Routh, Edward John

(1831-1907), mathematician

by A. T. Fuller

© Oxford University Press 2004 All rights reserved

Routh, Edward John (1831-1907), mathematician, was born on 20 January 1831 in Quebec, Canada, one of the older among the nine children of Sir Randolph Isham Routh (1782-1858) and his second wife, Marie Louise (1810-1891), daughter of Judge Taschereau of Quebec. His father was a British army officer who had served at Waterloo, his mother a sister of Cardinal Taschereau, archbishop of Quebec. The Routh family traced their ancestry back to the Norman conquest when they acquired land in Yorkshire--there is a village called Routh near Beverley. Routh was taken to England at the age of eleven, and attended University College School, London. He then studied mathematics at University College, London, under Augustus De Morgan, gaining his BA in 1849. He matriculated at Peterhouse, Cambridge in 1850, where he was taught by Isaac Todhunter and William Hopkins. He was senior wrangler in 1854, coming just above James Clerk Maxwell, said to be the cleverest man of the year.

After graduating Routh started work as a private tutor or coach in mathematics at Peterhouse; he took the pupils of William John Steele during the latter's illness, and insisted on paying the fees over to him. When Steele died, the pupils remained with Routh, who thus began his spectacularly successful career as a mathematical coach. From 1855 to 1888 he coached more than 600 pupils, and during that time produced twenty-seven senior wranglers--an unequalled feat (his own teacher William Hopkins had achieved seventeen). He was elected FRS on 6 June 1872.

Routh organized his tutorial work methodically, dividing his pupils into about a dozen classes, with up to ten men in each. From 7 or 8 a.m. to 2 p.m. he would talk to each class for the allotted hour, rarely forgetting to begin where he had left off, and seldom making a slip in working on the blackboard. For the abler men he prepared extra material in the form of manuscript digests of contemporary memoirs, which they were expected to copy out completely. He was unusually dedicated to his work, and regular in his habits, spending most evenings preparing tests for his pupils. His lectures were enlivened by mathematical jokes of a rather heavy kind. Despite this pedagogic activity Routh found the time to write books and original papers. Already as a young man he had collaborated with Lord Brougham in publishing the Analytical View of Sir Isaac Newton's Principia (1855). His textbook Dynamics of a System of Rigid Bodies was first published in one volume in 1860, and later expanded to two volumes (6th edn, 1897). The work was the main medium through which Routh's stability investigations reached a wider audience. In Germany it attracted the attention of Klein and Sommerfeld who were then working on the mathematical analysis of spinning tops and gyroscopes. Sommerfeld praised the unique variety and richness of the problems set down in Routh's book, whose publication in German was arranged by Klein. Other substantial books by Routh were his Treatise on Analytical Statics (2 vols., 1891-2) and the Treatise on the Dynamics of a Particle (1898).

Routh's most innovative work was Treatise on the Stability of a Given State of Motion (1877), in which he developed a tabular method for finding inequalities which determine whether or not a given linear dynamical system is stable. The resulting inequalities are known as the Routh criteria. He also generalized a method of Lagrange for treating the stability of equilibrium, enabling it to be applied also to the stability of systems containing rotating bodies.

In 1857 Routh was invited to accept a post at the Royal Observatory, Greenwich, under George Biddell Airy, the astronomer royal. He did not take the appointment, but at Greenwich he met Airy's eldest daughter, Hilda (1840-1916), whom he married on 31 August 1864. They had five sons and a daughter. After marrying he had to relinquish his college fellowship, and he subsequently lived at Newnham Cottage, Queen's Road, Cambridge. He was a kindly man and a good conversationalist with friends, but with strangers he was shy and reserved.

Routh was a firm believer in the competitive examination technique of mathematical education--hardly surprisingly, for he was both a notable product and a chief practitioner of that system. He strongly resisted the attempts of the Cambridge authorities to abolish the listing of examination candidates in order of merit. When the lists started to come out in alphabetical order, he is said to have remarked that 'They will want to run the Derby alphabetically next'. In April 1907 his strength failed rapidly, and he lost the power of concentration. He died at his home on 7 June 1907, and was buried on 10 June 1907 at Cherry Hinton, a village near Cambridge.


Proceedings of the London Mathematical Society, 2nd ser., 5 (1907), xiv-xx
J. L., 'Dr John Edward Routh', Nature, 76 (1907), 200-02; repr. PRS, 84A (1910-11), xii-xvi
Cambridge Review (13 June 1907), 480-81
H. H. T. [H. H. Turner], Monthly Notices of the Royal Astronomical Society, 68 (1907-8), 239-41
A. T. Fuller, 'Edward John Routh', International Journal of Control, 26 (1977), 169-73
J. J. Thomson, Recollections and reflections (1936), 34-63
A. R. Forsyth, 'Old tripos days at Cambridge', Mathematical Gazette, 19 (1935), 162-79
private information (2004) [C. W. F. Everett and Alex Routh]

CUL, notes of lectures
Peterhouse, Cambridge |  CUL, corresp. with Lord Kelvin
RAS, letters to Royal Astronomical Society

Hill & Saunders, photograph, 1880, RS; repro. in Thomson, Recollections and reflections
H. von Herkomer, oils, 1890 (after original, 1888), Peterhouse, Cambridge [see illus.]

Wealth at death  
£81,048 12s. 11d.: resworn probate, 12 July 1907, CGPLA Eng. & Wales

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