A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

Early Victorian analogical arguments were used to order the natural and the social world by maintaining a coherent collective experience across cultural oppositions such as the ideal and material, the sacred and profane, theory and fact. Maxwell's use of analogical argument in ‘On Faraday's lines of force’ was a contribution to that broad nineteenth-century discussion which overlapped theology and natural philosophy. I argue here that Maxwell understood his theoretical work as both a technical and a socially meaningful practice and that (...) embedding his use of analogy in the social and intellectual context of Victorian Britain provides a means of telling a sociocultural history of Maxwell's development of a new cognitive tool: a way of thinking on paper analogous to thinking with objects in the laboratory. (shrink)

More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...) Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’. (shrink)

With the coming of the French Revolution in 1789 and its attack on monarchy, the landed aristocracy, the religious establishment and religion itself, and especially with the coming of the sans culottes and the First French Republic and its ‘Terror’ in 1793–94, fear of revolution swept the British establishment. Sensing revolution everywhere, successive Tory governments, rooted in the alliance of the Church of England, the landed aristocracy and the monarchy, practised a consistent and harsh policy of repression. Neither the fear (...) nor the repression eased with the arrival of, or indeed, with the departure of, Napoleon who, as Emperor from 1804 to 1815, seemed determined to conquer Britain by means of revolutionary propaganda, economic blockade and/or military invasion. (shrink)

The ArgumentIt has long been apparent that in the nineteenth century, mathematics in France and England developed along different lines. The differences, which might well be labelled stylistic, are most easy to see on the foundational level. At first this may seem surprising because it is such a fundamental area, but, upon reflection, it is to be expected. Ultimately discussions about the foundations of mathematics turn on views about what mathematics is, and this is a question which is answered by (...) a variety of different groups including mathematicians, students, curricular planners, parents, etc. Mathematical practice rests on some kind of mixture of the answers to this fundamental question which come from these diverse groups. Comparing the cultural matrices which supported mathematics in France and Britain in the first decades of the nineteenth century sheds light on the real though often subtle differences in the ways the subject was pursued in the two countries. (shrink)