Victor J. Katz

Annette Imhausen

In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

A Sourcebook

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

Tanja Pommerening

Ancient cultures have left written evidence of a variety of scientific texts. But how can/should they be translated? Is it possible to use modern concepts (and terminology) in their translation and which consequences result from this practice? Scholars of various disciplines discuss the practice of translating ancient scientific texts and present examples of these texts and their translations.

Methodological Aspects with Examples

Translating Writings of Early Scholars in the Ancient Near East, Egypt, Greece and Rome

A survey of ancient Egyptian mathematics across three thousand years Mathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BC—and the earliest hints of writing and number notation—to the end of the pharaonic period in Greco-Roman times. Drawing from mathematical texts, architectural drawings, administrative documents, and other sources, Annette Imhausen surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.

A Contextual History

Mathematics in Ancient Egypt

Moritz Epple

Falk Müller

Many of us view the world of science as a firm bastion of knowledge, with each new discovery and further illumination adding to an unshakable foundation of natural truths. Weak Knowledge aims to rattle our faith, not in core certainties of scientific findings but in their strength as accessible resources. The authors show how, throughout history, many bodies of research have become precarious due to a host of factors. These factors have included cultural or social disinterest, feeble empirical evidence or theoretical justifications, and a lack of practical applications in a given field's findings. This book brings together cases from a range of historical periods and disciplines, ranging from personal medicine to climatology, to illuminate the specific forms, functions, and dynamics of so-called "weak" bodies of knowledge.

Forms, Functions, and Dynamics

Weak Knowledge

Daliah Bawanypeck

This volume is addressed to historians of science, Egyptologists and Assyriologists dealing with the history of early science. It presents the proceedings of two workshops held at the Goethe-University Frankfurt/Main, focusing on traditions of systematic knowledge in Ancient Egypt and Mesopotamia. Assuming that written knowledge was preserved and transmitted intentionally in both cultures, paradigms of knowledge can be reflected by the texts. Although the available source material is subject to their find spots and the vagaries of preservation, by asking specific questions the sources can provide insights into the work of the ancient scholars. The text corpora presented in this volume come from the fields of medicine, magic and ritual, astronomy, mathematics and law. The authors use the sources to provide overviews of the discussed knowledge areas and to discuss certain aspects of the traditions in more detail.

Proceedings of Two Workshops Held at Goethe-University, Frankfurt/Main in December 2011 and May 2012

Traditions of Written Knowledge in Ancient Egypt and Mesopotamia

Medicine, astronomy, dealing with numbers even the cultures of the pre-modern world offer a rich spectrum of scientific texts. But how are they best translated? Is it sufficient to translate the sources into modern scientific language, and thereby, above all, to identify their deficits? Or would it be better to adopt the perspective of the sources themselves, strange as they are, only for them not to be properly understood by modern readers? Renowned representatives of various disciplines and traditions present a controversial and constructive discussion of these problems."

Annette Imhausen

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