by Margaret E. Rayner

© Oxford University Press 2004 All rights reserved

**Greenhill, Sir Alfred George** (1847-1927), mathematician, was born on 29 November 1847 at Montpelier Row, Twickenham, the third son of Thomas Greenhill, an engineer, and his wife, Louisa, daughter of Thomas Tagg, a gardener in Oxford. In April 1856 he was admitted from St Pancras, London, as a pupil at Christ's Hospital; at that time his father had seven other children and an annual income of less than £250. He was presented to the school by the parish of Twickenham, which had been left money by John and Frances West, who were related to Greenhill, to endow a scholarship there. At school he showed considerable mathematical talent and when, in 1866, he went up to read mathematics at St John's College, Cambridge, he was successively Pitt Club exhibitioner, Somerset exhibitioner, and foundation scholar. Simultaneously he held a Whitworth engineering scholarship and a university scholarship at the University of London where he registered in 1868. In 1870 he was second wrangler in the Cambridge tripos, tied with the first wrangler for the Smith's prize and was elected to a fellowship at St John's; the following year he completed his London BA.

In 1872 Greenhill was appointed professor of applied mathematics at the newly founded Royal Indian Civil Engineering College at Cooper's Hill, but the next year he returned to Cambridge as fellow and lecturer at Emmanuel College. Three years later, in 1876, he became professor of mathematics to the advanced class of the Royal Artillery officers at Woolwich; he remained in that post until his retirement in 1907. Greenhill was elected FRS in 1888 and knighted in 1908. The De Morgan medal of the London Mathematical Society was among the numerous honours he received from British and foreign learned societies. He was greatly admired by many of his contemporary mathematicians, although some considered that he did not sufficiently appreciate the developments in mathematics and physics of his own time.

Greenhill's interests lay principally in applied mathematics; his work in pure mathematics grew out of a need to discover new tools to solve practical problems. He wrote many textbooks, was a prolific researcher, and examined in the tripos. In all these activities, and in his teaching, he insisted that mathematical problems and their solutions must correspond closely to the nature of the problems met with in engineering and everyday reality. He considered that numerical answers were an integral part of any solution--a view not commonly held at that time. His greatest successes were achieved in the context of dynamics, hydrodynamics, and elasticity. He made extensive use of elliptic functions and wrote a textbook on their application in 1892; he directed the preparation of a table of these functions for the Smithsonian collection in 1922.

Greenhill's text-book *Differential and Integral Calculus* (1885) broke new ground by developing the differential and the integral calculus side by side, a practice which later became standard. His *Treatise on Hydrostatics* (1894) was also an innovation; in order to write it, he hunted through the scientific and engineering literature for realistic problems in shipbuilding, aeronautics, and hot-air ballooning (among others) with which to introduce the principles of hydrostatics. Mathematics was only brought in when absolutely essential. He worked with Woolwich colleagues on ballistic and gunnery problems and derived particularly valuable results on the rifling of heavy breech-loading ordnance.

In retirement Greenhill, who did not marry, lived in London, first at New Inn and then at 1 Staple Inn, Holborn, working in seclusion on mathematical and historical research. Despite his kindliness and light-heartedness, his idiosyncratic behaviour and opinions added to his long-standing reputation for eccentricity. He enjoyed the social life of the combination room of St John's, the Savile Club, the Athenaeum, and the tearoom of the Royal Society. He died at 19 Queen Adelaide Road, Penge, London, on 10 February 1927, partly from the effects of a fall from a bus the previous year. He was buried at Lewisham cemetery on 16 February.

MARGARET E. RAYNER

**Sources **

*The Times* (14 Feb 1927)

*Nature,* 119 (1927), 323-5

*PRS,* 119A (1928), i-iv

*Proceedings of the London Mathematical Society,* 3 (1928), 27-32

*The Eagle,* 45 (1927-9), 46-8

*Emmanuel College Magazine,* 25 (1926-7), 68

Venn, *Alum. Cant.*

Christ's Hospital presentation papers, GL, GL MS 12, 818A/30, no. 19

University of London registration book, LUL

b. cert.

d. cert.

*CGPLA Eng. & Wales* (1927)

**Archives **

CUL, Sir G. Larmon MSS

**Likenesses **

J. W. Hicks, photograph, 1916, repro. in *PRS,* facing p. i

photograph, repro. in *The Times,* p. 16

**Wealth at death **

£13,225 17s. *5d.:* probate, 25 March 1927, *CGPLA Eng. & Wales*

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