# Past Lives: Part III Maths

I’ve been very lucky so far in my life, and have had many opportunities to work and study in interesting places. I’m not sure I’ve made the best use of those opportunities–there’s much that feels unfinished or that didn’t quite work out the way I’d hoped it would–but these “past lives” have given me a lot of experience working in different fields, living in different places, hanging out with different kinds of people.

Blogging is inherently self-indulgent: you have to assume that someone out there is interested in reading your maunderings. (Not really. Honestly, I do this for my own amusement.) The ultimate in self-indulgence has to be autobiographical blogging and reminiscing, where some old fart bends everyone’s ear about the “good old days”. Anyway, since this is for my own amusement and for a bit of writing practice, I don’t really care. I’m going to be brazenly self-indulgent and start writing “Past Lives” articles to see if I can dredge up any interesting memories.

In October 1997, I went to Cambridge to spend 9 months at DAMTPDepartment of Applied Mathematics and Theoretical Physics. to do the course that’s generally called Part III Maths, although it has the official title of the Certificate of Advanced Study in Mathematics. It’s a taught masters’ in mathematics, where you can choose from around 100 different courses on all aspects of maths (pure and applied). It’s examined at the end, and has a reputation as being one of the harder mathematics courses in the world.

It’s also used as a gatekeeper to determine who is offered maths PhD places in Cambridge. I went to Cambridge fresh from a stint in the delightful world of international financeSome of my worst jobs ever., all bright-eyed and bushy-tailed with the idea of doing a PhD in theoretical particle physics. Which meant that I needed to work hard and do well to have any chance of getting a studentship.

Part III is a funny sort of course. Cambridge undergraduates can do it as an optional fourth year of the standard undergraduate maths programme, but people also come in from outside to do it (like me). It’s very much a sink or swim affair. The courses are hard, the exams are harder, and there’s little or no pastoral guidance or help. Go to lectures, sit at home thinking hard and doing maths, go to tutorial classes, rinse and repeat (possibly with a pub visit or two in there somewhere). The lecturing ranges from the abysmally poor (no names...) to the very very good (Peter Goddard lecturing on conformal field theory sticks out as being one of thoseI sat next to a guy called Dave in this course. In about the third lecture, Goddard introduced a set of operators called the $L$s. We didn’t quite understand what they were, which was a bit of a shame, since they appeared in almost every lecture from then on, leading us to ask each other on the way out of every lecture “Do you know what the $L$s are yet?”. (They’re the generators of the Virasoro algebra, which is a bit like a Lie algebra for the funny infinite-dimensional symmetry group that crops up in two-dimensional conformal field theory. There. That cleared it up for you, didn’t it?)), no prisoners are taken, and you quickly get the impression that you’re surrounded by some very smart people indeed.

I mostly took courses in theoretical physics (quantum field theory, general relativity, elementary particle physics and group theory, more quantum field theory, conformal field theory, plus some other stuff that I don’t remember any more). Mostly it was fun, and I learnt a lot. Some of it was less fun, and I got quite seriously turned off the idea of a particle theory PhD. I think the straw that broke the camel’s back was talking to one of a PhD student who proudly showed me a six-inch stack of paper that was his work for the last couple of months. A single calculation. He described to me what it was about, and I understood perhaps 10% of what he said. “Could it be real?” I asked. “Oh no–no way. Definitely not real. Just a thought experiment. Just something that hadn’t been worked out.” And there was the rub. At that time, and maybe still, the life of a student wasn’t likely to be much more than filling in corners left by the big names. Now, I can look back and recognise that that wasn’t necessarily a bad approach to take for PhD students: they get to learn about the subject on a well-constrained problem, a problem with a definite end-point that’s attainable in three years. At the time though, it seemed pretty uninspiring, so I kicked back and didn’t work terribly hard for the rest of the year, then lit out for Oxford to work on remote sensing of the atmosphere of Mars...

In retrospect, Part III Maths for me served as a good interregnum, a short period between working and starting as a PhD student. It was also a period where I went through big changes in my personal life, splitting up with a long-term girlfriend (fiancée at that time), with all the trauma that that entailed. I wasn’t really in the right frame of mind to truly benefit from the teaching offered in Cambridge at that point, but it was still useful experience. I still don’t know what the $L$s are though.