1018 words on Uni
The text on Quantum Field Theory we read contains a funny starting section entitled
The life cycle of a theoretical physicist. Now what is the life cycle of a mathematician then? Equally strange and suprising I'd say.
Back in my second year I loved algebra – a word that may have a slightly different meaning at university than at school. Also I was convinced that analysis sucks and that I'll be an algebraic geometer later. I must admit I also started being intrigued by topology at the time – and not only for the number of 'o's in the word (which happens to be topped by 'cohomology'). Anyhow, I never managed to get more than a basic grasp of algebraic geometry.
I drifted off into differential geometry instead. 'But didn't you hate analysis?' the observant reader might ask. Yep, don't really like it, but with some extra perspective on it, it seems that it becomes better as you go – and you don't really need to get your hands dirty with epsilons most of the time. In fact, it seems to converge pretty much with algebraic topology and many of the other areas in mathematics. By now I am happy with many bits of differential geometry and even have come to think that you can conduct a casual conversation on the topic of manifolds and it happens more frequently than is suspected. And in a mathematical context, I find it quite hard by now to talk to people not conversant in manifolds, differential forms and their peers. It's a bit sad. And it makes conversations with the public harder – I attended a seminar on this and received my attendance slip this week; I'm not really sure how it will help me, but it's another piece of paper to add to my qualification.
Concerning my mathematical interests, by now I can actually quote Tom Lehrer for my specialisation:
on Analytic and Algebraic Topology of Locally Euclidean Metrisation of Infinitely Differentiable Riemannian Manifolds.
Tom Lehrer, Lobachevsky
Now this looks like I've swept all across mathematics (not true, as there are many more areas). So what's going to come next? Could I even end up doing some algebraic geometry in the end? I'd have to become more clever for that, probably. But apart from that, It doesn't seem entirely unlikely. My tutor is never tired of pointing out that knowing your algebraic geometry is as important as knowing your differential geometry. But he knows too much anyway.
That's right. Victor, aka my tutor, aka Professor Pidstrygach, aka my boss, seems to be able to talk on almost any topic I ask him about. He'll usually give even more information than I can digest and make it look easy at the same time. The 'looks easy' parts lasts about as long as it takes to get back to my desk and try things out myself. He already ruined the schedule for our seminar this term by talking too much. We're already two weeks behind the schedule and it's only the third week of term. It's not that the things he tells us are not interesting or told too slowly, quite the opposite. It's just such a lot. Amazing – sometimes a bit scary.
His quote for today
Why don't you simply use the spectral sequence? Riight, using the words 'simply' and 'spectral sequence' together in this way never occurred to me. Amazingly in the end everything seemed quite simple.
The book we discuss in the seminar is quite interesting but I don't like the language in it. A complete underuse of the Genitiv and overuse of apostrophes in words as
Riemannian and usually is spelled
Riemannsch. Quite an interesting word in English as well, by the way: Usage is
Riemannian Geometry but
Riemann Surfaces, with the
ian suppressed. I always puzzeled me why. The book we read – actually it's a whole series of books that's affected by this – has one of the ugliest covers, ever.
Other quotes by mathematicians this week:
Looks like magic, said by myself after Nakayama's lemma was invoked in our seminar on Monday. I know it's like magic but it looks like it, making whatever module you're looking at disappear in a puff of smoke.
It's a bit like magic, said by Sylvie Paycha after finishing her fifth talk in a series and trying to explain to us what physicists do. She also quoted Richard Melrose who gave a series of talks here this week as having said that
sometimes mathematicians seem closer to the world than string theorists.
Other university related chaos: The class I tutor was re-located into a larger room due to its size. Apparently the room was double-booked. Turned out it wasn't. People just mis-read the number. I keep telling people but no-one believes me: Mathematicians are bad at numbers. With the classes we teach and mark the work of having the inhumane size of 30, this is due to the fourth tutor for our lecture having been re-allocated to a different lecture that has more attendees. However, they're allowed to hand in their homework in groups of two or three there. Thus the workload is much lighter. Perhaps another lesson: Don't judge a situation by the sheer numbers without knowing the precise circumstances. – Particularly not if you're a mathematician.
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