The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook

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Princeton University Press, Aug 5, 2007 - Mathematics - 685 pages
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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.


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Victor Katz's body of work has been enjoyed for over 15 years, and several of his contributors almost as long. This book began and ended with practical Egyptian mathematics, omitting validated abstract Egyptian arithmetic facts.
Imhausen's review of the mathematical texts mentioned algorithmic aspects of certain calculations. Middle Kingdom scribes used an Old Kingdom doubling method to prove the arithmetic accuracy of many answers. At other times, scribes wrote in personalized shorthand styles, skipping over initial and intermediate steps, jumping to answers, leaving readers with many questions. To accurately parse each problem as the ancient scribes thought and calculated, missing initial and intermediate steps are required to be teased from hard-to-read raw data.
Despite being unobserved by 20th century scholars abstract arithmetic was used in the 1800 BCE Akhmim Wooden Tablet (AWT) as reported on Wikipedia
and journal articles that mention ancient theoretical building blocks. The ancient theoretical building blocks, against which muddled 20th century practical metrology information is increasingly measured, are being parsed by 21st century scholars that revisit transliterated hieratic data bases.
For example, a hekat unity was abstractly divided into binary quotients and scaled remainders. The AWT set of theoretical facts was not mentioned in Katz's book. One side of the hekat unity division method was proven by Hana Vymazalova, a Charles U. grad student in 2001 as (64/64). The method divided (64/64) by 3, 7, 10, 11 and 13 (facts that were not confirmed by Vymazalova). Vymazalova corrected Georges Daressy's 1906 garbled analysis of the 11 and 13 proof aspects of the text. By 2006 Ganita Bharati (Vol 28), David Pingree Memorial Volume, Bulletin of the Indian Society for the History of Mathematics, showed that:
(64/64)/n = Q/64 + (5R/n)*ro
was Q a binary quotient, and R a remainder scaled by 5/5 to a 1/320 hekat unit. Divisor n was limited to the range 1/64 < n < 64, a set of facts that are discussed in a meta context by:
and several Wikipedia and Planetmath encyclopedia entries that discuss the EMLR, Kahun Paprus, Moscow Mathematical Papyrus, Berlin Papyrus and the Rhind Mathematical Papyrus and broader theoretical and practical applications.
I look forward to updates of the raw hieratic data as discussed by 21st century interdisciplinary teams, directed by a July 2009 conference co-chaired by Annette Imhausen and Tanja Pemmerening, announced on EEF by:
Drs. Imhausen and Pemmerening are beginning the delayed correction process of re-reading and re-translating under valued aspects of the hieratic texts, and leading others to complete important projects, a point that Katz will be covering in future meta mathematics based books.
A new interdisciplinary standard is rescuing the Egyptian hieratic texts from well intended, but muddled 20th century publications.
Concerning the Mesopotamian, Indian, Chinese and Islamic meta math chapters, all ,were enjoyed, with no major omissions or understatements. Overall, Katz's book is excellent, though only 3-stars can be recommended. I look forward to future ancient meta math books, pointing out shared ancient math connections, that demand 5-star recommendations.
Milo Gardner
Sacramento, Calif.


Egyptian Mathematics
I Introduction
II Hieratic Mathematical Texts
III Mathematics in Administrative Texts
IV Mathematics in the GraecoRoman Period
V Appendices
Mesopotamian Mathematics
I Introduction
X Appendices
Mathematics in India
II Mathematical Texts in Ancient India
III Evolution of Mathematics in Medieval India
IV The Kerala School
V Continuity and Transition in the Second Millennium
VI Encounters with Modern Western Mathematics
VII Appendices

II The Long Third Millennium c 32002000 BCE
III The Old Babylonian Period c 20001600 BCE
IV Later Mesopotamia c 1400150 BCE
V Appendices
Chinese Mathematics
Counting Rods The OutIn Principle
The Earliest YetKnown Bamboo Text
The Zhou bi suan jing and Right Triangles The Gougu or Pythagorean Theorem
V The Chinese Euclid Liu Hui
VI The Ten Classics of Ancient Chinese Mathematics
VII Outstanding Achievements of the Song and Yuan Dynasties 9601368 CE
VIII Matteo Ricci and Xu Guangqi Prefaces to the First Chinese Edition of Euclids Elements 1607
IX Conclusion
Mathematics in Medieval Islam
II Appropriation of the Ancient Heritage
III Arithmetic
IV Algebra
V Number Theory
VI Geometry
VII Trigonometry
VIII Combinatorics
IX On Mathematics
X Appendices

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About the author (2007)

Victor J. Katz is professor emeritus of mathematics at the University of the District of Columbia. His many books include the textbook, A History of Mathematics: An Introduction, 2nd ed. (Addison-Wesley). He is the coeditor of Historical Modules for the Teaching and Learning of Mathematics.

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