A translation of the original 1986 French edition by Amy Dahan-Dalmedico and Jeanne Peiffer (both from Centre National de la Recherche Scientifique, Paris), this eminently readable book places the birth and development of mathematical activity in historical, cultural, and economic context.

The book offers an outstanding account, for instance, of how Arabs preserved Greek mathematics and extended it over an 800-year period, from 400’1200. The large number of illustrations supports the text and contributes to a fine read.

### Table of Contents

Translator's Preface

1. Landscapes

2. A Moment of Rationality: Greece

3. The Constitution of Classical Algebra

4. Figures, Spaces, and Geometries

5. Limits: From Initial Thoughts to the Concept

6. The Concept of Function and the Development of Analysis

7. At the Crossroads of Algebra, Analysis, and Geometry: Complex Numbers

8. New objects. New Laws. The Emergence of Algebraic Structures

Bibliography

Index

### Excerpt: (page 81-82)

The surge of Arab mathematics began in the seventh century C.E., that is at the beginnings of the Moslem religion. It developed starting from multiple problems posed by commerce, architecture, astronomy, geography, optics . . . and led to characterize itself by a profound synthesis between the aspirations aiming at a solution of these problems and intense theoretical work.

If an essential point of Arab mathematics is treated in this chapter, it is that the inventions are incontestable and progress particularly decisive in the domain of elaboration of algebraic calculation, as much abstract as technical, of the make-up of the theory of equations, and of algorithmic methods at the crossroads of algebra and arithmetic.

Two stages in their development can be distinguished: first, the assimilation of the Greek and oriental heritage in the seventh and eighth centuries. Baghdad was the first great scientific center under the reigns of Al-Mansur (754-775) and Haroun-al-Rashid (786-809), the libraries were numerous and scientific works often copied. The translation of the works of Greek antiquity was pursued intensely there (Euclid, Archimedes, Apollonius, Heron, Ptolemy, Diophantus) as well as the study of works from India, Persia, and Mesopotamia.

But from the ninth century, a true mathematical culture was formulated, properly Arab, and new works departed from the orbit of Hellenic mathematics.

### About the Author

**Amy Dahan-Dalmedico** is director of research at CNRS and assistant director of the Center Alexandre Koyré. Her research has focused on mathematics in the second half of the twentieth century and on climate change.

**Jeanne Peiffer** is a researcher at CNRS and editor-in-chief of the *Journal of the History of Mathematics*. Her research interests focus on geometry and its connections with Renaissance art, in particular the work of Albrecht Dürer. She has also written about women in mathematics.

### MAA Review

The authors, now at the Alexandre Koyré Center for Research in the History of Science and Technology in Paris, have produced a delightful and informative overview of some aspects of the history of mathematics aimed at students, teachers, and to a general audience. Continued...