Writing a research statement in mathematics without having any research experience It's pretty common that European universities ask for a Research Statement when applying to a PhD program. The problem is that at my current university where I did my undergraduate and where I'm currently in a masters degree program, I haven't had any research experience at all. My adviser told me that I should wait until enrolled in a PhD program to start worrying about doing research. (My B.Sc. is in physics and I want to work in mathematics - hence the M.S. in math - so he told me I should work on having a solid basis in maths first.)

I'm pretty sure I know in which area I want to focus my future work, but I haven't worked substantially in that area (it's quite advanced) and I'm far from being able to contribute academically to this area.

How should I formulate my Research Statement on my PhD application?
Your research statement should set out the background to the problems that interest you, what you think you could contribute to their analysis/solution, and an overview of the approach(es) that you anticipate that you might have to take. People want to be reassured that you understand the nature of research (ie. how it differs to an undergraduate programme of work), that you have a substantial and interesting problem in mind, and that you are potentially equipped to make an original and nontrivial contribution to knowledge.