This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

This paper challenges the use of the notion of “culture” to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to “geometrical equations,” objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to “geometrical equations,” and especially the technical aspects of these activities, is made on the basis of a sociological definition of “culture.” More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a “cultural system.”

The history of meteorology has focused a great deal on the “scaling up” of knowledge infrastructures through the development of national and global observation networks. This article argues that such efforts to scale up were paralleled by efforts to define a place for local knowledge. By examining efforts of the Blue Hill Meteorological Observatory, near Boston, Massachusetts, to issue local weather forecasts that competed with the centralized forecasts of the U.S. Signal Service, this article finds that Blue Hill, as a user of the Signal Service's observation network, developed a new understanding of local knowledge by combining local observations of the weather with the synoptic maps afforded by the nationwide telegraph network of the U.S. Signal Service. Blue Hill used these forecasts not only as a service, but also as evidence of the superiority of its model of local forecasting over the Signal Service's model, and in the process opened up larger questions about the value of a weather forecast and the value of different kinds of knowledge in meteorology.

Using the notion of styles of knowledge we refer to the ways diverse scientific communities claim to produce true knowledge, their understandings regarding the attitudes and values that scientists should have in order to grasp natural and social reality, and the practices and technologies developed within such styles. This paper analyzes scientific and medical enterprises that explored the relationship between environment, population, and society in Colombia between 1850 and 1920. We argue that similar styles of knowledge production were shared in human geography, medical geography, and climatic physiology at the mid-nineteenth century; and that some physicians working in bacteriology and physiology since the 1880s established epistemic boundaries between their work and earlier scientific activities, while others found these distinctions irrelevant. However, the historical actors committed to any of the styles of knowledge production explored in this article agreed on the local specificity of their objects of inquiry, therefore questioning European science. These styles of knowledge production also shaped different ways of perceiving and addressing national problems. Hence, this article is a contribution to the recent literature on both historical epistemology and social and cultural history of science and medicine.