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The History of the History of Mathematics

Case Studies for the Seventeenth, Eighteenth and Nineteenth Centuries

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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The Quarrel on the Invention of the Calculus in Jean E. Montucla and Joseph Jérôme de Lalande, Histoire des Mathématiques (1758/1799–1802) 73

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Niccolò Guicciardini Università di Bergamo The Quarrel on the Invention of the Calculus in Jean E. Montucla and Joseph Jérôme de Lalande, Histoire des Mathématiques (1758/1799–1802) The dispute between Newton and Leibniz concerning priority in the invention of the calculus is a very well researched chapter in the history of mathematics. This notorious squabble has never ceased in fact to attract a somewhat morbid attention. From the point of view of the historiogra- phy of mathematics, it is a very promising case study, not only because the amount of material concerning the dispute allows for comparative analyses of the various historical narratives woven across three centuries, but also because dif ferent historians have examined the question from dif ferent viewpoints.1 Nationalistic issues, of course, have played a prominent role. Even more interestingly, perhaps, what is at stake here is the question of what we mean by ‘inventing the calculus’, and of what criteria should be 1 A good starting point for gathering information on Newton’s biographies is Robert Ilif fe and Rebekah Higgitt, eds, Early biographies of Isaac Newton, 1660–1885 (2 vols, London: Pickering & Chatto, 2006). Rebekah Higgitt’s chapter in the present volume provides an analysis of the plurality of images of Newton as a mathematician that emerge from his biographies throughout the centuries. As she observes, the priority dispute is a theme which touched not only Newton’s achievement, but that was also instrumental in defining a narrative on his morality and personality. One of...

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