Calculus and analysis in early 19th-century Britain: The work of William Wallace

Scottish-born William Wallace (1768-1843) was an early exponent of the diff erential calculus in Britain and translator of French mathematical works. E ncyclopaedias published during the early 19th century provided a valuable e ducational resource, to which Wallace and his colleague, James Ivory, contr ibuted. Wallace's encyclopaedia articles on "Fluxions" and his other analyt ical writings are examined here, as are his relations with James Ivory, Joh n Herschel, and others. Wallace's long 1815 article on "Fluxions" in the Ed inburgh Encyclopaedia was the first complete account of calculus, using dif ferential notation, to be published in English. There, he attempted an orig inal and rigorous "doctrine of limits," which deserved more attention than it received. In 1832, while professor of mathematics in Edinburgh, he appli ed analysis to support the reform of taxation proposed in the Reform Bill. It is suggested that the later neglect of Wallace's achievements is attribu table to a mix of personal, institutional, political, and national rivalrie s. (C) 1999 Academic Press.