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At the University of Cambridge, a wrangler is a student who has completed the third year (called Part II) of the Mathematical Tripos with first-class honours.

The highest-scoring student is named the "senior wrangler"; the second highest-scoring student is the "second wrangler"; the third highest is the "third wrangler", and so on.

In contrast to the senior wrangler, the person who achieved the lowest exam marks, but still earned a third-class degree, is known as the wooden spoon.

Contents 1 Past wranglers 2 Senior Wranglers who achieved distinction outside mathematics 3 Lists 3.1 Senior wranglers 3.2 Second Wranglers 4 Sources 5 External links 6 See also

Senior wranglers have included some of Britain's most brilliant mathematicians and scientists, including John Herschel, Arthur Cayley, George Gabriel Stokes, Lord Rayleigh and J. E. Littlewood. John Couch Adams scored so well that there was a greater gap between him and the second wrangler than between the second wrangler and the wooden spoon.^{[citation needed]}

Interestingly, there are some equally if not more famous names associated with the rank of second wrangler (such as Alfred Marshall, James Clerk Maxwell, J.J. Thomson and Lord Kelvin). Legend has it that Kelvin was so confident that he had come top of the exam that he asked his servant to run to the Senate House and check who the second wrangler was. The servant returned and informed him, "You, sir"! It is also suggested that the final exam required the students to write a proof of a theorem which Kelvin himself had provided the proof for, earlier in the course; unfortunately, because he had created it, it hadn't occurred to him to learn it, and he spent a lot of time working it out from scratch - while the student who achieved Senior Wrangler put it down to having committed the proof to memory.^{[citation needed]}

There has long been a culture of fierce competition at mathematics exams at Cambridge. However, it is certainly not true to say that top marks in the Cambridge mathematics exam guaranteed the senior wrangler success in life; the exams were largely a test of speed in applying familiar rules, and some of the most inventive and original students of Mathematics at Cambridge did not come top of their class (Bragg was 3rd, Hardy was 4th, Sedgwick 5th, Malthus was 9th and Keynes was 12th) and some fared even worse (Klaus Roth was not even a wrangler).

The first woman to top the mathematics list, albeit unofficially, was Philippa Fawcett, who took the exams in 1890. At the time, women were not officially ranked, although they were told how they had done compared to the male candidates, so she was ranked "above the senior wrangler".

The examination was the most important in England at the time, and the results were given great publicity. In 1865 Lord Rayleigh was senior wrangler, and The Times of 30 January 1865 printed a story asserting that he had not gained this distinction through favouritism as heir to a peerage.

In the early 20th century, the order of merit was abolished and lists of students who had completed the mathematics exams were sorted alphabetically in each of the three classes of honours, and were not based on individual marks. The last official senior wrangler was P. J. Daniell, who graduated in 1909.

Students who achieve second-class and third-class mathematics degrees are known as Senior Optimes (second-class) and Junior Optimes (third-class). Cambridge did not divide its examination classification in mathematics into 2:1s and 2:2s until 1995 but now there are Senior Optimes Division 1 and Senior Optimes Division 2.

• Donald MacAlister, Senior Wrangler in 1877. MacAlister became a physician, and principal and vice-chancellor and, later, chancellor of the University of Glasgow. The postcard portrait was part of the cult of celebrity surrounding the senior wrangler.
• William Paley, Senior Wrangler in 1763 was a British divine, Christian apologist, utilitarian, and philosopher. He is best remembered for his watchmaker analogy, an argument for the existence of God in his book Natural Theology.
• George Pretyman, Senior Wrangler and Smith's prize winner in 1772, became Bishop of Winchester, Dean of St Paul's and a confidant of prime minister William Pitt the Younger where he made use of his mathematical skills in advising on the sinking fund.
• Edward Hall Alderson, Senior Wrangler and Smith's prize winner in 1809. Alderson became an eminent lawyer and judge. His mathematical background doubtless assisted his devastating cross-examination of George Stephenson over the surveying of the Liverpool and Manchester Railway. The young Alderson had been tutored by Edward Maltby who was eighth wrangler in 1792 and went on to become a controversial Bishop of Durham.
• Other senior wranglers who also won Smith's prize and went on to become eminent lawyers and judges include:
  • Thomas Starkie (1803);
  • Frederick Pollock (1806); and
  • William Henry Maule (1810).
• Henry Martyn who became a chaplain in the East India Company, and translated the New Testament into Urdu and Persian^[1]

See also Category:Senior wranglers and Category:Second wranglers.

• 1757 Edward Waring
• 1761 Sir J. Wilson, Judge, Common Pleas
• 1763 William Paley
• 1772 George Pretyman Tomline
• 1774 Isaac Milner
• 1779 Thomas Jones (mathematician)
• 1784 Robert Acklom Ingram
• 1786 John Bell
• 1787 Sir Joseph Littledale (1767-1842), Court of Queen's Bench, P.C.
• 1788 John Brinkley
• 1790 Bewick Bridge (1767-1833)
• 1794 George Butler
• 1795 Robert Woodhouse
• 1796 John Kempthorne
• 1800 James Inman
• 1801 Henry Martyn
• 1802 Thomas Penny White
• 1803 Thomas Starkie
• 1804 John Kaye (English bishop)
• 1805 Thomas Turton
• 1806 Sir Frederick Pollock, 1st Baronet
• 1808 Henry Bickersteth, 1st Baron Langdale
• 1809 Edward Hall Alderson
• 1810 William Henry Maule
• 1812 Cornelius Neale
• 1813 John Herschel
• 1819 Joshua King
• 1821 Solomon Atkinson (1797-1865) [1]
• 1823 George Airy
• 1824 John Cowling
• 1825 James Challis
• 1831 Samuel Earnshaw
• 1834 Philip Kelland (professor of mathematics at Edinburgh)
• 1836 Archibald Smith
• 1837 William Griffin
• 1838 (professor of mathematics at Royal Naval College)
• 1839 (professor of geometry at Gresham College)
• 1840 Robert Leslie Ellis, possibly H. Leslie Ellis
• 1841 George Gabriel Stokes
• 1842 Arthur Cayley
• 1843 John Couch Adams
• 1844 George Wingman Hemming, K.C.
• 1845 Stephen Parkinson
• 1852 P.G. Tait
• 1853 Thomas Bond Sprague (1830-1920), President of Institute of Actuaries
• 1854 Edward Routh
• 1855 J. Savage
• 1858 ? Slesser
• 1859 James Maurice Wilson
• 1860 Sir James Stirling (1836-1916), Lord Justice of Appeal, PC
• 1861 William Steadman Aldis, professor of mathematics at University of Auckland
• 1863 Robert Romer (1840-1918), Lord Justice of Appeal, PC
• 1864 ? Purkiss
• 1865 John Strutt, 3rd Baron Rayleigh
• 1867 Charles Niven (Peterhead, born 1845). M.A. Aberdeen 1863. Professor of Mathematics, Queen’s College, Cork, 1880. Professor natural philosophy Aberdeen.
• 1868 John Fletcher Moulton
• 1869 Numa E. Hartog, first Jewish SW
• 1871 John Hopkinson
• 1875 John William Lord (Ipswich July 27 1851 - Clarens Switzerland September 4 1883) Gold Medalist Of The London University; Fellow Of University College London; Fellow Of Trinity College Cambridge
• 1877 Donald MacAlister
• 1878 E. W. Hobson
• 1880 Joseph Larmor
• 1881 Andrew Forsyth
• 1883 G. B. Mathews
• 1884 William Fleetwood Sheppard
• 1885 Arthur Berry
• 1886 Alfred Cardew Dixon, Chair of Mathematics at Queen's College, Galway
• 1887 H. F. Baker
• 1889 Gilbert Walker
• 1890 G. T. Bennett
• 1895 Thomas John I'Anson Bromwich
• 1897 W. H. Austin
• 1898 Ronald William Henry Turnbull Hudson, author of Kummer's Quartic Surface
• 1899 T. Birtwhistle aeq
• 1899 R. P. Paranjpe, first Indian SW, aeq
• 1900 J. E. Wright
• 1902 Ebenezer Cunningham
• 1903 Harry Bateman
• 1904 Arthur Eddington
• 1905 John Edensor Littlewood
• 1908 Selig Brodetsky
• 1909 Percy John Daniell

• 1759 Richard Watson (bishop)
• 1780 W. Friend Actuary to Royal Life Assurance Company
• c1760 John Jebb (1736-1786)
• 1794 Lord Lyndhurst, Lord Chancellor
• 1810 Thomas Shaw Brandreth
• 1812 George Peacock
• 1816 William Whewell
• 1821 Henry Melvill
• c1830 Samuel Laing (science writer)
• 1835 Henry Goulburn (1813-1843), son of Henry Goulburn
• 1836 John William Colenso
• 1837 James Joseph Sylvester
• 1840 H. Goodwin Dean of Ely 1858-1869 Bishop of Carlisle 1869-1891
• 1843 Francis Bashforth(1819-1912), inventor of the Bashforth chronograph, professor of applied mathematics at Woolwich 1864-1872
• 1845 William Thomson, 1st Baron Kelvin
• 1848 Charles Mackenzie
• 1849 ? Phear
• 1850s Leonard Courtney, 1st Baron Courtney of Penwith
• 1850 Henry William Watson
• 1854 James Clerk Maxwell
• 1855 Leonard Courtney
• 1860s Alfred Marshall
• 1866 ? Aldis
• 1867 William Kingdon Clifford
• 1872 Horace Lamb
• 1874 W. W. Rouse Ball
• 1875 William Burnside, George Chrystal (aeq.)
• 1878 John Edward Aloysius Steggall, Assistant Master at Clifton College; Fielden lecturer at Owens College, Manchester; Professor of Pure and Applied Mathematics, University College Dundee
• 1880 J. J. Thomson
• 1885 Augustus Edward Hough Love
• 1895 E. T. Whittaker
• 1898 John Forbes Cameron aeq Master of Caius
• 1898 James Jeans aeq

The story about Rayleigh comes from

• Peter Groenewegen (2003). A Soaring Eagle: Alfred Marshall 1842-1924. Cheltenham: Edward Elgar. ISBN 1-85898-151-4.

Alfred Marshall was the commoner who came second to Rayleigh.

• D. O., Forfar ‘What became of the senior wranglers?’, Mathematical spectrum 29 (1996/7), 1-4.

Survey of the subsequent careers of senior wranglers during the 157 years (1753-1909) in which the results of Cambridge’s mathematical tripos was published in order of merit.

There is a very thorough account of the Cambridge system in the 19th century in

• Andrew Warwick (2003) Masters of Theory: Cambridge and the Rise of Mathematical Physics. Chicago: University of Chicago Press. ISBN 0-226-87374-9

Appendix A lists the top 10 wranglers from 1865 to 1909 with their coaches and their colleges.

Information on the wranglers in the period 1860-1940 can be extracted from the BritMath database

• BritMath

Many of the wranglers who made careers in mathematics can be identified by searching on "wrangler" in

• The MacTutor History of Mathematics archive

• Cambridge Mathematical Tripos: Wooden Spoons

• 'The Senior Wrangler' is a member of the faculty of Unseen University in Terry Pratchett's Discworld series of novels