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.
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Editorial Reviews
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"In her book Symbols, Impossible Numbers, and Geometric Entanglements, Helena Pycior paints a novel picture of British mathematical development in the seventeenth and eighteenth centuries. She has brought together much interesting material whose implications will interest scholars for years to come." Joan L. Richards, Isis
"This remarkable book describes the history of the development of British algebra in the seventeenth and early eighteenth centuries (early modern algebra), focusing on attention on the constitution of algebraic language." Massimo Galuzzi, Mathematical Reviews
"This remarkable book describes the history of the development of British algebra in the seventeenth and early eighteenth centuries (early modern algebra), focusing on attention on the constitution of algebraic language." Massimo Galuzzi, Mathematical Reviews
Book Description
This 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.
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Symbols, Impossible Numbers, and Geometric Entanglements,
By Sam Adams (Minnesota. USA) - See all my reviews
This review is from: Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick (Hardcover)
The author begins her introduction with the words: "As a history of algebra in England and Scotland from the early seventeenth century to the mid-eighteenth century, this book considers not only technical algebra but also the personal, philosophical, religious, and institutional factors that affected the introduction, elaboration, and reception of the subject." (p. 1)
The following algebra texts are discussed in this book: Girolamo Cardano - The Great Art (Ars magna) - 1545 Francois Viete - Introduction to the Analytic Art - 1591 William Oughtred - The Key of the Mathematicks - 1631, 1647 Thomas Harriot - Praxis (Artis analyticae praxis) - 1631 Rene Descartes - Geometrie - 1637 Johann Rahn w/John Pell - Algebra - 1659, 1668 John Kersey - Algebra - 1673 John Wallis - Treatise of Algebra - 1685 Isaac Newton - Universal Arithmetick - 1707 Nicholas Saunderson - Elements of Algebra - 1740 Colin MacLaurin - Treatise of Algebra - 1748 The author also discusses views concerning algebra or mathematics by Thomas Hobbes, Isaac Barrow, and George Berkeley. The main concerns and disagreements seem to have been around the status (epistemological, ontological, or otherwise) of negative and imaginary numbers, as well as the relative standings of geometry and algebra within the realm of mathematics. A reader wishing to know how algebra was presented within these various texts - in other words, what the algebra textbooks of the period looked like, what notation was used, how proofs were presented, what topics were included, and so forth - will need to look elsewhere. The author's main concern seems to be the controversies surrounding negative and imaginary numbers and the struggle of algebra to find respectability in the face of geometry. The following books are available from amazon. Cardano - The Rules of Algebra: (Ars Magna) Viete- The Analytic Art Thomas Harriot - Artis Analyticae Praxis: An English Translation with Commentary Descartes - Geometry For a look at what algebra was going to become in England during the early nineteenth century, see Thomas Peacock's 1830 Treatise on Algebra - Treatise on Algebra, Volume I: Arithmetical Algebra A Treatise on Algebra, Volume II: On Symbolical Algebra, and Its Applications to the Geometry of Position A century later, in 1930, B. L. Van Der Waerden published the enormously influential: Algebra: Volume I Algebra, Volume II And then in 1941, Garrett Birkhoff and Saunders Mac Lane published: A Survey of Modern Algebra
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Key Phrases - Statistically Improbable Phrases (SIPs):
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François Viète, conic sections, mean proportional, deviationary rule, early modern algebra, complex binomials, symbolical style, algebraic universe, symbolic logistic, surd binomials, analytic art, early modern mathematics, symbolical algebra, symbolical reasoning, mathematical thinkers, algebraic tradition, impossible roots, mathematical legacy, quadratura curvarum, geometric focus, geometric tradition, impossible quantities, pure algebra, algebra textbook, imaginary roots Key Phrases - Capitalized Phrases (CAPs): (learn more)
Geometric Entanglements, Universal Arithmetick, The Key, Treatise of Algebra, New York, The Analyst, Treatise of Fluxions, The Great Art, Cambridge University Press, John Wallis, Works of Berkeley, Isaac Newton, The Analytic Art, Mathematical Papers of Newton, George Berkeley, Isaac Barrow, Nicholas Saunderson, William Oughtred, John Collins, Correspondence of Scientific Men, The Scottish Response, Kersey's Algebra, Elements of Algebra, Rahn's Algebra, Thomas Hobbes Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
François Viète, conic sections, mean proportional, deviationary rule, early modern algebra, complex binomials, symbolical style, algebraic universe, symbolic logistic, surd binomials, analytic art, early modern mathematics, symbolical algebra, symbolical reasoning, mathematical thinkers, algebraic tradition, impossible roots, mathematical legacy, quadratura curvarum, geometric focus, geometric tradition, impossible quantities, pure algebra, algebra textbook, imaginary roots Key Phrases - Capitalized Phrases (CAPs): (learn more)
Geometric Entanglements, Universal Arithmetick, The Key, Treatise of Algebra, New York, The Analyst, Treatise of Fluxions, The Great Art, Cambridge University Press, John Wallis, Works of Berkeley, Isaac Newton, The Analytic Art, Mathematical Papers of Newton, George Berkeley, Isaac Barrow, Nicholas Saunderson, William Oughtred, John Collins, Correspondence of Scientific Men, The Scottish Response, Kersey's Algebra, Elements of Algebra, Rahn's Algebra, Thomas Hobbes Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
7
books
cite this book:
See all 7 books citing this book
- Labyrinth: A Search for the Hidden Meaning of Science by Peter Pesic in Back Matter
- Squaring the Circle: The War between Hobbes and Wallis (Science and Its Conceptual Foundations series) by Douglas M. Jesseph in Back Matter
- From Newton to Hawking: A History of Cambridge University's Lucasian Professors of Mathematics by Kevin C. Knox on page 203
- Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick by Helena M. Pycior in Front Matter
- The Application of Mathematics to the Sciences of Nature by Claudio Pellegrini on page 232
See all 7 books citing this book
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