This book examines how calculus developed in Britain during the century following Newton.

This book tells one of the greatest stories in the history of school mathematics. Two of the names in the title—Samuel Pepys and Isaac Newton—need no introduction, and this book draws attention to their special contributions to the history of school mathematics. According to Ellerton and Clements, during the last quarter of the seventeenth century Pepys and Newton were key players in defining what school mathematics beyond arithmetic and elementary geometry might look like. The scene at which most of the action occurred was Christ’s Hospital, which was a school, ostensibly for the poor, in central London. The Royal Mathematical School (RMS) was established at Christ’s Hospital in 1673. It was the less well-known James Hodgson, a fine mathematician and RMS master between 1709 and 1755, who demonstrated that topics such as logarithms, plane and spherical trigonometry, and the application of these to navigation, might systematically and successfully be taught to 12- to 16-year-old school children. From a wider history-of-school-education perspective, this book tells how the world’s first secondary-school mathematics program was created and how, slowly but surely, what was being achieved at RMS began to influence school mathematics in other parts of Great Britain, Europe, and America. The book has been written from the perspective of the history of school mathematics. Ellerton and Clements’s analyses of pertinent literature and of archival data, and their interpretations of those analyses, have led them to conclude that RMS was the first major school in the world to teach mathematics-beyond-arithmetic, on a systematic basis, to students aged between 12 and 16. Throughout the book, Ellerton and Clements examine issues through the lens of a lag-time theoretical perspective. From a historiographical perspective, this book emphasizes how the history of RMS can be portrayed in very different ways, depending on the vantage point from which the history is written. The authors write from the vantage point of international developments in school mathematics education and, therefore, their history of RMS differs from all other histories of RMS, most of which were written from the perspective of the history of Christ’s Hospital.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians. This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.

Sir Isaac Newton (1642–1727) was one of the greatest scientists of all time, a thinker of extraordinary range and creativity who has left enduring legacies in mathematics and the natural sciences. In this volume a team of distinguished contributors examine all the main aspects of Newton's thought, including not only his approach to space, time, mechanics, and universal gravity in his Principia, his research in optics, and his contributions to mathematics, but also his more clandestine investigations into alchemy, theology, and prophecy, which have sometimes been overshadowed by his mathematical and scientific interests.

James Jurin (1684-1750) occupied a central place in the medical and scientific circles of Augustan and Georgian England. His dispassionate yet forceful advocacy of smallpox inoculation using an innovative statistical approach brought him widespread recognition both in Britain and abroad. He was Secretary to the Royal Society for seven years and participated vigorously in the most important scientific debates of the period. Jurin's correspondence, recently made available to the public, provides rich material for the study of eighteenth-century natural philosophy and medicine, especially of the smallpox inoculation debates. This volume reproduces a broad and valuable selection of letters, as well as a list of Jurin's publications and a calendar of the complete correspondence. The introductory biographical essay describes how Jurin combined a career as a successful London physician with that of a natural philosopher.

Comprising fifteen essays by leading authorities in the history of mathematics, this volume aims to exemplify the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.

This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Some of the topics explored include Arabic editions of Euclid’s Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual tradition Portuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth century The mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literature The use of Latin squares for agricultural crop experiments at the Rothamsted Experimental Station The many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960s The volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Taking as its focus the wide-ranging character of the Enlightenment, both in geographical and intellectual terms, this second collection of articles by John Gascoigne explores this movement's filiation and influence in a range of contexts. In contrast to some recently influential views it emphasises the evolutionary rather than the revolutionary character of the Enlightenment and its ability to change society by adaptation rather than demolition. This it does by reference, firstly, to developments in Britain tracing the changing views of history in relation to the Biblical account, the ideological uses of science (and particularly the work of Newton) and their connections to developments in moral philosophy and the teaching of science and philosophy in response to Enlightenment modes of thought. The collection then turns to the wider global setting of the Enlightenment and the way in which that movement served to provide a justification for European exploration and expansion, developments which found one of their most potent embodiments in the diverse uses of mapping. The collection concludes with an exploration of the interplay between the experience of Pacific contact and the currents of thought which characterised the Enlightenment in Germany.

This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.

Literature After Euclid tells the story of the creative adaptation of geometry in Scotland during and after the long eighteenth century. Analyzing the work of Scottish literati, Matthew Wickman challenges how we perceive the Scottish Enlightenment and the modernist ethos that relegated "classical" Enlightenment to the dustbin of history.