Merely a speculation of the mind? William Henry Fox Talbot and mathematics

Barrow-Green, June (2013). Merely a speculation of the mind? William Henry Fox Talbot and mathematics. In: Brusius, Mirjam; Dean, Katrina and Ramalingam, Chitra eds. William Henry Fox Talbot: Beyond Photography. Yale Center for British Art -Studies in British Art (23). United States: Yale University Press, pp. 67–94.

URL: http://yalebooks.co.uk/display.asp?K=9780300179347

Abstract

A product of the Cambridge Mathematical Tripos of 1820, Talbot sustained an active interest in mathematics throughout his life. He published several mathematical papers—both his first and his last scientific publications were in mathematics—and in 1838 he was awarded the Royal Society’s Gold Medal for papers in which he proved theorems about elliptic integrals. But for Talbot mathematics was never a career—for example, he never taught it, even for a short while, as many of his Cambridge contemporaries did— and his mathematical achievements, rightly lauded at the time, were soon largely forgotten. (An exception took place in 1915 when readers of Nature were reminded of the fact that “W.H. Fox Talbot, now only vaguely remembered for photography” had investigated “some cases of Abel’s theorem in a very instructive and fundamental way.”) But to consider Talbot’s mathematics solely in terms of his contributions to the mathematical canon would be to do it an injustice. As his Notebooks show, mathematics for Talbot was not just about proving theorems; it was much more than that. It was a subject he enjoyed in its own right; it was a subject he used to assist his other researches in optics and astronomy; and it was a subject which provided him with a model for scientific investigation. For Talbot, proving a theorem was rarely enough. The proof had to be reinforced by numerical examples, often of a strikingly unwieldy nature; evidence that his training at Cambridge had not been forgotten. With the above observations in mind, this chapter will explore the four phases of Talbot’s mathematical life: his years at Cambridge; the early 1820s when he published in Gergonne’s Annales; the mid-1830s when he published in the journals of the Royal Society of London; and the 1850s and later when he published in the Transactions of the Royal Society of Edinburgh. That the last three phases can be delineated as effectively by journals as by time will allow for an entrée into the world of mathematical publishing and into the mathematical context in which Talbot was living and working.

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