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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

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Introduction [O]ur history will embrace all mathematicians […]. And not, moreover, in just a historical fashion – what age they lived in, what manner of life they led, what coun- try they inhabited – but rather mathematically: what they wrote in what field, how well they wrote it and how useful it is for teaching beginners. Since I intended to say this, I could not, without fault, omit a discussion of the whole of mathematics and each of its branches.1 Mathematical histories have been written in Europe since the sixteenth century, yet on the whole there has been relatively little ref lection on the trajectory which the history of mathematics itself has taken over time. Nor has sustained attention often been given to the historiography of a subject which by its nature involves methodological choices and dilemmas dif ferent from those of other kinds of history.2 Henry Savile’s demanding programme for the study of the history of mathematics, set out during his 1570 lectures on Ptolemy at Oxford and quoted above, illustrates the magnitude of the task facing the historian of mathematics. It also illustrates the tendency of mathematical histories to be dependent on particular understandings of the nature of mathematics, and of course to respond to the needs of particular audiences. 1 Oxford, Bodleian Library, MS Savile 29, fols 17r–17v, quoted and translated in Robert Goulding, Defending Hypatia: Ramus, Savile, and the Renaissance rediscovery of mathematical history (Dordrecht: Springer, 2010), 97. 2 Notable exceptions are Joseph W. Dauben and Christoph...

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