Edward Routh

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Edward Routh
Edward J Routh.jpg
Edward John Routh (1831–1907)
Born (1831-01-20)20 January 1831
Quebec, Canada
Died 7 June 1907(1907-06-07) (aged 76)
Cambridge, England
Residence United Kingdom of Great Britain and Ireland
Nationality English
Fields Mathematician
Institutions University of London
Peterhouse, Cambridge
Alma mater University College London
Peterhouse, Cambridge
Academic advisors William Hopkins
Augustus De Morgan
Isaac Todhunter
Notable students John Strutt (Rayleigh)
J. J. Thomson
George Darwin
Alfred North Whitehead[1]
Joseph Larmor
Known for Routh's rule
Routh-Hurwitz theorem
Routh stability criterion
Routh array
Routh's theorem
Routh's algorithm
Kirchhoff-Routh function
Notable awards Smith's Prize (1854)
Adams Prize (1877)
Routh's wife was the daughter of George Biddell Airy. Routh was the grandson of Jean-Thomas Taschereau

Edward John Routh FRS (/rθ/; 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[edit]

Routh was born of an English father and a French-Canadian mother in Quebec, at that time the British colony of Lower Canada. His father's family could trace its history back to the Norman conquest when it acquired land at Routh near Beverley, Yorkshire. His mother's family, the Taschereau family, was well-established in Quebec, tracing their ancestry back to the early days of the French colony. His parents were Sir Randolph Isham Routh (1782–1858) and his second wife, Marie Louise Taschereau (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.[2]

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.[3]

Routh obtained his B.A. (1849) and M.A. (1853) in London.[3] He attended Peterhouse, Cambridge, where he was taught by Isaac Todhunter and coached by "senior wrangler maker" William Hopkins.[2] 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.[4]

Mathematics tutor[edit]

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.[2] "His lectures were enlivened by mathematical jokes of a rather heavy kind."[2]

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".[2]

Private life[edit]

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."[2]



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. In fact, Klein arranged the German translation.[2] It also did much to influence William Thomson and Peter Guthrie Tait's Treatise on Natural Philosophy (1867).[3] The Routhian, which can be obtained from the Lagrangian by the Legendre transform, in classical mechanics is named in his honor.

Stability and control[edit]

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[edit]


  1. ^ Edward Routh at the Mathematics Genealogy Project
  2. ^ a b c d e f g h i Fuller (2004)
  3. ^ a b c O'Connor & Robertson (2003)
  4. ^ "Routh, Edward John (RT850EJ)". A Cambridge Alumni Database. University of Cambridge. 


By Routh[edit]


About Routh[edit]

External links[edit]