At least since the seventeenth century, the strange combination of epistemological certainty and ontological power that characterizes mathematics has made it a major focus of philosophical, social, and cultural negotiation. In the eighteenth century, all of these factors were at play as mathematical thinkers struggled to assimilate and extend the analysis they had inherited from the seventeenth century. A combination of educational convictions and historical assumptions supported a humanistic mathematics essentially defined by its flexibility and breadth. This mathematics was an (...) expression of l’esprit humain, which was unfolding in a progressive historical narrative. The French Revolution dramatically altered the historical and educational landscapes that had supported this eighteenth‐century approach, and within thirty years Augustin Louis Cauchy had radically reconceptualized and restructured mathematics to be rigorous rather than narrative. (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)

Sophia De Morgan’s Memoir of Augustus De Morgan highlights the difficulty of creating a unified picture of a scientific life. It also provides a critical perspective from which to view the chronological development of the modern “scientist” from the eighteenth through the twentieth centuries.

ArgumentThis paper traces the changing fortunes of natural theology in two generations of an English family. The group is represented in the first generation by the Unitarian radical, William Frend, and in the second by the spiritualist Sophia Frend De Morgan and her husband, the mathematician Augustus De Morgan. The Frend/DeMorgans were distinguished from the naturalistic Darwins by their commitment to reason; they were a quintessentially urban group whose impulses to natural theology flowed from a God they encountered through their (...) minds. For William Frend, natural theology was rooted in a tightly disciplined, linguistic view of reason that linked theological and mathematical understandings; in the De Morgan's generation, however, understandings of mathematics and of language changed in ways that undercut the power of Frend's reasoned approach. In its rise and fall this family story of reasoned theology is co-temporal with the natural theology that was wrecked on the rocks of Darwinian evolutionary theory. (shrink)

Mathematics is the most chameleon of subjects, whose meaning is differently defined in different circumstances. This essay considers the mathematics of Augustus De Morgan as an illustration of the ways that the essence of the subject, the very objects that are included within it, has been adjusted in response to cultural factors. Since these cultural factors are the same ones that shape scientific development, the argument is that the history of mathematics and the history of science are always inextricably bound (...) to one another. (shrink)