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Book DetailsSpectrumVolume: 43; 2004; 387 pp
Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history  and, in particular, by mathematics teachers at secondary, college, and university levels.

Table of Contents

Ancient Mathematics [ MR 2052832 ]

Foreword

Sherlock Holmes in Babylon, R. Creighton Buck

Words and Pictures: New Light on Plimpton 322, Eleanor Robson

Mathematics, 600 B.C.–600 A.D., Max Dehn

Diophantus of Alexandria, J. D. Swift

Hypatia of Alexandria, A. W. Richeson

Hypatia and Her Mathematics, Michael A. B. Deakin

The Evolution of Mathematics in Ancient China, Frank Swetz

Liu Hui and the First Golden Age of Chinese Mathematics, Philip D. Straffin, Jr.

Number Systems of the North American Indians, W. C. Eells

The Number System of the Mayas, A. W. Richeson

Before The Conquest, Marcia Ascher

Afterword

Medieval and Renaissance Mathematics [ MR 2052832 ]

Foreword

The Discovery of the Series Formula for $\pi $ by Leibniz, Gregory and Nilakantha, Ranjan Roy

Ideas of Calculus in Islam and India, Victor J. Katz

Was Calculus Invented in India?, David Bressoud

An Early Iterative Method for the Determination of sin $1^\circ $, Farhad Riahi

Leonardo of Pisa and his Liber Quadratorum, R. B. McClenon

The Algorists vs. the Abacists: An Ancient Controversy on the Use of Calculators, Barbara E. Reynolds

Sidelights on the CardanTartaglia Controversy, Martin A. Nordgaard

Reading Bombelli’s $x$purgated Algebra, Abraham Arcavi and Maxim Bruckheimer

The First Work on Mathematics Printed in the New World, David Eugene Smith

Afterword

The Seventeeth Century [ MR 2052832 ]

Foreword

An Application of Geography to Mathematics: History of the Integral of the Secant, V. Frederick Rickey and Philip M. Tuchinsky

Some Historical Notes on the Cycloid, E. A. Whitman

Descartes and ProblemSolving, Judith Grabiner

René Descartes’ CurveDrawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language, David Dennis

Certain Mathematical Achievements of James Gregory, Max Dehn and E. D. Hellinger

The Changing Concept of Change: The Derivative from Fermat to Weierstrass, Judith V. Grabiner

The Crooked Made Straight: Roberval and Newton on Tangents, Paul R. Wolfson

On the Discovery of the Logarithmic Series and Its Development in England up to Cotes, Josef Ehrenfried Hofmann

Isaac Newton: Man, Myth, and Mathematics, V. Frederick Rickey

Reading the Master: Newton and the Birth of Celestial Mechanics, Bruce Pourciau

Newton as an Originator of Polar Coordinates, C. B. Boyer

Newton’s Method for Resolving Affected Equations, Chris Christensen

A Contribution of Leibniz to the History of Complex Numbers, R. B. McClenon

Functions of a Curve: Leibniz’s Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey

Afterword

The Eighteenth Century [ MR 2052832 ]

Foreword

Brook Taylor and the Mathematical Theory of Linear Perspective, P. S. Jones

Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions, Judith Grabiner

Discussion of Fluxions: from Berkeley to Woodhouse, Florian Cajori

The Bernoullis and the Harmonic Series, William Dunham

Leonhard Euler 1707–1783, J. J. Burckhardt

The Number $e$, J. L. Coolidge

Euler’s Vision of a General Partial Differential Calculus for a Generalized Kind of Function, Jesper Lützen

Euler and the Fundamental Theorem of Algebra, William Dunham

Euler and Differentials, Anthony P. Ferzola

Euler and Quadratic Reciprocity, Harold M. Edwards

Afterword


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Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history  and, in particular, by mathematics teachers at secondary, college, and university levels.

Ancient Mathematics [ MR 2052832 ]

Foreword

Sherlock Holmes in Babylon, R. Creighton Buck

Words and Pictures: New Light on Plimpton 322, Eleanor Robson

Mathematics, 600 B.C.–600 A.D., Max Dehn

Diophantus of Alexandria, J. D. Swift

Hypatia of Alexandria, A. W. Richeson

Hypatia and Her Mathematics, Michael A. B. Deakin

The Evolution of Mathematics in Ancient China, Frank Swetz

Liu Hui and the First Golden Age of Chinese Mathematics, Philip D. Straffin, Jr.

Number Systems of the North American Indians, W. C. Eells

The Number System of the Mayas, A. W. Richeson

Before The Conquest, Marcia Ascher

Afterword

Medieval and Renaissance Mathematics [ MR 2052832 ]

Foreword

The Discovery of the Series Formula for $\pi $ by Leibniz, Gregory and Nilakantha, Ranjan Roy

Ideas of Calculus in Islam and India, Victor J. Katz

Was Calculus Invented in India?, David Bressoud

An Early Iterative Method for the Determination of sin $1^\circ $, Farhad Riahi

Leonardo of Pisa and his Liber Quadratorum, R. B. McClenon

The Algorists vs. the Abacists: An Ancient Controversy on the Use of Calculators, Barbara E. Reynolds

Sidelights on the CardanTartaglia Controversy, Martin A. Nordgaard

Reading Bombelli’s $x$purgated Algebra, Abraham Arcavi and Maxim Bruckheimer

The First Work on Mathematics Printed in the New World, David Eugene Smith

Afterword

The Seventeeth Century [ MR 2052832 ]

Foreword

An Application of Geography to Mathematics: History of the Integral of the Secant, V. Frederick Rickey and Philip M. Tuchinsky

Some Historical Notes on the Cycloid, E. A. Whitman

Descartes and ProblemSolving, Judith Grabiner

René Descartes’ CurveDrawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language, David Dennis

Certain Mathematical Achievements of James Gregory, Max Dehn and E. D. Hellinger

The Changing Concept of Change: The Derivative from Fermat to Weierstrass, Judith V. Grabiner

The Crooked Made Straight: Roberval and Newton on Tangents, Paul R. Wolfson

On the Discovery of the Logarithmic Series and Its Development in England up to Cotes, Josef Ehrenfried Hofmann

Isaac Newton: Man, Myth, and Mathematics, V. Frederick Rickey

Reading the Master: Newton and the Birth of Celestial Mechanics, Bruce Pourciau

Newton as an Originator of Polar Coordinates, C. B. Boyer

Newton’s Method for Resolving Affected Equations, Chris Christensen

A Contribution of Leibniz to the History of Complex Numbers, R. B. McClenon

Functions of a Curve: Leibniz’s Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey

Afterword

The Eighteenth Century [ MR 2052832 ]

Foreword

Brook Taylor and the Mathematical Theory of Linear Perspective, P. S. Jones

Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions, Judith Grabiner

Discussion of Fluxions: from Berkeley to Woodhouse, Florian Cajori

The Bernoullis and the Harmonic Series, William Dunham

Leonhard Euler 1707–1783, J. J. Burckhardt

The Number $e$, J. L. Coolidge

Euler’s Vision of a General Partial Differential Calculus for a Generalized Kind of Function, Jesper Lützen

Euler and the Fundamental Theorem of Algebra, William Dunham

Euler and Differentials, Anthony P. Ferzola

Euler and Quadratic Reciprocity, Harold M. Edwards

Afterword