Essays - to write or not to write

Write.  Do the essay.  Why?

• Part III needs to be a year of transformation, you start as a student, you need to end up as an (inexperienced) researcher. Part of the training undertaken in the year therefore really ought to include some attempt at learning to do research. In allowing you to do an essay in lieu of an exam the Faculty has done its best to provide this opportunity and encourage you to take it.
• You get credits equivalent to a 24 hour course. Generally speaking it is a safe option - people generally score well on essays relative to their performance in other course.
• You get a chance to interact with a member of staff on an individual basis - rare in Part III. It’s not actually all that much like being someone’s PhD supervisee, but it’s closer than listening to lectures and it's an opportunity for conversation.
• Particularly if you take advantage of giving a talk on your essay in the Lent Term Seminar Series, you are given a reasonable framework guiding you through what may be your first effort at writing a mathematical paper: a series of meetings with an adviser, a chance to give a talk on the subject at just the right time so you have to have settled on what material you are going to include in reasonable time to get it written and still have time to review the coursework.
• It really does feel a bit like research. Particularly in the first term of Part III, it is far too easy to get overwhelmed by coursework, and forget that mathematics is anything other than coursework. You can be forgiven if you are beginning to wonder whether you actually even like mathematics, and why you signed up for more of it. For many people, the essay is a relief. It is not a question of being responsible for everything in a paper, it is much more a question of what can you get out of it. When it comes to creative mathematics, that’s the point. 
• Often it is something that you can get stuck into over the Christmas holidays period of revision which is not actually revision, a pleasant relief, a cleansing of the palate between courses resembling so much cold fried eggs.
• It’s a good test whether academic research is something you might enjoy. If you enjoy reading the paper, testing ideas in it on examples, inventing examples, wondering why it works, wondering why the authors did it this way rather than that way, wondering why they left out this or that, or why they didn't generalise the idea, that’s a good omen for a contented future as a research mathematician, even if you are terminally fed up with the coursework now.

A few caveats:

• Do find out as much about the proposed topic as possible, even before talking to essay setters. PhD students are a useful resource. Also find out as much as possible about the essay setter. PhD students are a useful resource.  It is not possible to normalise the expectations of essay setters.
• Do take advantage of the chance to give a talk on the essay topic in the Lent Term Part III Seminar Series.  The timing of that series, inconvenient in other respects as it may be, is exactly what it needs to be to give students (at least those doing essays depending only on Michaelmas term courses) a hard deadline by which they should have a good outline for their essay.  Those doing essays depending on Lent term courses may find it a little rushed, but it is still a good deadline for getting at least the background for the essay in your head, and that is generally quite sufficient for a talk and a good leg up on an outline for the essay.
• Be aware of one common recipe for disappointment, particularly for talented student who are really going to enjoy research. Beware spending too long exploring the ideas for the essay, then too long in writing the essay, and therefore doing grave injustice to the business of revision.

 ————————Story time -  from last time - some weeks later - our (somewhat despondent) aspiring algebraist is snuffling round the mathematical waste heaps trying to find something that might turn into Thesis Attempt 34..

Thanksgiving. November, 1977. 

I always like Thanksgiving - that American feast that occurs at a nonsensical moment to punctuate the autumn term of almost any academic course.  It is a tradition strong enough that all schools respect it - the Thursday and the Friday are nearly always holidays, and most who live within convenient distance of home repair there for relatives and feasting. It's timing is a problem for almost all term schedules, causing an inconvenient break of nearly a week with less than four weeks of term to follow. But as both student and staff I always found something wonderfully heartening about it: if I made it to Thanksgiving, I felt I was almost certain to survive until the end of term.

Most people headed for homes and relatives, but not all.  That year I did, but Barbara, the Other Woman in my year, did not - California was a step too far.  Being a generous spirit and a competent cook she offered instead to make Thanksgiving dinner for her brother, a rising star amongst the Harvard theoretical physicists, and his friends. On the occasion, for perhaps ten minutes or so at table, conversation was general. Then, theoretical physicists being theoretical physicists, theory began to creep in. Before second helpings, Barbara was left listening, chin in hand, to a conversation that was, well, not inclusive.

Listening as she did, she began to recognise isolated words which cropped up with some persistence: “……supermanifold……..  ……supermanifold….” Seizing on an opportunity to re-engage in the conversation she offered a contribution “Marj says supermanifolds are essentially just vector bundles.” 

Silence. Heads turned. 

It seemed that this was something significant. Barbara relayed this information to me on my return; I dug down in my mortuary of deceased thesis attempts, pulled 33b out of the freezer, thawed it, dusted it off, and submitted it.

——————boring moralising

This stuff isn’t about Part III, it’s about being a PhD student, why am I telling you all this stuff? Shouldn’t I be addressing this, if at all, to PhD students?

I think I’m right in writing this stuff for you. Many of you will be PhD students, many of you are making up your minds whether to be PhD students. You are in a position of needing to make an important decision on the basis of extremely incomplete evidence: you have at best hearsay to rely on in the matter of what you are signing up for, what the experience of being a PhD student is actually like. 

I am providing you with a source of hearsay. By telling tales of my outrageous (mostly good) fortune in my PhD course I am hoping that I can convince you that luck plays a much greater role than you might imagine.  I hope you will  begin to understand that when you are engaged in research, the missing information, the connection lending significance to a result, may not come about as the result of systematic mining of information or deliberate enquiry, but may depend on chance encounters and blind luck. I hope I can convince you of the importance of helping blind luck in every way possible, by talking and listening to colleagues, by networking, by keeping an ear open for the unexpected.

I am not at all trying to discourage anyone from going on to do a PhD. Particularly if you enjoy the experience of preparing a talk, enjoy the experience of trying to read and thinking about a paper, whether you are one who is aiming for a distinction or one who will be grateful for a pass, if mathematics pleases, just go for it.

But recognise the capricious nature of the pursuit. Foreknowledge will give you strength to meet whatever twists the route might take.