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Edward John Routh FRS (20 January 1831–7 June 1907), was an Englishmarker mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridgemarker 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.

Biography

Early life

Routh was born of an English family in Quebecmarker, then in the British colony of Upper Canada. The family could trace its history back to the Norman conquest when it acquired land at Routhmarker near Beverleymarker, Yorkshiremarker. 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 Waterloomarker, and Marie Louise was the daughter of judge Jean-Thomas Taschereau and the sister of judge Jean-Thomas and cardinal Elzéar-Alexandre Taschereau.

Routh came to England aged eleven and attended University College School and then entered University College, Londonmarker 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.

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

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

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".

Private life

Astronomer Royal George Biddell Airy sought to entice Routh to work at the Royal Observatory, Greenwichmarker. 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."

Honours



Work

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. It also did much to influence William Thomson and Peter Guthrie Tait's Treatise on Natural Philosophy (1867).

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



References

  1. Fuller (2004)
  2. O'Connor & Robertson (2003)


Bibliography

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.


Obituaries

  • 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




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