This book presents an important aspect of Babylonian mathematics, namely the technique or discipline usually known as “Babylonian algebra.” This “algebra” is the earliest example of advanced mathematics that has come down to us, for which reason it is spoken of in most general expositions of the history of mathematics. However, most of these expositions rely on translations and interpretations going back to the 1930s. The present book, in contrast, builds on recent research.
The traditional interpretation made it possible to establish a list of the results obtained by the Babylonians; of the calculations they were able to perform; and, so to speak, of the formulas they knew. But since its starting point was contemporary mathematical thought, it was not able to reconstruct the different thinking that hides behind the Babylonian results. The aim of the present book is to highlight that difference, and thus to show that mathematics can be thought in several ways.
A first version of the book was written for students of the Danish high school system in 1998; another version—revised and augmented—appeared in French in 2010. This, as well as the present further updated version, addresses those who are interested in the history of mathematics but who do not necessarily have mathematical competence beyond what is acquired in high school. It further addresses Assyriologists who want an introduction to recent understandings of Babylonian mathematics.
Table of Contents
Preface
1 Introduction: The Issue – and Some Necessary Tools
2 Techniques for the First Degree
3 The Fundamental Techniques for the Second Degree
4 Complex Seconddegree Problems
5 Application of QuasialgebraicTechniques to Geometry
9 A Moral
Appendix A: Problems for the Reader
Appendix B: Transliterated Texts
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Series 
Information 
Institutes 
Service
