To highlight speculative trends specific to the mathematical tradition that developed in China, the paper analyzes an excerpt of a third-century commentary on a mathematical classic, which arguably contains a proof. The paper shows that the following three tasks cannot be dissociated one from the other: (1) to discuss how the ancient text should be read; (2) to describe the practice of mathematical proof to which this text bears witness; (3) to bring to light connections between philosophy and mathematics that it demonstrates were established in China. To this end the paper defines its use of the word “proof” and outlines a program for an international history of mathematical proof. It describes the sense in which the text conveys a proof and shows how it simultaneously fulfills algorithmic ends, bringing to light a formal pattern that appears to be fundamental both for mathematics and for other domains of reality. The interest in transformations that mathematical writings demonstrate in China at that time seems to have been influenced by philosophical developments based on The Book of Changes (Yi-jing), which the excerpt quotes. This quotation within a mathematical context makes it possible to suggest an interpretation for a rather difficult philosophical statement.

The belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of necessary stages inexorably leading to its current state — meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge.

Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs.

The group of mathematicians known as Bourbaki persuasively proclaimed the isolation of its field of research — pure mathematics — from society and science. It may therefore seem paradoxical that links with larger French cultural movements, especially structuralism and potential literature, are easy to establish. Rather than arguing that the latter were a consequence of the former, which they were not, I show that all of these cultural movements, including the Bourbakist endeavor, emerged together, each strengthening the public appeal of the others through constant, albeit often superficial, interaction. This codependency is partly responsible for their success and moreover accounts for their simultaneous fall from favor, which, however, can clearly be seen as also stemming from different internal problems. To understand this dynamics, I argue that Bourbaki's role can best be captured by using the notion of cultural connector, which I introduce here.

This paper makes use of the 1860 clash between T. H. Huxley and Richard Owen to examine the role of social context in scientific advance in the biological sciences. It shows how the social context of nineteenth-century England first favored the Coleridge-Owenite interpretation of the biological world and then, at mid-century and subsequently, allowed the Darwin-Huxley interpretation to win through. It emphasizes the complexity of the clash. Professional, personal, and generational agendas as well as scientific theory and fundamental philosophical intuition were at stake. The history, ultimately, provides a useful instance of Schutz ‘s and Scheler ‘s concept of societal factors controlling and selecting between flows of idealfactoren. Although Huxley is conventionally regarded as the victor I conclude by suggesting that the issue is not yet closed and that profound philosophical issues remain unresolved.

European ethology and North American comparative psychology have been the two most prominent approaches to the study of animal behavior through most of the twentieth century. In this paper I analyze sets of popular articles by ethologist Nikolaas Tinbergen and psychologist Frank Beach, in an effort to understand the contrasting rhetorical styles of the two. Among the numerous ways in which Tinbergen and Beach differed were with respect to expressing the joy of research, the kind of scientific approach adopted, their treatment of animals, their sense of history, and the types of illustrations they chose. In general, Tinbergen‘s articles placed him closer to nature and Beach‘s more in the tradition of dispassionate scientific inquiry. These differences in rhetoric may have been one factor in the greater success of ethology after World War II.