Academic journal article
*Carlyle Studies Annual*

# Revisiting Thomas Carlyle and Mathematics

## Article excerpt

Dr Brewster advises me to commence forthwith at Legendre for it will go on certainly. "I shall do it. " But I have got no desk yet

Thomas Carlyle to Alexander Carlyle, 21 November 1821

IN 1822, THE HRST EDITION OFYOUNG THOMAS CARLYLE'S TRANSLATION of the influential textbook Elements de géométrie (1784), by the French mathematician Adrien-Marie Legendre (17521833), was published in Edinburgh by Oliver and Boyd and G. and W. B. Whittaker. Included in this translation were notes and an introductory chapter entitled "On Proportion" written by Carlyle to address the prerequisites to understanding the text that he perceived the average British student to be lacking. Although Carlisle Moore's article on Carlyle and mathematics remains extremely useful, even definitive in terms of connecting Carlyle's early mathematical acumen with his developing literary mode of thinking, some insight into the mathematics presented in Carlyle's essay deserves a revisit, especially since Carlyle's geometric approach to quadratic equations remains elegantly relevant to mathematicians today.

Prior to the publication of Legendre 's Eléments, the primary text for the serious student of geometry was Euclid's Elements, which dates from about 300 bce.1 Legendre simplified Euclid's propositions, and the result was a more effective textbook that soon became a standard and later a prototype in Europe and the United States and replaced Euclid's as the primary geometry reference work for about the next hundred years. Carlyle's translation ofthe Elements alone ran to 33 editions.

Since Carlyle wrote "On Proportion" to help the British student in preparation for Legendre's Eléments, it makes sense to review the state of British mathematics and the state of mathematics as a whole at the beginning of the nineteenth century. Near the end of the seventeenth century, the important discovery of the calculus was made independently by Isaac Newton (1642-1727) and by Gottfried Leibniz (1646-1716). 2 Their discovery provided a way for mathematicians to calculate using infinite processes, about which the ancients had known but had avoided. Because Leibniz was more public than Newton about his work, the ideas of the calculus spread more rapidly on the European continent and were furthered by the brilliant Swiss mathematician Leonhard Euler (1707-83). With this powerful new mathematical tool, Euler and others began to solve a large number of previously insoluble problems. They had particular success when they separated the calculus from the geometric context in which Newton and Leibniz developed their ideas. This new line of thinking led to the development of the mathematical subject of analytic algebra. Eventually, geometry was ostracized by the mathematicians on the European continent until the work of Gaspard Monge (1746-1818) toward the end of the eighteenth century.

The less forthcoming Newton eventually grew jealous of the fame proffered to Leibniz for his work on the calculus. After an initial period of acknowledging his German rival's contribution as significant, a bitter dispute evolved from the charge that Leibniz had plagiarized from Newton. The controversy lasts to the present day, although the current view is that it is extremely unlikely that Leibniz would have had access to Newton's work. At the time, however, the controversy caused a deep and abiding rift between the mathematicians of Britain and of the Continent. To further complicate matters, in Britain, Newton's ideas were not universally accepted by the mathematical community. Even as late as 1734, the eminent British metaphysician Bishop George Berkeley (1685-1753) very convincingly attacked the fundamental ideas of Newton's "Method of Fluxions." In response to Berkeley's attack, Newton's friend Colin Maclaurin (1698-1746), mathematics professor at the University of Edinburgh, wrote a systematic, two-volume defense, A Treatise on Fluxions (1742), which sought rigorously to elevate Newton's ideas to the heights of the timeless Euclid, whom Carlisle Moore correctly refers to as "the symbol of imperishable truth" (63). …