I'm a first year PhD student in mathematics and I'm in a pretty bad spot.
Over the last year or so of undergrad and first semester of grad school, I've completely atrophied my problem solving skill. At some point I became more comfortable with looking up a solution than trying to solve it myself. At this point my first instinct is to google something instead of trying to solve something. I need to fix this; it's already been affecting my performance and well being across the board. I'm almost instinctually aversive to trying to solve a problem by myself at this point. I feel like I've lost the ability to actually do math. I initially justified it by saying that my interest in math stems from my interest in the theory, and that I'm not particularly interested in problem solving. It's clear now that that was just cognitive dissonance. I need to fix this.
I know what the obvious answer is- don't look stuff up. And try to do problems on my own. Practice, practice, practice.
But I feel like it's not so simple either. I'm doing graduate level math after all. I managed to get into a fairly top level, rigorous program. I have performed well enough in the past that I managed to place ahead of my peers, and am doing relatively advanced courses (after all, I wouldn't have resorted to looking up stuff if it wasn't working well for me, until recently). As such, it seems like I already need a solid, strong problem solving capability in order to deal with my classes, which are quite demanding. So when I'm faced with HW or other problems, I'm unable to solve most of the problems even if I try really hard, because my problem solving skill is just so bad at this point, and I have to resort to looking things up once more. This further worsens my skill and on and on. It's a negative feedback loop. And I'm struggling to break out of it. I wanted advice on how to escape this loop especially. The idea of simply not looking stuff up is sound, but it's hard to follow through when I have only a finite amount of time before I have to stop thinking and submit my answers, or when I simply don't possess the capability anymore to try and solve the problem.
These days the idea of solving a graduate level HW set seems impossible to me, and I'm just incredibly lucky graduate level courses tend not to have exams. It's reached the point where it's threatening my future in my PhD program so I really do need to fix it. Googling my way through life isn't possible (or desirable either). I really am desperate now. I feel like a lost cause at this point, like the damage has already been done to me, and I can't really fix it without going back to undergrad or something.
I was just hoping for concrete advice and from people who have had similar experiences, and what I should do.
- I am referring to problems/solutions in my graduate courses. The research portion of my PhD has not started yet.
- My advisor and I are not particularly close (only interacted a few times so far due to the pandemic), so my awkward attempt to bring it up with him didn't really go anywhere.