Wrangler

 For other uses, see Wrangler (disambiguation).
At the University of Cambridge in England, a wrangler is a student who has completed the third year (called Part II) of the mathematical tripos with firstclass honours.
The highestscoring student is named the "senior wrangler"; the second highestscoring student is the "second wrangler"; the third highest is the "third wrangler", etc.
Senior wranglers have included some of Britain's most brilliant scientists, including John Herschel, George Stokes and Lord Rayleigh. Interestingly, there are some equally if not more famous names associated with the rank of second wrangler (James Clerk Maxwell, J.J. Thomson, 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 man who got Senior Wrangler put it down having learnt it off by heart.
The culture of fierce competition at mathematics exams was typical of Cambridge for a long time, and for this reason Cambridge rather than Oxford is associated with most of England's best mathematical and scientific minds (the two universities were the only ones in England for several hundred years). However, it is certainly not true to say that top marks in the Cambridge maths 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 maths at Cambridge did not come top of their class (Hardy was 4th, Sedgwick 5th and Keynes was 12th).
The first woman to top the maths 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 men, so she came "above the senior wrangler"..
The examination was the most important in Britain and the results were given great publicity. In 1865 Lord Rayleigh was senior wrangler and the Times of 30 January had a leader saying there was no reason to fear that he had gained this distinction through favoritism accorded to the 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 senior wrangler was P. J. Daniell who graduated in 1909.
Students who achieve secondclass and thirdclass maths degrees are known as Senior Optimes (secondclass) and Junior Optimes (thirdclass); before 1995 Cambridge did not divide its examination classification in mathematics into 2:1s and 2:2s but now there are Senior Optimes Division 1 and Senior Optimes Division 2.
Discussion
The story about Rayleigh comes from
 Peter Groenewegen (2003). A Soaring Eagle: Alfred Marshall 18421924. Cheltenham: Edward Elgar. ISBN 1858981514
Alfred Marshall was the commoner who came second to Rayleigh.
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 0226873749
Appendix A lists the top 10 wranglers from 1865 to 1909 with their coaches and their colleges.
External links
Information on the wranglers in the period 18601940 can be extracted from the BritMath database
 BritMath (http://britmath.open.ac.uk/welcome.htm)
See also
 Donald MacAlister, Senior Wrangler in 1877. MacAlister was one of the many wranglers who achieved distinction outside of mathematics. The postcard portrait was part of the cult of celebrity surrounding the senior wrangler.