Eighteenth-century Scotland was an internationally-recognized center of knowledge, “a modern Athens in the eyes of an enlightened world.” [74, p. 40]  The importance of science, of the city of Edinburgh, and of the universities in the Scottish Enlightenment has often been recounted. Yet a key figure, Colin Maclaurin (1698–1746), has not been highly rated. It has become a commonplace not only that Maclaurin did little to advance the calculus, but that he did much to retard mathematics in Britain—although he had (fortunately) no influence on the Continent. Standard histories have viewed Maclaurin's major mathematical work, the two-volume Treatise of Fluxions of 1742, as an unread monument to ancient geometry and as a roadblock to progress in analysis. Nowadays, few people read the Treatise of Fluxions. Much of the literature on the history of the calculus in the eighteenth and nineteenth centuries implies that few people read it in 1742 either, and that it marked the end—the dead end—of the Newtonian tradition in calculus. [9, p. 235], [49, p. 429], [10, p. 187], [11, pp. 228–9], [43, pp. 246–7], [42, p. 78], [64, p. 144] But can this all be true? Could nobody on the Continent have cared to read the major work of the leading mathematician in eighteenth-century Scotland? Or, if the work was read, could it truly have been “of little use for the researcher” [42, p. 78] and have had “no influence on the development of mathematics”? [64, p. 144]
We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics.