Important shifts took place in the areas investigated by British experimental philosophers during the late eighteenth century. In particular, the phenomena of heat, light, electricity, and magnetism shifted from largely qualitative, non-mathematical subjects to increasingly quantitative, mathematically based subjects. Emphasizing the Scottish context of Edinburgh natural philosopher, John Robison, this paper traces developments in magnetic theory in Britain from the latter quarter of the eighteenth century to the beginning of the nineteenth century. Robison is an important transitional figure who practiced (...) a new style of experimental philosophy, which eventually emerged as 'physics' in the nineteenth century. In particular, Robison's works presented and disseminated the one-fluid magnetic theory of Franz Aepinus among British experimental philosophers. (shrink)

The “new math” curriculum, one version of which was developed in the 1950s and 1960s by the School Mathematics Study Group under the auspices of the National Science Foundation, occasioned a great deal of controversy among mathematicians. Well before its rejection by parents and teachers, some mathematicians were vocal critics, decrying the new curriculum because of the way it described the practice and history of the discipline. The nature of mathematics, despite the field’s triumphs in helping to win World War (...) II and its midcentury promotion as the key to a modern technological society, was surprisingly contested in this period. Supporters of the School Mathematics Study Group, like its director, Edward Begle, emphasized the importance of portraying mathematics as a system of abstract structures, while opponents like Morris Kline argued that math was essentially a tool for understanding the natural world. The debate about the curriculum—and the role of mathematicians in its design—was also a debate about the underlying identity of the subject itself. (shrink)

Johann Bernoulli in 1710 affirmed that Newton had not proved that conic sections, having a focus in the force centre, were necessary orbits for a body accelerated by an inverse square force. He also criticized Newton's mathematical procedures applied to central forces in Principia mathematica, since, in his opinion, they lacked generality and could be used only if one knew the solution in advance. The development of eighteenth-century dynamics was mainly due to Continental mathematicians who followed Bernoulli's approach rather than (...) Newton's. The ways of thinking of the British Newtonians have, therefore, been somewhat forgotten. This paper is an attempt to assess what Bernoulli was criticizing and what were the immediate reactions of the Newtonians. In particular, I will concentrate on two papers by John Keill, submitted to the Royal Society in 1708 and 1714, in which the results on central forces achieved by the British were summarized and their methods defended. (shrink)

The paper contends that neoclassical ideology stems, to a great extent, from mathematical analysis. It is suggested that mainstream economic thought can be comprehensively revisited if both histories of mathematical and economic thought are to be taken collaboratively into account. Ideology is understood as a 'social construction of reality' that prevents us from evaluating our own standpoint, and impedes us from realising our value judgments as well as our theories of society and nature. However, the mid-19th century's intellectual controversies about (...) the validity of mathematical thought, truth and knowledge can procure new interesting insights concerning the ideological stance of the first marginalists. In this respect, the methodological categories of analysis and synthesis serve as the basis for the crucial distinction between old geometry and mathematical analysis, indicating that the discipline of mathematics has its own history of fundamentally unresolved disputes. Lastly, this may also shed some light on Alfred Marshall's peculiarly reluctant attitude towards the use of mathematical analysis in his work. (shrink)