Thanks for the advice. It's reassuring that people keep telling me I don't need to know all about the areas these guys are doing research in.

Hi,

I'm looking for a PhD in Pure Maths. I've found someone who might be a good supervisor, and I want to e-mail them, but I'm not sure what to write. I've been told by my department contact at my current uni that you don't need to be as specific about what exactly you want to do for a Maths PhD than for other subjects, which is good since I don't know exactly what I want to do, but bad because it doesn't seem to leave me much to write. Any advice?

I should also point out that while the place I'm looking at "invites applications" they aren't advertising specific PhD programmes. Also, if it makes any difference, I'm in, and applying to, the UK.

Thanks.