Containing many previously unpublished letters, this third volume of a six volume collection of the complete correspondence of John Wallis (1616-1703), documents an important period in the history of the Royal Society and the University of Oxford. By providing access to these letters, this painstakingly crafted edition will enable readers to gain a deeper and richer awareness of the intellectual culture on which the growth of scientific knowledge in early modern Europe was based. Wallis was Savilian Professor of Geometry of Oxford from 1649 until his death, and was a founding member of the Royal Society and a central figure in the scientific and intellectual history of England. In the period covered Wallis is engaged in scientific debates on techniques for determining areas contained by curves (quadratures) and figures (cubatures), as well as on the theory of motion and the nature of the tides. He also continues to attack the mathematical undertakings of Thomas Hobbes and to respond to attacks which the philosopher in turn levels against him. We also find evidence for the consolidation of mathematics as an academic discipline in the University of Oxford just fifty years after the establishment of the first mathematical lecturerships. Wallis is called upon more than once to deliver ceremonial lectures on mathematical topics to foreign dignitaries visiting the University. At the same time the volume allows us to witness the beginnings of a remarkable development in mathematical publishing. Many of Wallis's letters to Henry Oldenburg, secretary of the Royal Society, on a variety of topics in the mathematical and physical sciences, are transformed into articles and published in Oldenburg's journal, the Philosophical Transactions. Part of the reason for this development also becomes clear in the letters: the long and costly process of publishing mathematical books such as Wallis's three part Mechanica: sive de motu. This volume not only signals the modernization of mathematics in the second half of the seventeenth century but we also see two new figures emerge for the first time, whose careers are in different ways closely associated with Wallis: Isaac Newton and Gottfried Wilhelm Leibniz.

Correspondence of John Wallis (1616-1703): Volume III (October 1668-1671)

Beeley, Philip

Scriba, Christoph J.

Biographies & Memoirs

Oxford University Press

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering.
Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries.
Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometry in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times.The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history.
From letters to the authors for the German language edition
I hope it gets a translation, as there is no comparable work.
Prof. J. Grattan-Guinness (Middlesex University London)
"Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically!
Prof. J.W. Dauben (City University of New York)
An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. …
The graphic design is also excellent.
Prof. Z. Nádenik (Czech Technical University in Prague)

5000 Years of Geometry: Mathematics in History and Culture

Science & Math

Schreiber, Peter

Mathematics

Birkhauser

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