Cambridge University’s Sean Eberhard ’08 recently joined a distinguished group of brilliant mathematicians when he was named Senior Wrangler, the highest-scoring Cambridge student who has completed the third year (called Part II) of the Mathematical Tripos.
“The whole Senior Wrangler thing is completely unofficial, yet it’s something that everybody knows,” Eberhard said. “The University used to publish the entire class list in rank order and publically announce the senior, second, and third wranglers in the newspaper, but that all ended about 100 years ago. Now all the senior wrangler gets from the University is a tip of the hat, literally.”
Today, a class list is read aloud by an examiner in the Cambridge University Senate House about a week after exams end, with the examiner only stating the class of the degree, not indicating a rank. When the examiner comes to the name of the highest ranking candidate, however, he traditionally tips his hat to indicate such. “Despite that, everybody, including Wikipedia, seems to know who came out on top,” Eberhard said.
Though there was no formal recognition of the achievement by the University, Eberhard’s college, Gonville and Caius, awarded him its highest academic prize – the Schuldham plate. “It’s a silver plate with a Latin inscription which basically says that I’m awesome,” Eberhard said.
Some notable Senior Wranglers include John Herschel, Arthur Cayley, James Inman, George Gabriel Stokes, Lord Rayleigh, Arthur Eddington, and J.E. Littlewood. Second wranglers include Alfred Marshall, James Clerk Maxwell, J.J. Thomson, and Lord Kelvin.
A mathematical physicist and engineer, who has a unit of absolute temperature (kelvin) named in his honor, Lord Kelvin was so sure that he would be named Senior Wrangler that he sent his servant to the Senate House on results day to find out who came second, Eberhard said. The servant returned and responded, “You, sir!”
The Mathematical Tripos consisted of four three-hour papers, all completely written. “Yes, they are hard, and I don’t like them,” Eberhard said.
Eberhard provided the following sample question from the exam:
16H Logic and Set Theory:
State and prove the Upward Lowenheim–Skolem Theorem.
[You may assume the Compactness Theorem, provided that you state it clearly.]
A total ordering (X, <) is called dense if for any x < y there exists z with x < z < y.
Show that a dense total ordering (on more than one point) cannot be a well-ordering.
For each of the following theories, either give axioms, in the language of posets,
for the theory or prove carefully that the theory is not axiomatisable in the language of
(i) The theory of dense total orderings.
(ii) The theory of countable dense total orderings.
(iii) The theory of uncountable dense total orderings.
(iv) The theory of well-ordering
Or, if you prefer:
20F Number Fields:
Calculate the class group for the ﬁeld K = Q(√−17).
[You may use any general theorem, provided that you state it accurately.]
Find all solutions in integers of the equation y^2 = x^5 -17.
Is your head spinning yet?
Eberhard says that Cambridge, as well as other United Kingdom universities in general, approach education quite differently from American universities.
“There are three very short eight-week terms per year, each packed with six days of lectures per week, twice weekly one-on-one supervisions, and no marked work until exams in June,” he said.
When he’s not immersed in math, Eberhard’s principal extracurricular activity is bridge. “I regularly play in the University club, and I have competed against Oxford twice – and won both times,” he said.
Earning a degree in the UK is typically a three year process. “I could have graduated this past June, but I chose instead to do the so-called ‘Part III,’ which consists of one further year ending with a master’s degree (in addition to a bachelor’s degree),” Eberhard said.
Eberhard also plans to pursue a doctoral degree.
After that? “Mathematics is my passion, and I want to continue doing research,” he said.