ThatsMaths

The Mathematical Tripos examinations, and the Wranglers who achieve honours in them, are the topic of the That’s Maths column ( TM023 ) in the Irish Times this week.
Today (20/06/13) the results of the final examinations in mathematics will be read out at the Senate House in Cambridge University. Following tradition, the class list will then be tossed over the balcony , and the names of this year’s wranglers will be known.

The Wranglers could be a rock group or a brand of American jeans, but they are also the students who gain first-class honours degrees in the examinations known as the Mathematical Tripos, the one ranked first being Senior Wrangler.

Great prestige attaches to the top few Wranglers, opening opportunities for their future professional careers.  To become Senior Wrangler was once regarded as “the greatest intellectual achievement attain able in Britain”. In the past, the rankings in the exams were made public. Since 1910, only the class of degree has been given, but the examiner tips his hat when announcing the name of the top student.

The Old Tripos
The notoriously difficult Triops were a test of speed and well-practised problem-solving techniques, and many brilliant students who were inadequately drilled failed to top the class. To have any hope, students needed to be coached like racing thoroughbreds.

The “Old Tripos” tested the metal of the strongest students. In 1854, when James Clerk Maxwell was beaten into second place by Edward Routh, the Tripos comprised 16 papers over eight days – more than 40 hours in total. Routh went on to become the most successful coach, training 27 Senior Wranglers. Maxwell made monumental contributions to the theory of electromagnetism.

During the nineteenth century, mathematics in Britain lagged behind developments in Germany and France. One of the most inventive and original students who did not make Senior Wrangler was G.H.Hardy, the leading British mathematician of the twentieth century. Hardy placed some blame for Britain’s poor performance on the Mathematical Tripos, stating that they were a poor training for a pure mathematician.

Substantial reforms, introduced in 1909, changed the nature of the Tripos. Prior to that, applications such as Maxwell’s electromagnetic theory had been emphasised. Hardy was largely responsible for the change of focus to more pure mathematics.

“Above the Senior Wrangler”

There were two individuals who were ranked number one but who did not become Senior Wrangler. One was Philippa Fawcett who, in 1890, was declared to be “above the Senior Wrangler”. Her marks were thirteen percent ahead of the next in line but, while women were permitted to take the examinations, they were not allowed at that time to be members of the University or to receive degrees.

The other was the Hungarian-born mathematician George Polya. He had contributed to the reform of the Tripos and, at the request of Hardy, had sat the examination in 1925. To the great surprise of Hardy, Polya achieved the highest mark which, were he a student, would have made him Senior Wrangler.

George Stokes and William Thompson, two Irish-born scientists, were both Wranglers. Stokes was Senior Wrangler in 1841. Thompson, later Lord Kelvin, reckoned himself a “shoo-in” for the honour in 1845. According th legend, he dispatched one of the college servants thus: “Just pop down to the Senate House and see who is Second Wrangler”. The servant returned with the answer: “You, Sir!”

Addendum

This year's Senior Wrangler is Arran Fernandez, the youngest ever, barely 18 years old.     
When he started at Cambridge, he was also the youngest undergraduate there since 
Pitt the Younger. See report in the Cambridge News,