Sherlock Holmes in Babylon: And Other Tales of Mathematical History (Spectrum)

At some point in history, abstract mathematics appeared. Sketchy histories tend to emphasize the role of the Greeks, which was substantial, but their ideas did not sprout from the mathematical equivalent of nothingness. Before there was Greek mathematics, the Babylonians and Egyptians were doing a good deal of mathematics. For this reason, I was pleased to see that the first few papers in this collection deal with Babylonian mathematics, and the title of the book is taken from the title of the first one. The book is divided into four sections: ancient mathematics, medieval and renaissance mathematics, the seventeenth century and the eighteenth century. Most of the papers examine a specific concept of mathematics as well as the people who developed it. The papers first appeared in mathematics journals such as "College Mathematics Journal" and "American Mathematical Monthly", over the last century. One paper by Florian Cajori appeared in 1917 and one by Eleanor Robson was published in 2002. A wide range of topics are covered in the papers of this collection and some early papers examine the development of mathematics in non-western cultures such as China, the number systems of North American Indians, the Mayas and the Incas. Some of the papers take an approach that raises possibilities that are outside the coverage found in most books on mathematical history. The paper, "Was Calculus Invented in India?" is overstated, but not by as much as we are often led to believe. Most books tend to state that calculus was simultaneously invented by Newton and Leibniz and largely ignore the shoulders upon which they stood when they made calculus. Two hundred years before Newton, Indian mathematicians were capable of deriving the infinite series expansions for the sine, cosine and arctangent functions. I was also amazed to learn that the first mathematical work published in the New World predates the voyage of Henry Hudson up the Hudson River by fifty years. I have never taught a course in the history of mathematics. However, if I ever do teach mathematical history, this will be a book that I will use. By presenting areas of mathematics developed in non-western cultures and outside what can be considered the historical mainstream, this book shows us that mathematics is truly a human endeavor. 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. Part I. Ancient Mathematics -- 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 -- Part Ii. Medieval And Renaissance Mathematics -- 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 Determinationof Sin 1° / 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 Cardan-tartaglia 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 -- Part Iii. The Seventeenth Century -- 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 The Problem-solving / Judith Grabiner -- René Descartes' Curve-drawing 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 / David Dennis And Jere Confrey -- Part Iv. The Eighteenth Century -- Brook Taylor And The Mathematical Theory Of Linear Perspectives / 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. Edited By Marlow Anderson, Victor Katz, Robin Wilson. Includes Bibliographical References And Index. Ancient mathematics. 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 Medieval and renaissance mathematics. 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 determinationof sin 10 / 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 Cardan-Tartaglia 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 The seventeenth century. 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 the problem-solving / Judith Grabiner René Descartes' curve-drawing 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 / David Dennis and Jere Confrey The eighteenth century. Brook Taylor and the mathematical theory of linear perspectives / 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.