I am a graduate student planning to apply in Australia for a PHd very soon.
I have observed that most of the universities require the applicant to provide a 100-words summary of the research they propose to undertake.
Now my graduate training was fairly general (MS doesn't really help you specialize). I am very clear on the field in which I want to pursue PHd (Mathematical Biology),
However the field is very wide in scope and I have not really narrowed down to a specific problem to which I want to dedicate the next four years of my life.
So my question is: what level of detail is being expected on such a "100-words summary"? Are recent graduate students really expected to have a project in mind they want to work on? (Am I finding this incredible only because I dont have one?)
Should I may be give an example of the kind of problems that excite me, while indicating my flexibility to be engaged in something new?
I vaguely understand that I should consider the area of work of the person I am writing to while preparing such an application, but more than that, I am not sure I understand.


Possibly related question
[Research statement in PhD applications--how much is too much?](https://mathoverflow.net/questions/27001/research-statement-in-phd-applications-how-much-is-too-much)


But I believe I am asking a different question.
Also, as further clarification to one of the answers given below, my MS did not involve writing a thesis. (If it did, that would certainly serve as a good starting point.)



Level of detail on a Phd application
I'm on the Mathematics faculty of an Australian university. The way it seems to work at my university, and maybe at other Australian universities as well, is that a PhD applicant is accepted only if there is a faculty member committed to acting as supervisor. So it seems to me that the indicated strategy is, when applying to the program at University X, to look at the faculty at University X, see if anyone there is working on something you could imagine being interested in, quickly learn enough about that area to write a few sensible sentences about it, and proclaim that you would be happy to work on that topic or on such other topics in Math Biology as people at University X might want you to work on. 


It does seem strange to me that a beginning postgraduate would be expected to have a research proposal - it certainly didn't work that way when I was applying to PhD programs in the US in ancient days - but I guess you have to go with it. 


