MacMahon, Percy Alexander

(1854-1929), mathematician

by H. W. Turnbull, rev. A. J. Crilly

© Oxford University Press 2004 All rights reserved

MacMahon, Percy Alexander (1854-1929), mathematician, was born on 26 September 1854 in Malta, the second son of Colonel Patrick William MacMahon and his wife, Ellen, daughter of George Savage Curtis, of Teignmouth. He was sent to Cheltenham College, and in 1871, at the age of sixteen, he entered the Royal Military Academy, Woolwich. He joined the Royal Artillery at Madras in 1873 as lieutenant, and was promoted captain in 1881 and major in 1889. His battery took part in 1877 with the Punjab frontier force in a punitive expedition against the Jawaki Afridis, penetrating into their country and capturing several villages.

MacMahon left India on medical certificate in 1877, was posted to the 9th brigade at Dover, and in 1882 returned to the Royal Military Academy as instructor in mathematics. This post brought him into contact with George Greenhill, then professor of mathematics at the Artillery College, Woolwich, whose friendship changed the course of MacMahon's life. In 1890 he was appointed professor of physics at the Ordnance College, and he held this post until 1897. In that year the eminent mathematician J. J. Sylvester died and MacMahon, who shared Sylvester's interests in number theory, was considered a possible successor to the Oxford Savilian chair of geometry. He retired from the army in 1898 (as was customary, taking the title 'major' into civilian life), and thereafter devoted himself to mathematical and scientific pursuits. From 1904 to 1920 he was deputy warden of the standards under the Board of Trade, a post which brought membership from 1920 onwards of the Conférence Générale and of the Comité Internationale des Poids et Mesures which were held in Paris. For twelve years (1902-14) he was one of the general secretaries of the British Association. His clarity of expression in extempore discussions of mathematics made him a welcome and prominent member of learned societies. He was elected a fellow of the Royal Society in 1890, and received the society's highest honours, the royal medal (1900) and the Sylvester medal (1919). The London Mathematical Society, of which he was president in 1894-6, awarded him the De Morgan medal in 1923, and he received honorary degrees from several universities. All these honours came to a man with no first degree and who, in his youth, had been associated with no university. He followed the notable Cambridge mathematicians Arthur Cayley and J. W. L. Glaisher in the tradition of pure mathematicians who took a keen interest in astronomy and who became presidents of the Royal Astronomical Society. He was its president (1917-18) and a member of the permanent eclipse committee. He was also a member of the council of the Royal Society of Arts.

On his return to Woolwich in 1882 MacMahon entered into a mathematical heritage peculiarly fitted to his powers. The theory of algebraic forms was in the full flight of development owing to the activities of Arthur Cayley and James Joseph Sylvester, and this was the one predominantly British domain in the mathematics of the time. From the outset MacMahon was captivated: he was attracted by the lightness of touch and daring playfulness, combined with an abiding sense of form, that the subject demanded. His military friends were proud of one of their number's making a reputation in such an abstract subject and one which they could not fathom. They cheerfully chaffed him as 'a good soldier spoiled'. MacMahon burst on the mathematical scene by making a direct correspondence between invariant theory and the theory of partitions, a branch of number theory. Cayley hailed MacMahon's discovery as 'very remarkable' and from that moment his mathematical reputation was assured. In the years that followed, Cayley enlisted MacMahon's help in some difficult problems in invariant theory. The theory of algebraic forms was MacMahon's speciality and he derived many results. One notable example is his master theorem, a way of analysing permutations using determinants.

MacMahon's work is mainly linked to combinatorics, a branch of abstract algebra in which he occupies a special niche. This area of mathematics grew significantly in the twentieth century. MacMahon's work was republished in an edition of his Collected Papers (2 vols., 1978-86). They show him to be no crabbed specialist. 'I do not believe in any branch of science being destitute of connexion with other branches', he said at a meeting of the British Association for the Advancement of Science in Glasgow (1901). This isolation was particularly characteristic of a certain tract of pure mathematics which appeared to be in a 'forlorn condition'. The timeliness of MacMahon's masterly rescue of this branch of mathematics became more evident as the twentieth century advanced, in its significance for the theory of groups and the quantum theory. At the same Glasgow meeting he illustrated a historical turn of mind by drawing attention to the London Spitalfields Mathematical Society, founded in 1717 and absorbed into the Royal Astronomical Society in 1845. In 1915 MacMahon brought together the substance of his principal discoveries in a two-volume work Combinatory Analysis, a ripe and penetrating account of a favourite theme, which retains throughout the impress of his personality. There followed An Introduction to Combinatory Analysis (1920) and New Mathematical Pastimes (1921). This last is in lighter vein, a book which gives the geometrical by-products of his characteristic algebra, as manifested in the construction of repeated patterns.

For many years MacMahon lived in London. On 9 February 1907 he married Grace Elizabeth, daughter of C. R. Howard, of 32 Gloucester Place, London; they had no children. His charming personality, his human sympathy, and the hospitality at his home at 27 Evelyn Mansions, Carlisle Place, Westminster, endeared him to a wide circle of friends. He encouraged many younger mathematicians by his infectious enthusiasm for algebra. He was also an expert billiards player at the Athenaeum. In 1922 MacMahon retired to Cambridge, becoming a member of St John's College, to which he had become attached in 1904 on receiving the university's honorary degree of ScD. Although his absorption in scientific problems became more pronounced in later life, he mixed very willingly in social gatherings until ill health compelled his retirement to Bognor; he died there at his home, Springfield, Normanton Avenue, on Christmas day 1929.

H. W. TURNBULL, rev. A. J. CRILLY

Sources  
H. F. Baker, 'Percy Alexander MacMahon, 1854-1929', PRS, 127A (1930), x-xix
Nature, 125 (1930), 243-5
H. H. T. [H. H. Turner], Monthly Notices of the Royal Astronomical Society, 90 (1929-30), 373-8
The Times (28 Dec 1929)
The Times (31 Dec 1929)
E. K. Lloyd, 'Redfield's proofs of MacMahon's conjecture', Historia Mathematica, 17 (1990), 36-47
m. cert.
d. cert.

Archives  
St John Cam.

Likenesses  
W. Stoneman, photographs, 1926, NPG
photograph, repro. in Baker, 'Percy Alexander MacMahon'

Wealth at death  
£2753 16s. 5d.: probate, 20 Feb 1930, CGPLA Eng. & Wales


© Oxford University Press 2004 All rights reserved

[http://www.oxforddnb.com/view/article/34796]

GO TO THE OUP ARTICLE (Sign-in required)