Gregory, Duncan Farquharson

(1813-1844), mathematician

by H. R. Luard, rev. Maria Panteki

© Oxford University Press 2004 All rights reserved

Gregory, Duncan Farquharson (1813-1844), mathematician, was born on 14 April 1813 in Edinburgh, the youngest of the ten children of James Gregory (1753-1821), professor of medicine at the University of Edinburgh, and his wife, Isabella McLeod. Gregory came from a family with a long tradition in science: one direct ancestor was the mathematician James Gregory (1638-1675), an associate of Isaac Newton. As a child he did not show any predilection for mathematics, and found amusement in astronomy and in inventing mechanical devices. His father died when he was seven, and until the age of ten he was educated entirely by his mother. Afterwards he was also attended by a private tutor.

In 1824 Gregory went to Edinburgh Academy for three years, and then spent a winter at a private academy in Geneva, where his mathematical talent became apparent. In 1828 he began studying at Edinburgh University, where he became a favourite pupil of William Wallace (1768-1843), under whose tuition he made significant progress in higher mathematics. He was also interested in chemistry, especially in experiments on polarized light. In 1833 he matriculated at Trinity College, Cambridge, graduating as fifth wrangler in 1837. During the first years of his residence at Cambridge he acted as assistant to the professor of chemistry. He was one of the founders of the Chemical Society in Cambridge, and occasionally lectured in its rooms. He also studied botany, astronomy, and natural philosophy, but on graduating devoted himself exclusively to the study of mathematics. In 1837, together with R. L. Ellis, he founded the Cambridge Mathematical Journal, which had an important role in the revival of the subject in Cambridge. Gregory acted as its chief editor until a few months before his death.

In 1838 Gregory was an unsuccessful candidate for the chair of mathematics at Edinburgh University. He was elected a fellow of Trinity College in 1840, and, on receiving his MA in 1841, he was offered a position at the University of Toronto. This he declined on the grounds of poor health, and he remained at Cambridge, serving as an assistant tutor (1840-43), and as a moderator of the tripos (1842).

Gregory's special field of study was the algebra of differential operators, which originated in the work of J. L. Lagrange, and had been particularly developed by the Alsatians L. F. A. Arbogast and F. J. Servois. Perceiving the utility of operator methods, he sought to establish them upon rigorous foundations and to deploy them successfully for the solution of linear differential equations with constant coefficients. He published more than twenty papers, covering a wide range of applications, in the first two volumes of the Cambridge Mathematical Journal. These were collected and edited after his death by his friend William Walton as The Mathematical Writings of D. F. Gregory (1865). Efforts by a recent biographer to attribute many other Cambridge Mathematical Journal articles to Gregory are, however, unconvincing. In particular, the signature S. S. G. refers to Samuel Stephenson Greatheed (1813-1887), who was a mathematician in his own right, though he is best known for his church music. It is not a pseudonym for Gregory.

Gregory's elaboration of differential operator methods formed the basis of his textbook, Examples of the Processes of the Differential and Integral Calculus (1841). Especially noteworthy was his treatment of partial differential equations and definite integrals largely connected with Fourier's theory of heat. A notable successor to the volume published by Babbage, Herschel, and Peacock in 1820, this was the first English treatise to make constant and well-founded use of the method of separation of symbols. Gregory's study of commutative operations led to Boole's work on non-commutative operations, thus furnishing the grounds for further research on the calculus of operations until the 1860s.

Gregory's other mathematical concern was with developing the system of solid geometry solely by means of symmetrical equations. In 1842 he commenced the writing of A Treatise on the Applications of Analysis to Solid Geometry, which was completed and published after his death by Walton in 1845. Gregory's novel development of analytic geometry largely superseded J. Hymers's earlier approach. On the whole, his work reveals a vast acquaintance with continental mathematics, and is often enlivened with historical remarks. The quality of his mathematical advances was indeed unusual for one who never held a senior position in the university. Of an amiable disposition and an active disinterested kindness, he unfailingly shared with others the extent and variety of his information, and his experience as an editor. On realizing the potential of the young and self-taught George Boole he helped him establish his reputation, by offering significant advice for his first contributions to his journal. Just as Gregory paid tribute to his mentor Wallace by saving from oblivion some of his unpublished discoveries, so too Boole would later acknowledge the value of his friendship with Gregory, in his 1859 treatise on differential equations.

Gregory died unmarried, in his thirty-first year, at his father's house, Canaan Lodge, Edinburgh, on 23 February 1844, having suffered from continuous ill health for the previous two years.

H. R. LUARD, rev. MARIA PANTEKI

Sources  
R. L. Ellis, 'Biographical memoir', The mathematical writings of D. F. Gregory, ed. W. Walton (1865), xi-xxiv
M. Panteki, 'Relationships between algebra, logic and differential equations in England, 1800-1860', PhD diss., CNAA, 1992, esp. 'The development of the calculus of operations from Murphy to Boole: 1837-1845', 253-314
R. Harley, 'George Boole FRS', British Quarterly Review, 44 (1866), 141-81
DSB
private information (2004)
b. cert.

Archives  
CUL, corresp. with Lord Kelvin, Add. MS 7342
Trinity Cam., letters to Greatheed, Add. MS c.1.136-141

Likenesses  
drawing, repro. in Ellis, 'Biographical memoir', frontispiece [see illus.]


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