The Mathematical Complement of David Rittenhouse

Abstract: David Rittenhouse (1732–1796) was considered the premier American scientist of his time, after Benjamin Franklin (1703–1790) died and Rittenhouse succeeded him as president of the American Philosophical Society (APS) in 1791. In eighteenth-century fashion, he was also termed a mathematician, as were a handful of his colleagues. In fact, Rittenhouse’s work, in one instance, was more advanced than that of his European contemporaries: when others were only able to optimally approximate algebraic irrationals, he was using continued fractions to approximate transcendental ones.1 My goal in this study was to more carefully examine the mathematical community around Rittenhouse, at home and abroad, to test whether Rittenhouse’s advanced facility with continued fraction approximation technique really was singular, or if, in fact, there was a broader mathematical community understanding of continued fractions and Rittenhouse’s work was only a slight variation of that of his contemporaries.