This article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.

Johannes Kepler published his Astronomia nova in 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical deduction. He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis.

Johann Heinrich Lambert (1728–1777) developed a very detailed theory of science and experiment. Using Lambert's hygrometric studies, this article provides an introduction to Lambert's theory and its practice. Of special interest is his well-founded theory on the emergence and definition of concepts and his neat eye for heuristics that should ultimately lead to a mathematization of physical phenomena. His use of visualizations in this context is especially remarkable.

This article offers a social history of the “Galois Affair,” which arose in 1831 when the French Academy of Sciences decided to reject a paper presented by an aspiring mathematician, Évariste Galois. In order to historicize the meaning of Galois's work at the time he tried to earn recognition for his research on the algebraic solution of equations, this paper explores two interrelated questions. First, it analyzes scholarly algebraic practices and the way mathematicians were trained in the nineteenth century to reconstruct the scientific meaning of Galois's research. By emphasizing the historically contingent nature of scientific debates, the paper argues that to historicize the work of a mathematician, we must historicize the scientific world as well. The second part of this article goes further to seek a fresh perspective on Galois's short career by analyzing the cultural, social, and institutional dynamics that governed how the mathematical community came to recognize an aspiring mathematician as one of its own.

Evolutionary psychologists argue that because humans are biological creatures, cultural explanations must include biology. They thus offer to unify the natural and social sciences. Evolutionary psychologists rely on a specific history of cultural anthropology, particularly the work of Alfred Kroeber to make this point. A close examination of the history of cultural anthropology reveals that Kroeber acknowledged that humans were biological and culture had a biological foundation; however, he argued that we should treat culture as autonomous because that would bring benefits to the biological sciences as well as the human sciences. Hence, the historical caricature of his work by evolutionary psychology fails. The paper concludes that cultural anthropologists were successful in creating their discipline, at least in part, because they argued by pragmatic definition. Evolutionary psychology, on the other hand, offers an essentialist definition of “culture” and thus offers a much less promising vision of interdisciplinary collaboration.