Duncan Farquharson Gregory was a British mathematician. He was also the first editor at the Cambridge Mathematical Journal.
Background
Duncan Gregory was born on April 13, 1813, in Aberdeen, Scotland. He was the youngest son of Isabella Macleod and James Gregory. Gregory came from a family with a long tradition of interest in science. His great-grandfather, his grandfather, and his father were each professor of medicine at the University of Edinburgh. His great-great-grandfather was the mathematician.
Education
Duncan was taught initially by his mother, and in October 1825 he was sent to the Edinburgh Academy, and after two years of study spent a winter at a private academy in Geneva. While there his mathematical talent attracted attention, specifically geometry. On his return to Scotland, he attended the University of Edinburgh. He matriculated at Trinity College, Cambridge, in 1833 and took the degrees of a Bachelor of Arts in 1838 and a Master of Arts in 1841.
Career
Acting as a tutor, Gregory was an examiner at Trinity College and lectured occasionally in chemistry. At the suggestion of his friend, Archibald Smith, in 1838 Gregory, together with Robert Ellis, founded the Cambridge Mathematical Journal. Gregory was the first editor, and in this role considerably aided George Boole, who submitted his earliest papers to that journal. Many of his articles for the CMJ were collected in The Mathematical Writings of D. F. Gregory, edited by his friend and colleague William Walton. Gregory also published two books, both designed for use at Cambridge: one on the calculus and one on applications of analysis to geometry.
In 1841 Gregory was offered a position at the University of Toronto, but as he was in poor health, he declined it. Illness overtook him in 1842. Incapacitated, he left Cambridge in the spring of 1843, and died in Edinburgh the following February, at 30 years of age.
Views
Duncan Gregory's earliest papers were on differential and difference equations, in which Gregory used a method that came to be known as the calculus of operations. This method involved treating the symbols of operation as if they were symbols of quantity. In his attempt to justify the validity of this method, Gregory examined the laws governing the combination of these symbols with constants and by iteration. As a result of these studies, he came to a definition of algebra as the study of the combination of operations defined not by their specific nature but rather by the laws of combination to which they were subject.
Membership
Gregory was elected a member of the Philological Society on 12 May 1843.