Some days, research happens. Other days…
One of the things that distinguishes mathematics from the sciences (and from almost every other field of academia) is that a mathematician needs no lab, no physical apparatus, no research subjects; while all of these things can be employed, it’s entirely reasonable to do mathematics with no external aids at all. ecogrrl likes to joke about how I do research by sitting on her sofa and staring off into space, and that’s a pretty accurate account.
But I do, in a sense, have an apparatus. I’ve called it my math-brain in the past, which isn’t entirely accurate; one of the characters in Proof refers to “the machinery”, which might be closer. It’s the part of my mind that delights in mathematical research, and is apparently reasonably good at it, when it’s working. The trouble is, sometimes it works and sometimes it doesn’t. (“Math-brain” isn’t accurate because I can still work through calculations, explain concepts, etc. the rest of the time; it’s just my ability to come up with interesting questions and the desire to pursue them that comes and goes.)
I don’t generally time it, but it seems like my machinery is capable of running for periods of a month or so at a time; during such intervals (the most recent of which, I think, ended last week) I tend to be fairly productive in that special technical sense of “productive” that doesn’t necessarily indicate that anything concrete is being produced. I get ideas, I pursue ideas, I tell other people about ideas, and if I’m really smart I write ideas down in a form that I’ll be able to comprehend after time has passed. Because when the machinery shuts down, it often does so for weeks at a time & during those periods I’m not terrifically useful research-wise.
It’s frustrating, because it means that even though I’d like to work on something, I find that I can’t. I can’t focus my attention, or I can’t come up with any way to develop the concepts in question, or (often) it just doesn’t occur to me to even try working (except in the form of the idlest sort of fancy: lying in bed in the morning, thinking “I should work” before drifting off again for ten minutes or so).