both advances the culture made, and the impact that these advances had on their society. In other words, Robson analyzes both the knowledge the civilization obtained, as well as the many ways they put it to use within their society. In another relevant article by James Ritter entitled “Egyptian Mathematics,” Egyptian mathematics are discussed, including how it was used within different cultures and the modern interpretations of its meaning.