John Playfair on British decline in mathematics

Abstract

This article considers the role John Playfair (1748–1819) played in creating and popularizing the myth that mathematical development halted in Great Britain in the eighteenth century due to mathematicians' irrational attachment to a geometrical approach to the calculus. By the turn of the nineteenth century, Playfair had established his reputation as an energetic teacher, gifted expositor, and skilled natural philosopher. He served as joint professor of mathematics at the University of Edinburgh and as general secretary of the Royal Society of Edinburgh, editing the Society's Transactions, while his written accomplishments included Elements of geometry (1795) and Illustrations of the Huttonian theory of the earth (1802). He then contributed his talents to the opinionated journal, Edinburgh Review, where his assessments of the contemporary state of mathematics reached a wide audience of intellectuals, gentlemen, and merchants, albeit anonymously. The article expands upon a section of a talk delivered to the Fourth Joint Meeting of the BSHM and CSHPM in Montreal, 27–29 July 2007 (see also Ackerberg-Hastings 2007).

Notes

¹ This is a broader statement of Judith V Grabiner's fifth myth in Grabiner 2007.

² John Toplis and Robert Woodhouse were also among those who found certain aspects of British mathematics wanting in comparison to Continental techniques. See, for example, Toplis 1805, Woodhouse 1802, and Enros 1983.

³ This decline statement is also quoted at length in Parshall and Rowe 1994, 4–5, while Helena Pycior instead briefly noted Playfair's arguement in his review of Samuel Horsley's Latin edition of Euclid's Elements and Data (Pycior 1997, 275; Playfair 1804b).

⁴ Playfair also owned the 1799 second edition of Laplace's Exposition du système du monde, although he did not discuss the historical or any other chapters of this 312-page book in this review. The disappointment in Playfair's neglect or ignorance of the supplements is that they included Laplace's detailed and novel experimental results with the barometer, an instrument Playfair studied in one of his few original research papers and about which he surely held firm opinions (Playfair 1788).

⁵ On the content and contributions of this periodical, see Perl 1979 and Costa 2002.

⁶ Although Playfair indicates on page 406 that he did not yet own the original Italian edition, that work and a 1775 French translation, Traités élémentaires de calcul differèntiel et de calcul intègral, as well as the lengthy translation from volume 2 that Charles Bossut incorporated into his 1798 two-volume Traités de calcul différential et de calcul integral, were added to Playfair's library before his death.

⁷ Like most other aspects of his life, Playfair's relationship with Christian tenets and institutions was multi-faceted. His first salaried employment was as the successor to his father's parishes at Liff and Benvie (1773–83), and we saw above that he believed a Designer was responsible for the universe. However, he also challenged Edinburgh clergy for interfering in nonreligious matters, most notably when Moderates attempted to prevent the appointment of John Leslie when Playfair vacated the mathematics chair in 1805, in order to install their own candidate (Morrell 1975).