Miss Warren's Profession
Miss Warren’s Profession
Graham Nelson
This is a (hopefully constructive) protest article about the
Mathematical Tripos, or rather the terminus it currently leads to.
The reader who finds subjective polemic of rather limited interest is
encouraged to stop reading now, with my apologies.
In classic soap-box style, one should begin by quoting a famous but
long dead socialist. The title arises from the following passage from
Act I of Bernard Shaw’s play ‘Mrs Warren’s
Profession’, an Unpleasant play which was immediately censored
when it was written in 1894: its message is that women become
prostitutes because of hopeless poverty and not, as was conventionally
considered, wanton immorality. Mrs Warren’s
‘respectably’ brought up daughter Vivie, the other main
character, has just made the acquaintance of Praed, a middle-aged
architect:
PRAED: ... It was perfectly
splendid, your tieing with the third wrangler.
Just the right place, you know. The first wrangler is always a
dreamy, morbid fellow, in whom the thing is pushed to the length
of a disease.
To Praed’s shock, Vivie then explains that she only did so
because her mother had bribed her to do so for £50, and this
was certainly too little.
PRAED: But surely it’s practical to consider not only the work
these
honors cost, but also the culture they bring.
VIVIE: Culture! My dear Mr Praed: do you know what the
mathematical tripos
means? It means grind, grind, grind for six to eight hours a day
at mathematics, and nothing but mathematics. I’m supposed to know
something about science; but I know nothing except the mathematics
it involves.
People often look back on dreadful old Cambridge customs as
quaintly romantic, like the annual reading of the results ceremony in
the Senate House: great fun if you can close your ears to the sound of
crying. (Although that’s not nearly as bad as the gathering of
would-be research students in DPMMS common room immediately after,
where ashen-faced people walk one by one into an office and silently
emerge, with or without a blue piece of paper.) The Tripos has been
reformed a little in the intervening ninety-six years; Cambridge has
finally conceded that women may be capable of thought, and nowadays
the pretence is maintained that nobody is told exactly where they came
in the exams. But, as I hope to demonstrate, the old profession of
wrangling for places is very much alive.
1. How Part III works at the moment
At present, after the three-year Tripos is complete, there is a
fourth year called Part III, which is exceptionally funded
directly by the State so that quite a large number of people are able
to read it. It is primarily intended as a preparation for research,
although quite a number of people take it in order to spend another
comfortable year at Cambridge (despite the miscellaneous selection of
diplomas ideal for that purpose). Students register with either the
Pure or Applied departments, which have very little to do with each
other (so that pure and applied lectures on dynamical systems may
clash, for example!). This distance is such that, having been Pure, I
have hardly any idea of the situation in the Applied department apart
from the general impression that it is more organised.
Teaching is done by offering a choice of a couple of dozen lecture
courses on specialist subjects, usually so that members of the
department give courses on the subjects they are experts in. Some
courses have a few example classes as well, and these can be fairly
helpful, but there aren’t any supervisions and in effect
lectures are the only source. There is little contact with the
departments; Part III students don’t often go to seminars,
for example, as would be thought quite normal for first-year graduates
at most universities. In effect, for someone going on to a doctorate,
this year is the most isolated and cut off of all seven or so; which
is unfortunate given how easy it is to be at a loose end during it.
Having said this, students are provided with careers advice and are
usually made welcome when they go and talk to people in the
departments.
At the end of the time, candidates choose six of these courses to
take examinations in, although they have the option (which in practice
almost everyone exercises) of writing an extended essay in place of
one of them. This can be quite rewarding and at least feels like real
mathematics.
Unfortunately, many of the courses are very specialized, and the
degree to which you have to focus on them is such that you never get
time to look at anything else. The effect is like looking through a
telescope in five or six different directions and pretending to have
seen a landscape. What is perhaps worse is that after this process,
you may have the mistaken impression that you are now too specialized
to be able to look at any of the things missed out: in Dr
Körner’s memorable observation, in a few years you find
yourself at the top of an ever narrowing gum tree.
But the really dreadful thing about Part III is the
examination itself. The courses are (rightly) about difficult things
and most of them are lectured at great speed so as to pack a large
amount of material in. The result is that most reasonable questions
that could be posed about them might take a research student a week to
work out, so that it’s quite hard to set questions which test
understanding. In consequence, most of the examinations test rote
learning on a grand scale; of the papers I took, only small parts of
two questions on one of the papers had answers which did not consist
of recital of the appropriate passage from the lecture notes. The
hardest part of programming a computer to pass the course would be
teaching it to read the rubric and work out what combinations of
questions are legal. There are some papers which call for actual
thought, but they are a somewhat dangerous proposition since you are
bound to get less marks on them than others will get on the memory
tests: which matters a great deal if you want to stay in Cambridge,
since research students are selected solely on the basis of the mark
ordering. (Other universities have been known to treat the results as
meaningful, as well.) In general the papers vary greatly in
difficulty which must make it difficult for the examiners to
normalize.
In any event, the amount of theory required is such that there is
no way to stop and try to think how to derive things, any more than
school Latin and a rough knowledge of the plot is enough to be able to
translate the Aeneid at writing speed. So you need to memorize about
120 lectures of writing, basically symbol by symbol. It might be
thought that this is so large a task that you would be forced to
understand it pretty thoroughly. There is some truth in this; then
again, you also end up learning exactly where every lemma lies on the
page in your notes. A year later, I could still leaf through these
pages in the mind’s eye. Also, you understand what is in the
notes, but little else; it is mostly theory you have no motivation
for. To give an extreme example, immediately before the Commutative
Algebra paper, several of us who could all have recited all the main
theorems and proofs of dimension theory of rings had an argument about
whether there were or were not any rings whose dimension was not
1.
Miss Warren’s estimate of the amount of time this takes is
definitely on the conservative side. Her modern counterparts resort
to devices such as tieing themselves to their chairs with string,
wearing earplugs to prevent them from hearing any conversation they
would be tempted to join, keeping appalling graphs of their daily
twelve-hour workloads, and so on. (In the end people really do become
dreamy and morbid; I can distinctly remember holding a toothbrush on
the night before one of the papers and not being entirely sure what to
do with it.) When it is over, you tend to recoil so much that it may
be months before you are prepared to look a maths book in the contents
page again.
2. Reform
The above notwithstanding, Part III is a way of learning some
useful maths and effectively getting an extra year’s funding
before beginning research, and it has some good features, such as the
essay. Also, it must not be thought that the Cambridge departments
are indifferent to the lot of their students. Anyone who has ever
attended the (variably effectual) meetings of the Faculty Board will
realise that many lecturers are genuinely concerned about reform. At
present, a large-scale reform of the undergraduate Tripos is under
way, which aims to remove some of the arbitrary division of teaching
between Pure and Applied mathematics (vector spaces and
differentiation are Pure, but distributions and vector fields are
Applied, and so forth) and to make it accessible to more A-level
students. Much time and effort has gone into this thoroughly
worthwhile aim. It was interesting to note that in the early stages,
many people were very concerned that at almost any cost, Part III
had to be maintained, that being the jewel in the crown of the
Cambridge Tripos.
Also, two years ago an attempt was made by the Pure department to
reform the problem of overspecialized courses. It was decided that
the old system of having many courses which only one or two people
would study, would have to go; a broad range of introductory courses
would be added. (This did not stop them from quietly allowing a few
people to take specially set second papers on combinatorics and
category theory, however; although as the existence of these papers
was not directly communicated even to those who had attended the first
courses, this number might have been artificially few.) This was
partially successful, although many of the lecture courses seemed to
be still fundamentally about specific theories in great detail without
much reference to their relevance to each other. The problem of
overspecialization in effect remains, except that now there are fewer
courses available, it is no longer always possible for this
specialization to be in subjects people intend to work in.
Having said this, complaining to the powers that be about
Part III is like the guests at Fawlty Towers complaining about
Manuel to Basil Fawlty, who replies “I know, he’s awful,
isn’t he?” Owing to the rather odd election rules for
student representatives on the Faculty Board, it is essentially
impossible for a Part III student to be one (if you are an
undergraduate but graduate part-way through the time, you must step
down; if you are a Part III student, you have no certainty of
still being in Cambridge for any more than one term from when the
elections take place); so it is a cause with no obvious spokesman.
But at least there will be an excellent opportunity to do something
about it when the first intake to the reformed Tripos reach
Part III.
As for how to reform it, at this point I slide yet further into
subjectivity. In many ways a useful way to spend the year would be to
take another selection of Part II courses passed over in the year
before (for example, General Relativity and Linear Analysis is not
that unlikely a combination of courses, but sheer pressure on
timetables usually clashes them), but this is unrealistic. At the
other extreme, moving over to a full MPhil course would result in the
exceptional funding status of Part III being lost, which would
mean that very few people could take it and it would not be feasible
to offer such a range of courses. I propose that the balance between
course-work (i.e. on dissertations of some kind) and examinations
be drastically shifted, possibly so that the examination part could be
just on a few of the ‘core’ courses; other lecture courses
would be to provide background, understanding of which would be
necessary to work on the dissertations part of it, as well as being
useful to research students. Ideally, students would work on several
different essays, but on different subjects.
Shaw would probably have considered these proposals dismally
unradical, but the Faculty Board (or, more importantly, the staff
meetings) may well disagree. Most of my argument, which has perhaps
itself been pushed to the point of a disease, has been to propose
reform just to make the course more humane for students, but the
departments have just as much to gain: a more sensible system for
selecting research students and (more optimistically) some integration
of all these potential future mathematicians into the institutions
they nominally belong to.
Reproduced from Eureka 51 pages 36-39.
