HISTORIA MATHEMATICA 23 (1996), 1–5 ARTICLE NO. 0001 EDITORIAL The History of Mathematics, the History of Science, Mathematics, and Historia Mathematica As an academic discipline, the history of science has both an enviable and a difficult role: enviable because of its potential to promote a dialogue between what C. P. Snow termed the ‘‘two cultures,’’ difficult because of the diversity of the audience it seeks to inform. To some extent this dichotomy has manifested itself in the emergence of two seemingly distinct—although not mutually exclusive— methodological approaches to questions in the history of science. The internalistic approach treats of the development of new scientific ideas from those established within a given scientific research program or, more generally, within a given disci- pline, and so requires technical discussions in its attempt to trace the evolution of a particular scientific idea or theory. In taking this methodological stance, the historian of science assumes an audience—almost necessarily a scientifically ori- ented one—with a certain amount of technical expertise and a shared interest in the deep internal coherence of a particular scientific discipline. The externalistic approach, on the other hand, focuses on questions of a different nature: how did the broader religious, philosophical, or political climate in a given time period affect the way in which scientists worked or thought? or how did the social organization of science—scientific societies, educational institutions, lines of communication, technologies—influence the production of scientific knowledge? The historical anal- ysis of such queries tends to concentrate on science and scientific thought in the large rather than in technical detail, and the historian of science who undertakes an examination of this kind presupposes not so much a scientifically skilled audience as one wishing to understand science within some other intellectual context. In our view, both of these methodological styles address questions of historical interest and import; both are needed to reach a satisfactory understanding of the historical development of science as a part of human culture. In recent years, however, researchers in the broader community of historians of science have tended to move further away from the work of the scientists; they have tended to write increasingly for one another rather than for a potentially broader audience of historians of science and scientists. Science studies—whether they concern the history, philosophy, or sociology of science—are about science, and yet, increasingly, the investigation of the actual content of science has become peripheral (to the point of near exclusion) to the analysis (see, for example, [1], [2], or [7]). While these broader studies are valuable and add to our understanding of the overall scientific endeavor, in our view it is short-sighted to regard these issues in a sort of technical vacuum, ignoring the scientific ideas themselves. The 1 0315-0860/96 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved.