To be honest, I'm not entirely sure how I'm still in grad school.
I've been researching under one professor's wing for two years now, ostensibly shooting for a PhD (note: no topic yet), and I have accomplished nothing except write a lot of code, fill a bunch of notebooks with theorems and scratchwork, and whine a lot.
Insofar as I can surmise, my precise set of skills is good for one thing and one thing only: Solving problems that have already been solved... but only from scratch, my way. And I'm too stubborn to know when to give up.
For homeworks I go in completely unprepared and take them like a puzzle, and somehow, this usually doesn't work out too poorly (note, I am a physics student, so these homeworks are of the mathy, proofy, yet still occassionally handwavey kind). I hack and hack away at a problem unassisted for hours to days with no progress until I finally make a crack in the wall and can see the light shining through. Then I beat it eight ways to Sunday, making my solution simpler and simpler until I am satisfied that every step has both a clean form and a clear motivation. My test-taking strategy is similarly devoid of preparation, and also fortuitously manages to work out well.
As far as I can tell, my strategy works in these cases only because homeworks and tests are problems which are hand-crafted to be surmountable. In these cases, my stubbornness alone is enough to pull me through eventually. It was enough, in fact, to pull me all the way through primary and secondary school and to my Bachelor's.
But obviously, grad school isn't about homeworks and tests.
For one, I can't read academic papers in my field. Or rather, every academic paper I try to read goes one of two ways:
- If it is a very abstract and theoretical paper, then I can't read it because I'll get too easily excited; I'll get to maybe the second page of definitions and axioms before my head is flooded with ideas and I absolutely need to pull out my notebook and begin trying to gain an intuition for them. (This seldom goes anywhere and I usually just end up tiring myself out after several hours of hacking on some theorem orthogonal to the paper)
- If it's an experimental paper, I can't read it because it means nothing to me. There are no ideas I can synthesize from "we did X using Y and found Z." My mind races about other things as I'm reading and I can't shut it up! In the end, I don't remember a word I read.
And as far as it concerns me, computational papers and applied theory might as well be experimental, because ultimately there's a point where everything goes into a black box and the result pops out. This is a shame, because I know that these computations can expose new and interesting emergent properties of the theory; but sometimes it's just too difficult finding the ladder down from my ivory tower.
My research is going about as well as one would expect for somebody who can't read any papers!
For any problem I've ever worked on for research, I've always begun with trying to solve the aspects that stand out to me; enumerating the set of solutions to some nasty-looking equation, or devising an algorithm to compute something which is faster than the obvious brute force strategy. Months fly by and I either fail, or I successfully, unwittingly, and needlessly derive my own formalism of e.g. the theory behind HNF matrices and unimodular matrices after several strokes of dumb luck.
In all cases, papers already existed which solved these problems. I just couldn't bear the thought of having to seek them out and read them!
I've discussed various aspects of my struggles with my parents and a number of faculty (including, of course my research advisor) and everyone I've talked to has advised me to continue. I gathered from these discussions that feelings of inadequacy are rather par for the norm in grad school, and that evidently my classwork has impressed a portion of the faculty who still appear to have confidence that I can succeed... But unfortunately, as far as I can see, I am a one-trick pony.
Is there really any place in academia for somebody who is incapable of recognizing and building upon the existing work of others?