Ructions over Fluxions

Abstract

Following the publication of Berkeley's caustic critique of calculus, The Analyst (1734), numerous figures in the scientific world responded to the text's allegations of rigour violations and a culture of mathematics-laced heresy. Maclaurin's Treatise on Fluxions (1742) shaped the reception of Berkeley's mathematical views. The published version of the Treatise focused on securing the foundations of Newton's fluxions against Berkeley's claims that they were unrigorous. However, an earlier draft has a different, ideological focus, and engaging with this text sheds new light on both Maclaurin and Berkeley. I will argue that Maclaurin was concerned with much more than simply mathematical foundations and rigour and that his initial response helps us to understand Berkeley's hostilities to mathematics in their proper context. The ultimate aim of this paper is to demonstrate that what was at stake were issues of mathematical rhetoric and reputation, and questions about the morality of mathematicians in an emerging culture of mathematical authority.