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1/ What I tell first year PhD students on the first day of class: Grad school is not intentionally designed to make you feel stupid. But, if you were going to design something to make someone feel stupid it would look an awful lot like grad school.
2/ The first thing you learn is how much knowledge exists in the world. The second thing you learn is that you don't know most of it. That's pretty intimidating. It's OK to feel intimidated - it's a natural part of the process for most people.
3/ Feeling overwhelmed or inadequate can be dealt with. I had a panic attack during seminar my 3rd week of grad school as it dawned on me what I had gotten myself into. But I got through it, and now that I'm faculty I've helped my students get through similar feelings.
4/ The ones I worry about the most are super-confident students who just know they've got this. Because most of them really don't got this. Often (not always) their confidence gets in the way of them putting in the work necessary to be successful. And they flame out.
5/ Contrary to what some people think, academia doesn't typically reward the lone genius who sits in his office thinking great thoughts. Academia rewards slow and steady progress toward a goal. So be persistent. Keep doing the work and chances are you'll be fine.
6/ You've got a long way to go, but you've also got years to get there.
