Archive for December, 2011

Farewell to a pen-friend

December 18, 2011

A few days ago I learnt from the Guardian of the death of the novelist and critic Gilbert Adair. I was saddened by this, partly because I have hugely enjoyed his writing (though I’m glad to say that I haven’t read his entire oeuvre, so there are still treats in store) and partly because I knew him. The title of this post is a pun of a kind I hope he would have approved of: our interactions were mostly by email, but one can also take the “pen” to mean “almost” (as in “peninsula”), which is why I used a hyphen. We met a couple of times, and might have become proper friends if I had been less socially lazy. It turns out that he had a stroke a year ago, but I didn’t hear about it, so his death just over a week ago came as a surprise and leaves me regretting that I didn’t see more of him while I had the chance.

Since there’s nothing I can do about that, I thought that I’d try to use this blog as an outlet for the resulting feeling of loss, which is out of proportion to the amount that I actually had to do with him. Or perhaps it isn’t, since the very fact that I didn’t see him much is part of what now bothers me. It is also why I had no idea that my last contact with him might be my last, and why his death now seems a bit unreal.

A maths blog is not a completely inappropriate place to write about him, because I met him through mathematics and it was because of mathematics, which fascinated him, that that initial meeting led to a couple of further meetings. A secondary purpose of this post is to recommend his books, which are extremely clever in a way that many mathematicians would like. I’ll describe some of them as I go along.

Group actions IV: intrinsic actions

December 10, 2011

I have a confession to make. When I was an undergraduate at Cambridge (hmm, that sounds as though it might be the beginning of quite an interesting confession, so I’d better forestall any disappointment by saying right now that it isn’t), there was a third-year course in group theory, taught by John Thompson no less, on which I did not do very well. For a few weeks it seemed to cover material that we’d done in our first year, and then suddenly it got serious, with things like the Sylow theorems. And at that point I got lost, and was unable to do the questions on the examples sheets. I can’t remember much about the questions, but I think my difficulty was that there was a slightly indirect style of proof that caused me to find arguments hard to remember and even harder to come up with. And I never got round to doing anything about it: I went into a different area of maths, and even now I don’t know the proofs of the Sylow theorems. In fact, I don’t even know the statements, though I know they’re about the existence of subgroups of various cardinalities, and I know that they are proved using cleverly defined group actions. I’ve skim-read the proofs, so I have a fairly good idea of their flavour, but I don’t know the details. In particular, I don’t know which action does the job.