ArgumentA plagiarism charge in 1827 sparked a public controversy centered between Jean-Victor Poncelet (1788–1867) and Joseph-Diez Gergonne (1771–1859) over the origin and applications of the principle of duality in geometry. Over the next three years and through the pages of various journals, monographs, letters, reviews, reports, and footnotes, vitriol between the antagonists increased as their potential publicity grew. While the historical literature offers valuable resources toward understanding the development, content, and applications of geometric duality, the hostile nature of the exchange (...) seems to have deterred an in-depth textual study of the explicitly polemical writings. We argue that the necessary collective endeavor of beginning and ending this controversy constitutes a case study in the circulation of geometry. In particular, we consider how the duality controversy functioned as a medium of communicating new fundamental principles to a wider audience of practitioners. (shrink)

In their publications during the 1820s, Jakob Steiner and Julius Plücker frequently derived the same results while claiming different methods. This paper focuses on two such results in order to compare their approaches to constructing figures, calculating with symbols, and representing geometric magnitudes. Underlying the repetitive display of similar problems and theorems, Steiner and Plücker redefined synthetic and analytic methods in distinctly personal practices.

As mathematics departments in the United States began to shift toward standards of original research at the end of the nineteenth century, many adopted journal clubs as forums to engage with new periodical literature. The Bryn Mawr Mathematics Journal Club, maintained episodically between 1896 and 1924, began as a supplement to the graduate course offerings. Each semester student and professor participants focused on a single disciplinary area or surveyed what had been published lately. The Notebooks containing these reports were stored (...) on the open shelves of the college library. These collectively composed documents record ways in which graduate students transcribed and interpreted contemporary literature from the front to the back of mathematics. This article will consider the entries of a single student in which published mathematics was rewritten for a local audience and how the process of relocation animated research at Bryn Mawr. (shrink)

Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...) Monistto uphold disciplinary standards ofgeometrical reasoning, authors opposed tonon-Euclidean geometry aligned theirreasoning with practical applications, universal know-how, and nonhierarchicaldemocracy. As one contributorinquired,“How isthe professional expert betterfit-ted to see more lucidly in dealing with the elements of geometry than any otherperson of good geometric faculty?”. (shrink)

Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references (...) and citations. This article will focus on Scott’s striking and consistent use of geometric to describe a reality of dynamic points, lines, planes, and spaces that could be manipulated analogously to physical objects. By providing geometric interpretations of algebraic derivations, Scott committed to an early-nineteenth-century aesthetic vision of a “whole” analytical geometry that she adapted to modern research areas. (shrink)