Rags, riches and Royal Society rebellion

Notices of the American Mathematical Society

Historia Mathematica, 1998

1991

A new culture of mathematics was developed in sixteenth-century England, the culture of 'the mathematicalls'. Its representatives were the self-styled mathematical practitioners who presented their art as a practical and worldly activity. The careers of two practitioners, Thomas Bedwell and Thomas Hood, are used as case studies to examine the establishment of this culture of the mathematicalls. Both practitioners self-consciously used mathematical instruments as key resources in negotiating their own roles. Bedwell defined his role in contrast to mechanicians and he secured patronage in military engineering and the service of the commonwealth; Hood worked in the commercial setting of London as a teacher, author, chartmaker, and retailer. Working in new contexts and dealing with new audiences of gentlemen and mechanicians, Bedwell and Hood used instruments to construct a public consensus on the status and aims of mathematics.

Intellectual History Review

The paper discusses some of the contributions of Duncan Farquharson Gregory and Robert Leslie Ellis to symbolical algebra and their views on the philosophy of mathematics with the aim of revisiting the accepted characterisation of the second generation of reformers of British mathematics found in Crosbie Smith and Norton Wise's seminal Energy and Empire. It is argued that at least some of the features brought to the fore in their treatment of the work of Gregory and Ellisnamely "geometrical methods" in mathematics and "anti-metaphysical", "non-hypothetical" and "practical" knowledgecannot be straightforwardly upheld. On the one hand, Gregory's generalisation of George Peacock's symbolical algebra was connected to several natural philosophical considerations underlying the Scottish Newtonians' "abstractionism" and "geometrical fluxional analysis". On the other hand, Ellis's idealist philosophy of mathematics and science insisted that the a priori necessary truths of mathematics could inform the "hypothetical part of scientific induction". A more nuanced understanding of the place of the second generation of reformers within the analytical revolution in Victorian Britain should thus take into account the eclectic foundational position that arises from the work of Gregory and Ellis.

Historia Mathematica, 1995

Economic Thought, 2012

In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced by the Newtonian approach that still characterised many aspects of the Cambridge Mathematical Tripos, where the emphasis was on geometrical and mechanical examples rather than on symbolic (Cartesian) mathematics. Keynes, who criticised (Cartesian) symbolic mathematics, was indeed an admirer of Newton and of his method. Sraffa's mathematical constructions are also in line with the Newtonian approach where arithmetic and geometry were strictly separated, since Sraffa's mathematical constructions typically use arithmetic without engaging in the mixture between geometry and arithmetic that occurs in the Cartesian approach.

The British Journal for the History of Science

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree of interdependency even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in di...

Mathematical Intelligencer, 2011

Annales (English ed.), 2012

To what extent did scholars use science to pursue the good life in the seventeenth century? How to articulate the Scientific Revolution with ethical questions? These are the questions at the core of the investigation led by the historian of science Matthew Jones in his bookThe Good Life in the Scientific Revolution. At first glance, his project is simply an extension of research on the social history of truth that has encouraged historians for two decades to decipher the moral norms that gave credit to the use and production of scientific knowledge. Civility, politeness, honor led to specific research that highlighted the cultural and social context surrounding the practices of scientific innovation in the Classical Age. This book deepens these questions by asking how mathematical practices were considered moral reflections. This article will discuss the contribution of this book by first examining the three attempts at experimenting mathematical morals led by Descartes, Pascal and ...

SVEC. Architecture, Cultural history, Autobiography, Voltaire Foundation, 2008(6), Oxford, pp. 45-55