Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick

by Helena M. Pycior

• ISBN13: 9780521027403
• ISBN10: 0521027403
• Edition: 1st
• Format: Paperback
• Copyright: 2006-11-02
• Publisher: Cambridge University Press

Summary

Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

Table of Contents

Introduction

1. Setting the scene

2. William Oughtred and Thomas Harriot

3. John Collins's campaign for a current English algebra textbook

4. John Pell's English edition of Rahn's Algebra and John Kersey's Algebra

5. The arithmetic formulation of algebra in John Wallis's Treatise of Algebra

6. English mathematical thinkers take sides on early modern algebra

7. The mixed mathematical legacy of Newton's Universal Arithmetick

8. George Berkeley at the intersection of algebra and philosophy

9. The Scottish response to Newtonian algebra

10. Algebra 'considered as thelogical institutes of the mathematician'.