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The History of the History of Mathematics

Case Studies for the Seventeenth, Eighteenth and Nineteenth Centuries

Edited By Benjamin Wardhaugh

The writing of mathematical histories has a long history, one which has seldom received scholarly attention. Mathematical history, and mathematical biography, raise distinctive issues of method and approach to which different periods have responded in different ways. At a time of increasing interest in the history of mathematics, this book attempts to show something of the trajectory that history has taken in the past. It presents seven case studies illustrating the different ways that mathematical histories have been written since the seventeenth century, ranging from the ‘historia’ of John Wallis to the recent re-presentation of Thomas Harriot’s manuscripts online. It considers both the ways that individual reputations and biographies have been shaped differently in different circumstances, and the ways that the discipline of mathematics has itself been variously presented through the writing of its history.

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Introduction 1 Philip Beeley The progress of Mathematick Learning: John Wallis as historian of mathematics 9 Benjamin Wardhaugh ‘It must have commenced with mankind’: some ancient histories of arithmetic in eighteenth-century Britain 31 Rebekah Higgitt The ‘epitome of intellectual sagacity’: Biographical treatments of Newton as a mathematician 47 Niccolò Guicciardini The Quarrel on the Invention of the Calculus in Jean E. Montucla and Joseph Jérôme de Lalande, Histoire des Mathématiques (1758/1799–1802) 73 Adrian Rice Vindicating Leibniz in the calculus priority dispute: The role of Augustus De Morgan 89 Henrik Kragh Sørensen Reading Mittag-Lef f ler’s biography of Abel as an act of mathematical self-fashioning 115 vi Jacqueline Stedall Thomas Harriot (1560–1621): history and historiography 145 Bibliography 165 Notes on Contributors 181 Index 183

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