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Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.


Early life

Routh was born of an English family in Quebec, then in the British colony of Upper Canada. The family could trace its history back to the Norman conquest when it acquired land at Routh near Beverley, Yorkshire. His parents were Sir Randolph Isham Routh (1782–1858) and his second wife, Marie Louise (1810–1891). Randolph was a commissariat officer who had served at the Battle of Waterloo, and Marie Louise was the daughter of judge Jean-Thomas Taschereau and the sister of judge Jean-Thomas and cardinal Elzéar-Alexandre Taschereau.[1]

Routh came to England aged eleven and attended University College School and then entered University College, London in 1847, having won a scholarship. There he studied under Augustus De Morgan, whose influence led to Routh to decide on a career in mathematics.[2]

Routh obtained his B.A. (1849) and M.A. (1853) in London.[2] He attended Peterhouse, Cambridge, where he was taught by Isaac Todhunter and coached by "senior wrangler maker" William Hopkins.[1] In 1854, Routh graduated just above James Clerk Maxwell, as Senior Wrangler, sharing the Smith's prize with him. Routh was elected fellow of Peterhouse in 1855.[3]

Mathematics tutor

On graduation, Routh took up work as a private mathematics tutor in Cambridge and took on the pupils of William John Steele during the latter's fatal illness, though insisting that Steele take the fees. Routh inherited Steele's pupils, going on to establish an unbeaten record as a coach. He coached over 600 pupils between 1855 and 1888, 27 of them making Senior Wrangler, as to Hopkins' 17.

Routh worked conscientiously and systematically, taking rigidly timetabled classes of ten pupils during the day and spending the evenings preparing extra material for the ablest men.[1] "His lectures were enlivened by mathematical jokes of a rather heavy kind."[1]

Routh was a staunch defender of the Cambridge competitive system and despaired when the university started to publish examination results in alphabetical order, observing "They will want to run the Derby alphabetically next".[1]

Private life

Astronomer Royal George Biddell Airy sought to entice Routh to work at the Royal Observatory, Greenwich. Though Airy did not succeed, at Greenwich Routh met Airy's eldest daughter Hilda (1840-1916) whom he married in 1864. The couple had five sons and a daughter. Routh was a "kindly man and a good conversationalist with friends, but with strangers he was shy and reserved."[1]


* Fellow of the Royal Society, (1872);[1]
* Adams Prize, (1877).[1]


Routh collaborated with Henry Brougham on the Analytical View of Sir Isaac Newton's Principia (1855).

He published a textbook, Dynamics of a System of Rigid Bodies (1860, 6th ed. 1897) in which he did much to define and systematise the modern mathematical approach to mechanics.

This influenced Felix Klein and Arnold Sommerfeld, Klein arranging the German translation.[1] It also did much to influence William Thomson and Peter Guthrie Tait's Treatise on Natural Philosophy (1867).[2]

The Routhian of classical mechanics in named in honor of him.

Stability and control

In addition to his intensive work in teaching and writing, which had a persistent effect on the presentation of mathematical physics, he also contributed original research such as the Routh-Hurwitz theorem.

Central tenets of modern control systems theory relies upon the Routh stability criterion, an application of Sturm's Theorem to evaluate Cauchy indices through the use of the Euclidean algorithm.

See also

* List of Old Gowers
* People in systems and control
* Control theory


1. ^ a b c d e f g h i Fuller (2004)
2. ^ a b c O'Connor & Robertson (2003)
3. ^ Routh, Edward John in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.


By Routh

* Brougham and Vaux, Henry Brougham, Baron & Routh, E. J. (ed. I. B. Cohen) [1855] (1972) Analytical View of Sir Isaac Newton's Principia, New York: Johnson Reprint Corp.
* Routh, E. J. (1877). Treatise on the Stability of a Given State of Motion.
* — (1898). A Treatise on Dynamics of a Particle. With Numerous Examples. Cambridge: Cambridge University Press.
* —. The Elementary Part Of a Treatise on the Dynamics of a System of Rigid Bodies: Being Part I of a Treatise on the Whole Subject. With Numerous Examples.
* — (1905). The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies: Being Part II of a Treatise on the Whole Subject. With Numerous Examples. London: Macmillan and Co. Ltd.
* — (1909a). A Treatise on Analytical Statics with Numerous Examples Volume I. Cambridge University Press.
* — (1909b). A Treatise on Analytical Statics with Numerous Examples Volume II. Cambridge University Press.


* The Times, 8 June 1907 (available at O'Connor & Robertson (2003))
* Proceedings of the London Mathematical Society, 2nd ser., 5 (1907), xiv–xx;
* Nature, 76 (1907), 200–02;
* Cambridge Review, 13 June 1907, 480–81;
* H. H. T., Monthly Notices of the Royal Astronomical Society, 68 (1907–8), 239–41

About Routh

* Forsyth, A. R. (1935). "Old tripos days at Cambridge". Mathematical Gazette (The Mathematical Association) 19 (234): 162–79. doi:10.2307/3605871.
* Fuller, A. T. (1977). "Edward John Routh". International Journal of Control 26: 169–73. doi:10.1080/00207177708922300.
* — (2004) "Routh, Edward John (1831–1907)", Oxford Dictionary of National Biography, Oxford University Press, accessed 10 September 2007 subscription or UK public library membership required
* O'Connor, John J.; Robertson, Edmund F., "Edward Routh", MacTutor History of Mathematics archive, University of St Andrews, . (2003)
* Sneddon, I. N. (1970-1990) "Routh, Edward John", in Gillispie, C. C. (ed.) Dictionary of Scientific Biography, New York: Charles Screibner's Sons
* Thomson, J. J. (1936). Recollections and Reflections. pp. 34–63.
* Venn, J. & Venn, J. A. (1922). Alumni Cantabrigienses. Cambridge University Press.


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