TheSenior Wrangler is the top mathematics undergraduate at theUniversity of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain".^[1]

Specifically, it is the person who achieves the highest overall mark among theWranglers – the students at Cambridge who gainfirst-class degrees in mathematics. The Cambridge undergraduate mathematics course, orMathematical Tripos, is famously difficult.

Many Senior Wranglers have become world-leading figures in mathematics, physics, and other fields. They includeGeorge Airy,Jacob Bronowski,Christopher Budd,Kevin Buzzard,Arthur Cayley,Henry Cotterill,Donald Coxeter,Arthur Eddington,Ben Green,John Herschel,James Inman,J. E. Littlewood,Lee Hsien Loong,Jayant Narlikar,Morris Pell,John Polkinghorne,Frank Ramsey,Lord Rayleigh (John Strutt), SirGeorge Stokes,Isaac Todhunter, SirGilbert Walker, andJames H. Wilkinson.

Senior Wranglers were once fêted with torchlit processions and took pride of place in the university's graduation ceremony.^[2] Years in Cambridge were often remembered by who had been Senior Wrangler that year.^[1]

The annual ceremony in which the Senior Wrangler becomes known was first held in the 18th century. Standing on the balcony of the university'sSenate House, the examiner reads out theclass results for mathematics,^[3] and printed copies of the results are then thrown to the audience below. The examiner no longer announces the students' exact rankings, but they still identify the Senior Wrangler, nowadays tipping theiracademic hat when reading out the person's name.

Those who have achieved second place, known as Second Wranglers, includeAlfred Marshall,James Clerk Maxwell,J. J. Thomson,Lord Kelvin,William Clifford, andWilliam Whewell.

Those who have finished between third and 12th includeArchibald Hill,Karl Pearson andWilliam Henry Bragg (third),George Green,G. H. Hardy, andAlfred North Whitehead (fourth),Adam Sedgwick (fifth),John Venn (sixth),Bertrand Russell,Nevil Maskelyne andSir James Timmins Chance (seventh),Thomas Malthus (ninth), andJohn Maynard Keynes andWilliam Henry Fox Talbot (12th).

Between 1748 and 1909 the university publicly announced the ranking,^[4] which was then reported in newspapers such asThe Times. The examination was considered to be by far the most important in Britain and the Empire. The prestige of being a high Wrangler was great; the respect accorded to the Senior Wrangler was immense. Andrew Warwick, author ofMasters of Theory, describes the term 'Senior Wrangler' as "synonymous with academic supremacy".^[5]

Since 1910 successful students in the examinations have been told their rankings privately, and not all Senior Wranglers have become publicly known as such. In recent years, the custom of discretion regarding ranking has progressively vanished, and all Senior Wranglers since 2010 have announced their identity publicly.

The youngest person to be Senior Wrangler is probablyArran Fernandez, who came top in 2013, aged 18 years and 0 months.^[6] The previous youngest was probablyJames Wilkinson in 1939, aged 19 years and nine months.^[7] The youngest up to 1909 wereAlfred Flux in 1887, aged 20 years and two months^[8] andPeter Tait in 1852, aged 20 years and eight months.^[9]

Two individuals have placed first without becoming known as Senior Wrangler. One was the studentPhilippa Fawcett in 1890. At that time, although the university allowed women to take the examinations, it did not allow them to be members of the university, nor to receive degrees. Therefore, they could not be known as 'Wranglers', and were merely told how they had performed compared to the male candidates, for example, "equal to the Third Wrangler", or "between the Seventh and Eighth Wranglers". Having gained the highest mark, Fawcett was declared to have finished "above the Senior Wrangler".

The other was the mathematics professorGeorge Pólya. As he had contributed to reforming the Tripos with the aim that an excellent performance would be less dependent on solving hard problems and more so on showing a broad mathematical understanding and knowledge,G.H. Hardy asked Pólya to sit the examinations himself, unofficially, during his stay in England in 1924–5. Pólya did so, and to Hardy's surprise, received the highest mark, an achievement which, had he been a student, would have made him the Senior Wrangler.^[10]

Senior Wrangler's Walk is a path in Cambridge, the walk to and along which was considered to be sufficientconstitutional exercise for a student aspiring to become the Senior Wrangler. The route was shorter than other walks, such as Wranglers' Walk and theGrantchester Grind, undertaken by undergraduates whose aspirations were lower.^[11]

Senior Wrangler sauce is a Cambridge term forbrandy butter, a type ofhard sauce made frombrandy, butter, and sugar, traditionally served in Britain withChristmas pudding and warmmince pies.^[12]

Senior Wrangler is also the name of asolitaire card game, alternatively known as Mathematics and Double Calculation, played with twodecks ofcards and involving elementarymodular arithmetic.^[13][14]

Fictional Senior Wranglers appearing in novels include Roger Hamley, a character inElizabeth Gaskell'sWives and Daughters, and Tom Jericho, thecryptanalyst inRobert Harris's novelEnigma, who is described as having been Senior Wrangler in 1938. InCatherine Hall'sThe Proof of Love, Victor Turner is listed as having been Senior Wrangler in 1968.

InGeorge Bernard Shaw's playMrs. Warren's Profession, the title character's daughter Vivie is praised for "tieing with the third wrangler," and she comments that "the mathematical tripos" means "grind, grind, grind for six to eight hours a day at mathematics, and nothing but mathematics."

InFord Madox Ford'sParade's End, the characterChristopher Tietjens is described as having settled deliberately for only being Second Wrangler, to avoid the weight of expectation that the title would create.

In hisDiscworld series of novels,Terry Pratchett has a character called the Senior Wrangler, afaculty member at theUnseen University, whose first name is Horace.

The compiler of crosswords forThe Leader in the 1930s used 'Senior Wrangler' as a pseudonym.^[15]

The two most successful 19th-century coaches of Senior Wranglers wereWilliam Hopkins andEdward Routh. Hopkins, the 'Senior Wrangler Maker', who himself was the 7th Wrangler, coached 17 Senior Wranglers. Routh, who had himself been the Senior Wrangler, coached 27.^[16] Another, described by his student (and Senior Wrangler)J.E. Littlewood as "the last of the great coaches", was another Senior Wrangler,Robert Alfred Herman.^[17]

During 1748–1909 the top two colleges in terms of number of Senior Wranglers wereTrinity andSt John's with 56 and 54 respectively.Gonville and Caius was third with 13.

Senior Wranglers since 1910 also include:

• David Hobson^[71] (Christ's College) (1940s)
• Peter Swinnerton-Dyer^[72] (Trinity College) (1940s)
• Jack Leeming^[73] (St John's College)
• Michael Hall^[74] (Trinity College) (1950s)

• Wooden spoon (award)

• Galton, Francis (2000). "Classification of Men According to their Natural Gifts". In James Roy Newman (ed.).The World of Mathematics. Vol. 2. Courier Dover Publications.ISBN 0-486-41150-8.
• ed. H.C.G Matthew and Brian Harrison, ed. (2004).Oxford Dictionary of National Biography.Oxford University Press.
• Tanner, Joseph Robson (1917).The historical register of the University of Cambridge, being a supplement to the Calendar with a record of University offices, honours and distinctions to the year 1910(PDF).Cambridge University Press. Retrieved19 September 2008.
• Venn, John (1922–27).Alumni Cantabrigienses. Cambridge University Press.
• Paul, Margaret (2012).Frank Ramsey (1903–1930): A Sister's Memoir. Smith-Gordon.