Dating fellow grad student
Here you decide what constitutes an important problem.
You must arrive at this decision independently for two reasons.
This is one point where you can start a whole new area of research.
Only with a proposal before them can they give you constructive criticism. There could be two or three model systems that all seem to have equally good chances on paper of providing appropriate tests for your ideas, but in fact practical problems may exclude some of them. If you do not get along with your professors, change advisors early on.
In fact, some professors care about you and some don’t. Assume that everything you read is bullshit until the author manages to convince you that it isn’t.
If you want to pick somebody’s brains, you’ll have to go to him or her, because they won’t be coming to you. When you first arrive, read and think widely and exhaustively for a year.
It is much more efficient to discover this at the start than to design and execute two or three projects in succession after the first fail for practical reasons. Pick a date for the presentation of your thesis and work backwards in constructing a schedule of how you are going to use your time. Don’t worry - it goes on like this for awhile, then it gradually gets worse. Spend two to three weeks writing the proposal after you’ve finished your reading, then give it to as many good critics as you can find. You already have the introduction to your thesis written, and you have only been here 12 to 18 months. Keep your advisors aware of what you are doing, but do not bother them. At least once a year, submit a written progress report 1-2 pages long on your own initiative. Be very careful about choosing your advisors in the first place. This is the worst kind of thesis, but in a pinch it will get you through.
Hope that their comments are tough, and respond as constructively as you can. Most important is their interest in your interests. Never elaborate a baroque excrescence on top of existing but shaky ideas. A critique of the foundations of an important body of research. This takes courage, especially in a department loaded with bedrock empiricists, but can be pulled off if you are genuinely good at math and logic. To certain kinds of people lots of data, even if they don’t test a hypothesis, will always be impressive.