I realise a maths PhD is completely different from other science PhD, like we don't have any lab work. I still have this confidence issue. I can't stop thinking, can I really solve some unsolved problems? What if I can't prove anything new in 3 years' time? My supervisor seems very supportive, but sometimes I am scared to ask him to explain something, in case it might sound stupid. Don't know what to do really. It would be great to hear how other people are doing.

Don't worry about asking what appear to be silly questions. I'm doing a PhD that involves a lot of mathematical modelling and I am liasing with the maths department. During my first meeting I asked about the possibility of deriving analytical solutions to the problem. This I was told would be virtually impossible(in his opinion)to what is a highly non-linear problem. What I'm trying to say is that you should ask everything to begin with, then as you understand the problem better, you'll find out the areas where there are limits to what can be achieved and areas that are ripe for research. No questions are silly in the beginning.